summary |
shortlog |
log |
commit | commitdiff |
tree
raw |
patch |
inline | side by side (from parent 1:
3199f2a)
- GrafiteAstPp: coercion and inline pretty printing patched
- CoRN-Decl: regenerated: starts to compile :) but inline is broken :(
162 files changed:
+include ../../../Makefile.defs
+
H=@
REQUIRES = unix str helm-grafite_parser
H=@
REQUIRES = unix str helm-grafite_parser
+LIBRARIES = $(shell $(OCAMLFIND) query -recursive -predicates "byte $(PREDICATES)" -format "%d/%a" $(REQUIRES))
+LIBRARIES_OPT = $(shell $(OCAMLFIND) query -recursive -predicates "native $(PREDICATES)" -format "%d/%a" $(REQUIRES))
+
CMOS = $(MLS:%.ml=%.cmo)
CMXS = $(MLS:%.ml=%.cmx)
CMIS = $(MLIS:%.mli=%.cmi)
CMOS = $(MLS:%.ml=%.cmo)
CMXS = $(MLS:%.ml=%.cmx)
CMIS = $(MLIS:%.mli=%.cmi)
opt: transcript.opt $(EXTRAS) .depend.opt
#echo -n
opt: transcript.opt $(EXTRAS) .depend.opt
#echo -n
-transcript: $(CMIS) $(CMOS) $(EXTRAS)
+transcript: $(CMIS) $(CMOS) $(EXTRAS) $(LIBRARIES)
@echo " OCAMLC $(CMOS)"
$(H)$(OCAMLC) -o $@ $(CMOS)
@echo " OCAMLC $(CMOS)"
$(H)$(OCAMLC) -o $@ $(CMOS)
-transcript.opt: $(CMIS) $(CMXS) $(EXTRAS)
+transcript.opt: $(CMIS) $(CMXS) $(EXTRAS) $(LIBRARIES_OPT)
@echo " OCAMLOPT $(CMXS)"
$(H)$(OCAMLOPT) -o $@ $(CMXS)
@echo " OCAMLOPT $(CMXS)"
$(H)$(OCAMLOPT) -o $@ $(CMXS)
include ../../../Makefile.defs
include ../../../Makefile.defs
-ifeq ($(MAKECMDGOALS), opt)
- include .depend.opt
+ifeq ($(MAKECMDGOALS),)
+ include .depend
endif
ifeq ($(MAKECMDGOALS), all)
include .depend
endif
endif
ifeq ($(MAKECMDGOALS), all)
include .depend
endif
+ifeq ($(MAKECMDGOALS), opt)
+ include .depend.opt
+endif
+
+ifeq ($(MAKECMDGOALS), test)
+
+ifeq ($(MAKECMDGOALS), test.opt)
+ include .depend.opt
+endif
let baseuri = Filename.concat st.output_base_uri name in
set_items st name [T.BaseUri baseuri]
let baseuri = Filename.concat st.output_base_uri name in
set_items st name [T.BaseUri baseuri]
+let require st name =
+ set_items st name [T.Include st.package]
+
let commit st name =
let i = get_index st name in
let script = st.scripts.(i) in
let commit st name =
let i = get_index st name in
let script = st.scripts.(i) in
let produce st =
let init name = set_heading st name; set_baseuri st name in
let produce st =
let init name = set_heading st name; set_baseuri st name in
- let partition = function
- | T.Coercion _
+ let partition = function
| T.Notation _ -> false
| _ -> true
in
let produce st name =
| T.Notation _ -> false
| _ -> true
in
let produce st name =
- let base_uri = Filename.concat st.input_base_uri name in
+ let in_base_uri = Filename.concat st.input_base_uri name in
+ let out_base_uri = Filename.concat st.output_base_uri name in
let filter = function
| T.Inline (k, obj) ->
let s = obj ^ G.string_of_inline_kind k in
let filter = function
| T.Inline (k, obj) ->
let s = obj ^ G.string_of_inline_kind k in
- Some (T.Inline (k, Filename.concat base_uri s))
+ Some (T.Inline (k, Filename.concat in_base_uri s))
+ | T.Include s ->
+ begin
+ try Some (T.Include (List.assoc s st.requires))
+ with Not_found -> None
+ end
+ | T.Coercion obj ->
+ let s = obj ^ G.string_of_inline_kind T.Con in
+ Some (T.Coercion (Filename.concat out_base_uri s))
| item -> Some item
in
Printf.eprintf "processing file name: %s ...\n" name; flush stderr;
| item -> Some item
in
Printf.eprintf "processing file name: %s ...\n" name; flush stderr;
let comment = T.Line (Printf.sprintf "From %s" name) in
if global_items <> [] then
set_items st st.package (comment :: global_items);
let comment = T.Line (Printf.sprintf "From %s" name) in
if global_items <> [] then
set_items st st.package (comment :: global_items);
- init name; set_items st name local_items; commit st name
+ init name; require st name;
+ set_items st name local_items; commit st name
with e ->
prerr_endline (Printexc.to_string e); close_in ich
in
with e ->
prerr_endline (Printexc.to_string e); close_in ich
in
module NP = CicNotationPp
module GP = GrafiteAstPp
module G = GrafiteAst
module NP = CicNotationPp
module GP = GrafiteAstPp
module G = GrafiteAst
let require value =
command_of_obj (G.Include (floc, value ^ ".ma"))
let require value =
command_of_obj (G.Include (floc, value ^ ".ma"))
+let coercion value =
+ command_of_obj (G.Coercion (floc, UM.uri_of_string value, true, 0))
+
let inline value =
command_of_macro (G.Inline (floc, value))
let inline value =
command_of_macro (G.Inline (floc, value))
let commit = function
| T.Heading heading -> out_preamble och heading
| T.Line line -> out_line_comment och line
let commit = function
| T.Heading heading -> out_preamble och heading
| T.Line line -> out_line_comment och line
- | T.BaseUri baseuri -> out_command och (set "baseuri" baseuri)
- | T.Include inc -> out_unexported och "INCLUDE" inc (**)
- | T.Coercion coercion -> out_unexported och "COERCION" coercion (**)
+ | T.BaseUri uri -> out_command och (set "baseuri" uri)
+ | T.Include script -> out_command och (require script)
+ | T.Coercion uri -> out_command och (coercion uri)
| T.Notation notation -> out_unexported och "NOTATION" notation (**)
| T.Notation notation -> out_unexported och "NOTATION" notation (**)
- | T.Inline (_, uri) -> out_command och (inline uri)
+ | T.Inline specs -> out_command och (inline (snd specs))
| T.Comment comment -> out_comment och comment
| T.Unexport unexport -> out_unexported och "UNEXPORTED" unexport
| T.Verbatim verbatim -> out_verbatim och verbatim
| T.Comment comment -> out_comment och comment
| T.Unexport unexport -> out_unexported och "UNEXPORTED" unexport
| T.Verbatim verbatim -> out_verbatim och verbatim
id: ID spcs { $1 ^ $2 };
coerc: COERC spcs { $1 ^ $2 };
id: ID spcs { $1 ^ $2 };
coerc: COERC spcs { $1 ^ $2 };
idents:
| ident { [$1] }
| ident idents { $1 :: $2 }
idents:
| ident { [$1] }
| ident idents { $1 :: $2 }
| unexport_r spcs unexports_r { fst $1 ^ $2 ^ fst $3, snd $1 @ snd $3 }
;
field:
| unexport_r spcs unexports_r { fst $1 ^ $2 ^ fst $3, snd $1 @ snd $3 }
;
field:
- | ident cn unexports_r { $1 ^ $2 ^ fst $3, snd $3 }
- | ident coe unexports_r { $1 ^ $2 ^ fst $3, snd $3 @ [T.Coercion $1] }
+ | ident cn unexports_r
+ { $1 ^ $2 ^ fst $3, snd $3 }
+ | ident coe unexports_r
+ { $1 ^ $2 ^ fst $3, snd $3 @ [T.Coercion (trim $1)] }
| var idents xres FS
{ out "VAR" (cat $2); mk_vars $2 }
| ind ident unexports FS
| var idents xres FS
{ out "VAR" (cat $2); mk_vars $2 }
| ind ident unexports FS
- { out "IND" $2; snd $3 @ [T.Inline (T.Ind, trim $2)] }
+ { out "IND" $2; T.Inline (T.Ind, trim $2) :: snd $3 }
| sec unexports FS
{ out "UNX" (fst $2); [T.Unexport ($1 ^ fst $2 ^ trim $3)] }
| req xp ident FS
| sec unexports FS
{ out "UNX" (fst $2); [T.Unexport ($1 ^ fst $2 ^ trim $3)] }
| req xp ident FS
(* real macros *)
| Check (_, term) -> sprintf "check %s" (term_pp term)
| Hint _ -> "hint"
(* real macros *)
| Check (_, term) -> sprintf "check %s" (term_pp term)
| Hint _ -> "hint"
- | Inline (_,suri) -> sprintf "inline %s" suri
+ | Inline (_,suri) -> sprintf "inline \"%s\"" suri
let pp_associativity = function
| Gramext.LeftA -> "left associative"
let pp_associativity = function
| Gramext.LeftA -> "left associative"
(String.concat " " (List.map UriManager.string_of_uri uris))
let pp_coercion uri do_composites arity =
(String.concat " " (List.map UriManager.string_of_uri uris))
let pp_coercion uri do_composites arity =
- sprintf "coercion %s %d (* %s *)" (UriManager.string_of_uri uri) arity
+ sprintf "coercion \"%s\" %d (* %s *)" (UriManager.string_of_uri uri) arity
(if do_composites then "compounds" else "no compounds")
let pp_command ~term_pp ~obj_pp = function
(if do_composites then "compounds" else "no compounds")
let pp_command ~term_pp ~obj_pp = function
Notation Proj2 := (proj2 (B:=_)).
*)
Notation Proj2 := (proj2 (B:=_)).
*)
-(* COERCION
-Z_of_nat
-*)
-
-(* From algebra/CAbGroups *************************************************)
-
-(* COERCION
-cag_crr
-*)
-
-(* From algebra/CAbMonoids ************************************************)
-
-(* COERCION
-cam_crr
-*)
-
(* From algebra/CFields ***************************************************)
(* From algebra/CFields ***************************************************)
-(* COERCION
-cf_crr
-*)
-
(* NOTATION
Notation "x [/] y [//] Hy" := (cf_div x y Hy) (at level 80).
*)
(* NOTATION
Notation "x [/] y [//] Hy" := (cf_div x y Hy) (at level 80).
*)
(* From algebra/CGroups ***************************************************)
(* From algebra/CGroups ***************************************************)
-(* COERCION
-cg_crr
-*)
-
(* NOTATION
Notation "[--] x" := (cg_inv x) (at level 2, right associativity).
*)
(* NOTATION
Notation "[--] x" := (cg_inv x) (at level 2, right associativity).
*)
(* From algebra/CMonoids **************************************************)
(* From algebra/CMonoids **************************************************)
-(* COERCION
-cm_crr
-*)
-
(* NOTATION
Notation Zero := (cm_unit _).
*)
(* NOTATION
Notation Zero := (cm_unit _).
*)
Notation AbsBig := (absBig _).
*)
Notation AbsBig := (absBig _).
*)
-(* From algebra/COrdCauchy ************************************************)
-
-(* COERCION
-CS_seq
-*)
-
(* From algebra/COrdFields ************************************************)
(* From algebra/COrdFields ************************************************)
-(* COERCION
-cof_crr
-*)
-
(* NOTATION
Infix "[<]" := cof_less (at level 70, no associativity).
*)
(* NOTATION
Infix "[<]" := cof_less (at level 70, no associativity).
*)
(* From algebra/CRings ****************************************************)
(* From algebra/CRings ****************************************************)
-(* COERCION
-cr_crr
-*)
-
(* NOTATION
Notation One := (cr_one _).
*)
(* NOTATION
Notation One := (cr_one _).
*)
(* From algebra/CSemiGroups ***********************************************)
(* From algebra/CSemiGroups ***********************************************)
-(* COERCION
-csg_crr
-*)
-
(* NOTATION
Infix "[+]" := csg_op (at level 50, left associativity).
*)
(* NOTATION
Infix "[+]" := csg_op (at level 50, left associativity).
*)
Notation Conj := (conjP _).
*)
Notation Conj := (conjP _).
*)
-(* COERCION
-bpfpfun
-*)
-
(* NOTATION
Notation BDom := (bpfdom _ _).
*)
(* NOTATION
Notation BDom := (bpfdom _ _).
*)
-(* COERCION
-pfpfun
-*)
-
(* NOTATION
Notation Dom := (pfdom _).
*)
(* NOTATION
Notation Dom := (pfdom _).
*)
(* From algebra/CSetoids **************************************************)
(* From algebra/CSetoids **************************************************)
-(* COERCION
-cs_crr
-*)
-
(* NOTATION
Infix "[=]" := cs_eq (at level 70, no associativity).
*)
(* NOTATION
Infix "[=]" := cs_eq (at level 70, no associativity).
*)
Infix "[~=]" := cs_neq (at level 70, no associativity).
*)
Infix "[~=]" := cs_neq (at level 70, no associativity).
*)
-(* COERCION
-csp_pred
-*)
-
-(* COERCION
-csp'_pred
-*)
-
-(* COERCION
-csr_rel
-*)
-
-(* COERCION
-Ccsr_rel
-*)
-
-(* COERCION
-csf_fun
-*)
-
-(* COERCION
-csbf_fun
-*)
-
-(* COERCION
-un_op_fun
-*)
-
-(* COERCION
-bin_op_bin_fun
-*)
-
-(* COERCION
-outer_op_bin_fun
-*)
-
-(* COERCION
-scs_elem
-*)
-
(* From algebra/CVectorSpace **********************************************)
(* From algebra/CVectorSpace **********************************************)
-(* COERCION
-vs_vs
-*)
-
(* NOTATION
Infix "[']" := vs_op (at level 30, no associativity).
*)
(* NOTATION
Infix "[']" := vs_op (at level 30, no associativity).
*)
Infix "[+I*]" := cc_set_CC (at level 48, no associativity).
*)
Infix "[+I*]" := cc_set_CC (at level 48, no associativity).
*)
-(* From fta/CC_Props ******************************************************)
-
-(* COERCION
-CC_seq
-*)
-
-(* From fta/FTAreg ********************************************************)
-
-(* COERCION
-z_el
-*)
-
-(* COERCION
-Kntup
-*)
-
(* From ftc/FTC ***********************************************************)
(* NOTATION
(* From ftc/FTC ***********************************************************)
(* NOTATION
Notation Integral := (integral _ _ Hab).
*)
Notation Integral := (integral _ _ Hab).
*)
-(* From ftc/MoreIntervals *************************************************)
-
-(* COERCION
-iprop
-*)
-
-(* From ftc/Partitions ****************************************************)
-
-(* COERCION
-Pts
-*)
-
(* From ftc/RefLemma ******************************************************)
(* NOTATION
(* From ftc/RefLemma ******************************************************)
(* NOTATION
Infix "**" := prodT (at level 20).
*)
Infix "**" := prodT (at level 20).
*)
-(* From metrics/CMetricSpaces *********************************************)
-
-(* COERCION
-scms_crr
-*)
-
(* From metrics/CPseudoMSpaces ********************************************)
(* From metrics/CPseudoMSpaces ********************************************)
-(* COERCION
-cms_crr
-*)
-
(* NOTATION
Infix "[-d]" := cms_d (at level 68, left associativity).
*)
(* NOTATION
Infix "[-d]" := cms_d (at level 68, left associativity).
*)
Notation "{-Q}" := Qopp (at level 1, left associativity).
*)
Notation "{-Q}" := Qopp (at level 1, left associativity).
*)
-(* COERCION
-inject_Z
-*)
-
(* From model/structures/Zsec *********************************************)
(* NOTATION
Infix "{#Z}" := ap_Z (no associativity, at level 90).
*)
(* From model/structures/Zsec *********************************************)
(* NOTATION
Infix "{#Z}" := ap_Z (no associativity, at level 90).
*)
(* From reals/Bridges_LUB *************************************************)
(* NOTATION
(* From reals/Bridges_LUB *************************************************)
(* NOTATION
(* From reals/CMetricFields ***********************************************)
(* From reals/CMetricFields ***********************************************)
-(* COERCION
-cmf_crr
-*)
-
(* NOTATION
Notation MAbs := (cmf_abs _).
*)
(* NOTATION
Notation MAbs := (cmf_abs _).
*)
-(* COERCION
-MCS_seq
-*)
-
-(* From reals/CReals ******************************************************)
-
-(* COERCION
-crl_crr
-*)
-
(* From reals/CauchySeq ***************************************************)
(* NOTATION
(* From reals/CauchySeq ***************************************************)
(* NOTATION
(* From reals/Q_dense *****************************************************)
(* From reals/Q_dense *****************************************************)
-(* COERCION
-pair_crr
-*)
-
(* NOTATION
Notation "( A , B )" := (pairT A B).
*)
(* NOTATION
Notation "( A , B )" := (pairT A B).
*)
-(* From reals/Q_in_CReals *************************************************)
-
-(* COERCION
-nat_of_P
-*)
-
-(* From reals/R_morphism **************************************************)
-
-(* COERCION
-map
-*)
-
(* From tactics/FieldReflection *******************************************)
(* NOTATION
(* From tactics/FieldReflection *******************************************)
(* NOTATION
Notation "F {!} G" := (FPower F G) (at level 20).
*)
Notation "F {!} G" := (FPower F G) (at level 20).
*)
-(* From devel/loeb/per/lst2fun ********************************************)
-
-(* COERCION
-F_crr
-*)
-
-(* COERCION
-to_nat
-*)
-
set "baseuri" "cic:/matita/CoRN-Decl/algebra/Basics".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/Basics".
(* $Id: Basics.v,v 1.7 2004/04/09 15:58:31 lcf Exp $ *)
(*#* printing alpha %\ensuremath{\alpha}% #α# *)
(* $Id: Basics.v,v 1.7 2004/04/09 15:58:31 lcf Exp $ *)
(*#* printing alpha %\ensuremath{\alpha}% #α# *)
(*#* printing Z %\ensuremath{\mathbb Z}% #<b>Z</b># *)
(*#* printing Z %\ensuremath{\mathbb Z}% #<b>Z</b># *)
-(* INCLUDE
-Omega
-*)
-
-(* INCLUDE
-Even
-*)
-
-(* INCLUDE
-Max
-*)
-
-(* INCLUDE
-Min
-*)
-
-(* INCLUDE
-ListType
-*)
+include "algebra/ListType.ma".
(*#* *Basics
This is random stuff that should be in the Coq basic library.
*)
(*#* *Basics
This is random stuff that should be in the Coq basic library.
*)
-inline cic:/CoRN/algebra/Basics/lt_le_dec.con.
+inline "cic:/CoRN/algebra/Basics/lt_le_dec.con".
-inline cic:/CoRN/algebra/Basics/lt_z_two.con.
+inline "cic:/CoRN/algebra/Basics/lt_z_two.con".
-inline cic:/CoRN/algebra/Basics/le_pred.con.
+inline "cic:/CoRN/algebra/Basics/le_pred.con".
-inline cic:/CoRN/algebra/Basics/lt_mult_right.con.
+inline "cic:/CoRN/algebra/Basics/lt_mult_right.con".
-inline cic:/CoRN/algebra/Basics/le_mult_right.con.
+inline "cic:/CoRN/algebra/Basics/le_mult_right.con".
(*#* The power function does not exist in the standard library *)
(*#* The power function does not exist in the standard library *)
-inline cic:/CoRN/algebra/Basics/power.con.
+inline "cic:/CoRN/algebra/Basics/power.con".
(*#* Factorial function. Does not exist in Arith.
Needed for special operations on polynomials. *)
(*#* Factorial function. Does not exist in Arith.
Needed for special operations on polynomials. *)
-inline cic:/CoRN/algebra/Basics/fac.con.
+inline "cic:/CoRN/algebra/Basics/fac.con".
-inline cic:/CoRN/algebra/Basics/nat_fac_gtzero.con.
+inline "cic:/CoRN/algebra/Basics/nat_fac_gtzero.con".
(* needed for computational behavior of "Inversion" tactic *)
(* needed for computational behavior of "Inversion" tactic *)
-inline cic:/CoRN/algebra/Basics/not_r_sumbool_rec.con.
+inline "cic:/CoRN/algebra/Basics/not_r_sumbool_rec.con".
-inline cic:/CoRN/algebra/Basics/not_l_sumbool_rec.con.
+inline "cic:/CoRN/algebra/Basics/not_l_sumbool_rec.con".
+coercion "cic:/matita/CoRN-Decl/algebra/Basics/Z_of_nat.con" 0 (* compounds *).
+
-inline cic:/CoRN/algebra/Basics/POS_anti_convert.con.
+inline "cic:/CoRN/algebra/Basics/POS_anti_convert.con".
-inline cic:/CoRN/algebra/Basics/NEG_anti_convert.con.
+inline "cic:/CoRN/algebra/Basics/NEG_anti_convert.con".
-inline cic:/CoRN/algebra/Basics/lt_O_positive_to_nat.con.
+inline "cic:/CoRN/algebra/Basics/lt_O_positive_to_nat.con".
-inline cic:/CoRN/algebra/Basics/anti_convert_pred_convert.con.
+inline "cic:/CoRN/algebra/Basics/anti_convert_pred_convert.con".
-inline cic:/CoRN/algebra/Basics/p_is_some_anti_convert.con.
+inline "cic:/CoRN/algebra/Basics/p_is_some_anti_convert.con".
-inline cic:/CoRN/algebra/Basics/convert_is_POS.con.
+inline "cic:/CoRN/algebra/Basics/convert_is_POS.con".
-inline cic:/CoRN/algebra/Basics/min_convert_is_NEG.con.
+inline "cic:/CoRN/algebra/Basics/min_convert_is_NEG.con".
-inline cic:/CoRN/algebra/Basics/inject_nat_convert.con.
+inline "cic:/CoRN/algebra/Basics/inject_nat_convert.con".
-inline cic:/CoRN/algebra/Basics/Z_exh.con.
+inline "cic:/CoRN/algebra/Basics/Z_exh.con".
-inline cic:/CoRN/algebra/Basics/nats_Z_ind.con.
+inline "cic:/CoRN/algebra/Basics/nats_Z_ind.con".
-inline cic:/CoRN/algebra/Basics/pred_succ_Z_ind.con.
+inline "cic:/CoRN/algebra/Basics/pred_succ_Z_ind.con".
-inline cic:/CoRN/algebra/Basics/Zmult_minus_distr_r.con.
+inline "cic:/CoRN/algebra/Basics/Zmult_minus_distr_r.con".
-inline cic:/CoRN/algebra/Basics/Zodd_Zeven_min1.con.
+inline "cic:/CoRN/algebra/Basics/Zodd_Zeven_min1.con".
-inline cic:/CoRN/algebra/Basics/caseZ_diff.con.
+inline "cic:/CoRN/algebra/Basics/caseZ_diff.con".
-inline cic:/CoRN/algebra/Basics/caseZ_diff_O.con.
+inline "cic:/CoRN/algebra/Basics/caseZ_diff_O.con".
-inline cic:/CoRN/algebra/Basics/caseZ_diff_Pos.con.
+inline "cic:/CoRN/algebra/Basics/caseZ_diff_Pos.con".
-inline cic:/CoRN/algebra/Basics/caseZ_diff_Neg.con.
+inline "cic:/CoRN/algebra/Basics/caseZ_diff_Neg.con".
-inline cic:/CoRN/algebra/Basics/proper_caseZ_diff.con.
+inline "cic:/CoRN/algebra/Basics/proper_caseZ_diff.con".
-inline cic:/CoRN/algebra/Basics/diff_Z_ind.con.
+inline "cic:/CoRN/algebra/Basics/diff_Z_ind.con".
-inline cic:/CoRN/algebra/Basics/Zlt_reg_mult_l.con.
+inline "cic:/CoRN/algebra/Basics/Zlt_reg_mult_l.con".
-inline cic:/CoRN/algebra/Basics/Zlt_opp.con.
+inline "cic:/CoRN/algebra/Basics/Zlt_opp.con".
-inline cic:/CoRN/algebra/Basics/Zlt_conv_mult_l.con.
+inline "cic:/CoRN/algebra/Basics/Zlt_conv_mult_l.con".
-inline cic:/CoRN/algebra/Basics/Zgt_not_eq.con.
+inline "cic:/CoRN/algebra/Basics/Zgt_not_eq.con".
-inline cic:/CoRN/algebra/Basics/Zmult_absorb.con.
+inline "cic:/CoRN/algebra/Basics/Zmult_absorb.con".
(* UNEXPORTED
Section Well_foundedT.
*)
(* UNEXPORTED
Section Well_foundedT.
*)
-inline cic:/CoRN/algebra/Basics/A.var.
+inline "cic:/CoRN/algebra/Basics/A.var".
-inline cic:/CoRN/algebra/Basics/R.var.
+inline "cic:/CoRN/algebra/Basics/R.var".
(*#* The accessibility predicate is defined to be non-informative *)
(*#* The accessibility predicate is defined to be non-informative *)
-inline cic:/CoRN/algebra/Basics/Acc.ind.
+inline "cic:/CoRN/algebra/Basics/Acc.ind".
(* UNEXPORTED
End Well_foundedT.
(* UNEXPORTED
End Well_foundedT.
-inline cic:/CoRN/algebra/Basics/A.var.
+inline "cic:/CoRN/algebra/Basics/A.var".
-inline cic:/CoRN/algebra/Basics/well_founded.con.
+inline "cic:/CoRN/algebra/Basics/well_founded.con".
-inline cic:/CoRN/algebra/Basics/A.var.
+inline "cic:/CoRN/algebra/Basics/A.var".
-inline cic:/CoRN/algebra/Basics/R.var.
+inline "cic:/CoRN/algebra/Basics/R.var".
(* UNEXPORTED
Section AccIter.
*)
(* UNEXPORTED
Section AccIter.
*)
-inline cic:/CoRN/algebra/Basics/P.var.
+inline "cic:/CoRN/algebra/Basics/P.var".
-inline cic:/CoRN/algebra/Basics/F.var.
+inline "cic:/CoRN/algebra/Basics/F.var".
-inline cic:/CoRN/algebra/Basics/Acc_inv.con.
+inline "cic:/CoRN/algebra/Basics/Acc_inv.con".
-inline cic:/CoRN/algebra/Basics/Acc_iter.con.
+inline "cic:/CoRN/algebra/Basics/Acc_iter.con".
(* UNEXPORTED
End AccIter.
*)
(* UNEXPORTED
End AccIter.
*)
-inline cic:/CoRN/algebra/Basics/Rwf.var.
+inline "cic:/CoRN/algebra/Basics/Rwf.var".
-inline cic:/CoRN/algebra/Basics/well_founded_induction_type.con.
+inline "cic:/CoRN/algebra/Basics/well_founded_induction_type.con".
-inline cic:/CoRN/algebra/Basics/A.var.
+inline "cic:/CoRN/algebra/Basics/A.var".
-inline cic:/CoRN/algebra/Basics/f.var.
+inline "cic:/CoRN/algebra/Basics/f.var".
-inline cic:/CoRN/algebra/Basics/ltof.con.
+inline "cic:/CoRN/algebra/Basics/ltof.con".
-inline cic:/CoRN/algebra/Basics/well_founded_ltof.con.
+inline "cic:/CoRN/algebra/Basics/well_founded_ltof.con".
-inline cic:/CoRN/algebra/Basics/induction_ltof2T.con.
+inline "cic:/CoRN/algebra/Basics/induction_ltof2T.con".
(* UNEXPORTED
End InductionT.
(* UNEXPORTED
End InductionT.
-inline cic:/CoRN/algebra/Basics/lt_wf_rect.con.
+inline "cic:/CoRN/algebra/Basics/lt_wf_rect.con".
(* UNEXPORTED
End InductionTT.
(* UNEXPORTED
End InductionTT.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CAbGroups".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CAbGroups".
+include "CoRN.ma".
+
+include "algebra/CGroups.ma".
(* UNEXPORTED
Section Abelian_Groups.
(* UNEXPORTED
Section Abelian_Groups.
Now we introduce commutativity and add some results.
*)
Now we introduce commutativity and add some results.
*)
-inline cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con.
+inline "cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con".
+
+inline "cic:/CoRN/algebra/CAbGroups/CAbGroup.ind".
-inline cic:/CoRN/algebra/CAbGroups/CAbGroup.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/CAbGroups/cag_crr.con" 0 (* compounds *).
(* UNEXPORTED
Section AbGroup_Axioms.
*)
(* UNEXPORTED
Section AbGroup_Axioms.
*)
-inline cic:/CoRN/algebra/CAbGroups/G.var.
+inline "cic:/CoRN/algebra/CAbGroups/G.var".
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
%\end{convention}%
*)
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
%\end{convention}%
*)
-inline cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con.
+inline "cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con".
-inline cic:/CoRN/algebra/CAbGroups/cag_commutes.con.
+inline "cic:/CoRN/algebra/CAbGroups/cag_commutes.con".
-inline cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.con.
+inline "cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.con".
(* UNEXPORTED
End AbGroup_Axioms.
(* UNEXPORTED
End AbGroup_Axioms.
** Subgroups of an Abelian Group
*)
** Subgroups of an Abelian Group
*)
-inline cic:/CoRN/algebra/CAbGroups/G.var.
+inline "cic:/CoRN/algebra/CAbGroups/G.var".
-inline cic:/CoRN/algebra/CAbGroups/P.var.
+inline "cic:/CoRN/algebra/CAbGroups/P.var".
-inline cic:/CoRN/algebra/CAbGroups/Punit.var.
+inline "cic:/CoRN/algebra/CAbGroups/Punit.var".
-inline cic:/CoRN/algebra/CAbGroups/op_pres_P.var.
+inline "cic:/CoRN/algebra/CAbGroups/op_pres_P.var".
-inline cic:/CoRN/algebra/CAbGroups/inv_pres_P.var.
+inline "cic:/CoRN/algebra/CAbGroups/inv_pres_P.var".
(*#*
%\begin{convention}%
(*#*
%\begin{convention}%
-inline cic:/CoRN/algebra/CAbGroups/subcrr.con.
+inline "cic:/CoRN/algebra/CAbGroups/subcrr.con".
-inline cic:/CoRN/algebra/CAbGroups/isabgrp_scrr.con.
+inline "cic:/CoRN/algebra/CAbGroups/isabgrp_scrr.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con.
+inline "cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con".
(* UNEXPORTED
End SubCAbGroups.
(* UNEXPORTED
End SubCAbGroups.
Hint Resolve cag_commutes_unfolded: algebra.
*)
Hint Resolve cag_commutes_unfolded: algebra.
*)
-inline cic:/CoRN/algebra/CAbGroups/G.var.
+inline "cic:/CoRN/algebra/CAbGroups/G.var".
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
%\end{convention}%
*)
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
%\end{convention}%
*)
-inline cic:/CoRN/algebra/CAbGroups/cag_op_inv.con.
+inline "cic:/CoRN/algebra/CAbGroups/cag_op_inv.con".
(* UNEXPORTED
Hint Resolve cag_op_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve cag_op_inv: algebra.
*)
-inline cic:/CoRN/algebra/CAbGroups/assoc_1.con.
+inline "cic:/CoRN/algebra/CAbGroups/assoc_1.con".
-inline cic:/CoRN/algebra/CAbGroups/minus_plus.con.
+inline "cic:/CoRN/algebra/CAbGroups/minus_plus.con".
-inline cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con.
+inline "cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con".
-inline cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con.
+inline "cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con".
-inline cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_lft.con.
+inline "cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_lft.con".
(* UNEXPORTED
End Various.
(* UNEXPORTED
End Various.
function [inv] which inverts elements respective to [plus].
*)
function [inv] which inverts elements respective to [plus].
*)
-inline cic:/CoRN/algebra/CAbGroups/S.var.
+inline "cic:/CoRN/algebra/CAbGroups/S.var".
-inline cic:/CoRN/algebra/CAbGroups/unit.var.
+inline "cic:/CoRN/algebra/CAbGroups/unit.var".
-inline cic:/CoRN/algebra/CAbGroups/plus.var.
+inline "cic:/CoRN/algebra/CAbGroups/plus.var".
(*#*
%\begin{convention}%
(*#*
%\begin{convention}%
-inline cic:/CoRN/algebra/CAbGroups/plus_lext.var.
+inline "cic:/CoRN/algebra/CAbGroups/plus_lext.var".
-inline cic:/CoRN/algebra/CAbGroups/plus_lunit.var.
+inline "cic:/CoRN/algebra/CAbGroups/plus_lunit.var".
-inline cic:/CoRN/algebra/CAbGroups/plus_comm.var.
+inline "cic:/CoRN/algebra/CAbGroups/plus_comm.var".
-inline cic:/CoRN/algebra/CAbGroups/plus_assoc.var.
+inline "cic:/CoRN/algebra/CAbGroups/plus_assoc.var".
-inline cic:/CoRN/algebra/CAbGroups/inv.var.
+inline "cic:/CoRN/algebra/CAbGroups/inv.var".
-inline cic:/CoRN/algebra/CAbGroups/inv_inv.var.
+inline "cic:/CoRN/algebra/CAbGroups/inv_inv.var".
-inline cic:/CoRN/algebra/CAbGroups/plus_rext.con.
+inline "cic:/CoRN/algebra/CAbGroups/plus_rext.con".
-inline cic:/CoRN/algebra/CAbGroups/plus_runit.con.
+inline "cic:/CoRN/algebra/CAbGroups/plus_runit.con".
-inline cic:/CoRN/algebra/CAbGroups/plus_is_fun.con.
+inline "cic:/CoRN/algebra/CAbGroups/plus_is_fun.con".
-inline cic:/CoRN/algebra/CAbGroups/inv_inv'.con.
+inline "cic:/CoRN/algebra/CAbGroups/inv_inv'.con".
-inline cic:/CoRN/algebra/CAbGroups/plus_fun.con.
+inline "cic:/CoRN/algebra/CAbGroups/plus_fun.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con.
+inline "cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con.
+inline "cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con.
+inline "cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con.
+inline "cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con".
(* UNEXPORTED
End Nice_Char.
(* UNEXPORTED
End Nice_Char.
-inline cic:/CoRN/algebra/CAbGroups/G.var.
+inline "cic:/CoRN/algebra/CAbGroups/G.var".
-inline cic:/CoRN/algebra/CAbGroups/nmult.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_wd.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_wd.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_one.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_one.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_Zero.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_Zero.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_plus.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_plus.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_mult.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_mult.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_inv.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_inv.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_plus'.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_plus'.con".
(* UNEXPORTED
Hint Resolve nmult_wd nmult_Zero nmult_inv nmult_plus nmult_plus': algebra.
*)
(* UNEXPORTED
Hint Resolve nmult_wd nmult_Zero nmult_inv nmult_plus nmult_plus': algebra.
*)
-inline cic:/CoRN/algebra/CAbGroups/zmult.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult.con".
(*
Lemma Zeq_imp_nat_eq : forall m n:nat, m = n -> m = n.
(*
Lemma Zeq_imp_nat_eq : forall m n:nat, m = n -> m = n.
-inline cic:/CoRN/algebra/CAbGroups/zmult_char.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_char.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_wd.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_wd.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_one.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_one.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_min_one.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_min_one.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_zero.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_zero.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_Zero.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_Zero.con".
(* UNEXPORTED
Hint Resolve zmult_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve zmult_zero: algebra.
*)
-inline cic:/CoRN/algebra/CAbGroups/zmult_plus.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_plus.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_mult.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_mult.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_plus'.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_plus'.con".
(* UNEXPORTED
End Group_Extras.
(* UNEXPORTED
End Group_Extras.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CAbMonoids".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CAbMonoids".
-(* INCLUDE
-CMonoids
-*)
+include "CoRN.ma".
+
+include "algebra/CMonoids.ma".
(* UNEXPORTED
Section Abelian_Monoids.
(* UNEXPORTED
Section Abelian_Monoids.
Now we introduce commutativity and add some results.
*)
Now we introduce commutativity and add some results.
*)
-inline cic:/CoRN/algebra/CAbMonoids/is_CAbMonoid.con.
+inline "cic:/CoRN/algebra/CAbMonoids/is_CAbMonoid.con".
+
+inline "cic:/CoRN/algebra/CAbMonoids/CAbMonoid.ind".
-inline cic:/CoRN/algebra/CAbMonoids/CAbMonoid.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/CAbMonoids/cam_crr.con" 0 (* compounds *).
(* UNEXPORTED
Section AbMonoid_Axioms.
*)
(* UNEXPORTED
Section AbMonoid_Axioms.
*)
-inline cic:/CoRN/algebra/CAbMonoids/M.var.
+inline "cic:/CoRN/algebra/CAbMonoids/M.var".
(*#*
%\begin{convention}% Let [M] be an abelian monoid.
%\end{convention}%
*)
(*#*
%\begin{convention}% Let [M] be an abelian monoid.
%\end{convention}%
*)
-inline cic:/CoRN/algebra/CAbMonoids/CAbMonoid_is_CAbMonoid.con.
+inline "cic:/CoRN/algebra/CAbMonoids/CAbMonoid_is_CAbMonoid.con".
-inline cic:/CoRN/algebra/CAbMonoids/cam_commutes.con.
+inline "cic:/CoRN/algebra/CAbMonoids/cam_commutes.con".
-inline cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con.
+inline "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con".
(* UNEXPORTED
End AbMonoid_Axioms.
(* UNEXPORTED
End AbMonoid_Axioms.
** Subgroups of an Abelian Monoid
*)
** Subgroups of an Abelian Monoid
*)
-inline cic:/CoRN/algebra/CAbMonoids/M.var.
+inline "cic:/CoRN/algebra/CAbMonoids/M.var".
-inline cic:/CoRN/algebra/CAbMonoids/P.var.
+inline "cic:/CoRN/algebra/CAbMonoids/P.var".
-inline cic:/CoRN/algebra/CAbMonoids/Punit.var.
+inline "cic:/CoRN/algebra/CAbMonoids/Punit.var".
-inline cic:/CoRN/algebra/CAbMonoids/op_pres_P.var.
+inline "cic:/CoRN/algebra/CAbMonoids/op_pres_P.var".
(*#*
%\begin{convention}%
(*#*
%\begin{convention}%
-inline cic:/CoRN/algebra/CAbMonoids/subcrr.con.
+inline "cic:/CoRN/algebra/CAbMonoids/subcrr.con".
-inline cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con.
+inline "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con".
-inline cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con.
+inline "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con".
(* UNEXPORTED
End SubCAbMonoids.
(* UNEXPORTED
End SubCAbMonoids.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CFields".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CFields".
(* $Id: CFields.v,v 1.12 2004/04/23 10:00:52 lcf Exp $ *)
(*#* printing [/] %\ensuremath{/}% #/# *)
(* $Id: CFields.v,v 1.12 2004/04/23 10:00:52 lcf Exp $ *)
(*#* printing [/] %\ensuremath{/}% #/# *)
(*#* printing [/]?[//] %\ensuremath{/?\ddagger}% #/?‡# *)
(*#* printing [/]?[//] %\ensuremath{/?\ddagger}% #/?‡# *)
+include "algebra/CRings.ma".
(* UNEXPORTED
Transparent sym_eq.
(* UNEXPORTED
Transparent sym_eq.
** Definition of the notion Field
*)
** Definition of the notion Field
*)
-inline cic:/CoRN/algebra/CFields/is_CField.con.
+inline "cic:/CoRN/algebra/CFields/is_CField.con".
+
+inline "cic:/CoRN/algebra/CFields/CField.ind".
-inline cic:/CoRN/algebra/CFields/CField.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/CFields/cf_crr.con" 0 (* compounds *).
-inline cic:/CoRN/algebra/CFields/f_rcpcl'.con.
+inline "cic:/CoRN/algebra/CFields/f_rcpcl'.con".
-inline cic:/CoRN/algebra/CFields/f_rcpcl.con.
+inline "cic:/CoRN/algebra/CFields/f_rcpcl.con".
(* UNEXPORTED
Implicit Arguments f_rcpcl [F].
(* UNEXPORTED
Implicit Arguments f_rcpcl [F].
we have a proof of [y [#] Zero].
*)
we have a proof of [y [#] Zero].
*)
-inline cic:/CoRN/algebra/CFields/cf_div.con.
+inline "cic:/CoRN/algebra/CFields/cf_div.con".
(* UNEXPORTED
Implicit Arguments cf_div [F].
(* UNEXPORTED
Implicit Arguments cf_div [F].
-inline cic:/CoRN/algebra/CFields/F.var.
+inline "cic:/CoRN/algebra/CFields/F.var".
-inline cic:/CoRN/algebra/CFields/CField_is_CField.con.
+inline "cic:/CoRN/algebra/CFields/CField_is_CField.con".
-inline cic:/CoRN/algebra/CFields/rcpcl_is_inverse.con.
+inline "cic:/CoRN/algebra/CFields/rcpcl_is_inverse.con".
(* UNEXPORTED
End Field_axioms.
(* UNEXPORTED
End Field_axioms.
-inline cic:/CoRN/algebra/CFields/F.var.
+inline "cic:/CoRN/algebra/CFields/F.var".
-inline cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con.
+inline "cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con".
-inline cic:/CoRN/algebra/CFields/field_mult_inv.con.
+inline "cic:/CoRN/algebra/CFields/field_mult_inv.con".
(* UNEXPORTED
Hint Resolve field_mult_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve field_mult_inv: algebra.
*)
-inline cic:/CoRN/algebra/CFields/field_mult_inv_op.con.
+inline "cic:/CoRN/algebra/CFields/field_mult_inv_op.con".
(* UNEXPORTED
End Field_basics.
(* UNEXPORTED
End Field_basics.
-inline cic:/CoRN/algebra/CFields/F.var.
+inline "cic:/CoRN/algebra/CFields/F.var".
-inline cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con.
+inline "cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con".
-inline cic:/CoRN/algebra/CFields/mult_lft_resp_ap.con.
+inline "cic:/CoRN/algebra/CFields/mult_lft_resp_ap.con".
-inline cic:/CoRN/algebra/CFields/mult_rht_resp_ap.con.
+inline "cic:/CoRN/algebra/CFields/mult_rht_resp_ap.con".
-inline cic:/CoRN/algebra/CFields/mult_resp_neq_zero.con.
+inline "cic:/CoRN/algebra/CFields/mult_resp_neq_zero.con".
-inline cic:/CoRN/algebra/CFields/mult_resp_neq.con.
+inline "cic:/CoRN/algebra/CFields/mult_resp_neq.con".
-inline cic:/CoRN/algebra/CFields/mult_eq_zero.con.
+inline "cic:/CoRN/algebra/CFields/mult_eq_zero.con".
-inline cic:/CoRN/algebra/CFields/mult_cancel_lft.con.
+inline "cic:/CoRN/algebra/CFields/mult_cancel_lft.con".
-inline cic:/CoRN/algebra/CFields/mult_cancel_rht.con.
+inline "cic:/CoRN/algebra/CFields/mult_cancel_rht.con".
-inline cic:/CoRN/algebra/CFields/square_eq_aux.con.
+inline "cic:/CoRN/algebra/CFields/square_eq_aux.con".
-inline cic:/CoRN/algebra/CFields/square_eq_weak.con.
+inline "cic:/CoRN/algebra/CFields/square_eq_weak.con".
-inline cic:/CoRN/algebra/CFields/cond_square_eq.con.
+inline "cic:/CoRN/algebra/CFields/cond_square_eq.con".
(* UNEXPORTED
End Field_multiplication.
(* UNEXPORTED
End Field_multiplication.
-inline cic:/CoRN/algebra/CFields/x_xminone.con.
+inline "cic:/CoRN/algebra/CFields/x_xminone.con".
-inline cic:/CoRN/algebra/CFields/square_id.con.
+inline "cic:/CoRN/algebra/CFields/square_id.con".
(* UNEXPORTED
End x_square.
(* UNEXPORTED
End x_square.
-inline cic:/CoRN/algebra/CFields/F.var.
+inline "cic:/CoRN/algebra/CFields/F.var".
-inline cic:/CoRN/algebra/CFields/inv_one.con.
+inline "cic:/CoRN/algebra/CFields/inv_one.con".
-inline cic:/CoRN/algebra/CFields/f_rcpcl_wd.con.
+inline "cic:/CoRN/algebra/CFields/f_rcpcl_wd.con".
-inline cic:/CoRN/algebra/CFields/f_rcpcl_mult.con.
+inline "cic:/CoRN/algebra/CFields/f_rcpcl_mult.con".
-inline cic:/CoRN/algebra/CFields/f_rcpcl_resp_ap_zero.con.
+inline "cic:/CoRN/algebra/CFields/f_rcpcl_resp_ap_zero.con".
-inline cic:/CoRN/algebra/CFields/f_rcpcl_f_rcpcl.con.
+inline "cic:/CoRN/algebra/CFields/f_rcpcl_f_rcpcl.con".
(* UNEXPORTED
End Rcpcl_properties.
(* UNEXPORTED
End Rcpcl_properties.
-inline cic:/CoRN/algebra/CFields/F.var.
+inline "cic:/CoRN/algebra/CFields/F.var".
(*#*
The multiplicative monoid of NonZeros.
*)
(*#*
The multiplicative monoid of NonZeros.
*)
-inline cic:/CoRN/algebra/CFields/NonZeroMonoid.con.
+inline "cic:/CoRN/algebra/CFields/NonZeroMonoid.con".
-inline cic:/CoRN/algebra/CFields/fmg_cs_inv.con.
+inline "cic:/CoRN/algebra/CFields/fmg_cs_inv.con".
-inline cic:/CoRN/algebra/CFields/plus_nonzeros_eq_mult_dom.con.
+inline "cic:/CoRN/algebra/CFields/plus_nonzeros_eq_mult_dom.con".
-inline cic:/CoRN/algebra/CFields/cfield_to_mult_cgroup.con.
+inline "cic:/CoRN/algebra/CFields/cfield_to_mult_cgroup.con".
(* UNEXPORTED
End MultipGroup.
(* UNEXPORTED
End MultipGroup.
%\end{nameconvention}%
*)
%\end{nameconvention}%
*)
-inline cic:/CoRN/algebra/CFields/F.var.
+inline "cic:/CoRN/algebra/CFields/F.var".
-inline cic:/CoRN/algebra/CFields/div_prop.con.
+inline "cic:/CoRN/algebra/CFields/div_prop.con".
-inline cic:/CoRN/algebra/CFields/div_1.con.
+inline "cic:/CoRN/algebra/CFields/div_1.con".
-inline cic:/CoRN/algebra/CFields/div_1'.con.
+inline "cic:/CoRN/algebra/CFields/div_1'.con".
-inline cic:/CoRN/algebra/CFields/div_1''.con.
+inline "cic:/CoRN/algebra/CFields/div_1''.con".
(* UNEXPORTED
Hint Resolve div_1: algebra.
*)
(* UNEXPORTED
Hint Resolve div_1: algebra.
*)
-inline cic:/CoRN/algebra/CFields/x_div_x.con.
+inline "cic:/CoRN/algebra/CFields/x_div_x.con".
(* UNEXPORTED
Hint Resolve x_div_x: algebra.
*)
(* UNEXPORTED
Hint Resolve x_div_x: algebra.
*)
-inline cic:/CoRN/algebra/CFields/x_div_one.con.
+inline "cic:/CoRN/algebra/CFields/x_div_one.con".
(*#*
The next lemma says $x\cdot\frac{y}{z} = \frac{x\cdot y}{z}$
#x.(y/z) = (x.y)/z#.
*)
(*#*
The next lemma says $x\cdot\frac{y}{z} = \frac{x\cdot y}{z}$
#x.(y/z) = (x.y)/z#.
*)
-inline cic:/CoRN/algebra/CFields/x_mult_y_div_z.con.
+inline "cic:/CoRN/algebra/CFields/x_mult_y_div_z.con".
(* UNEXPORTED
Hint Resolve x_mult_y_div_z: algebra.
*)
(* UNEXPORTED
Hint Resolve x_mult_y_div_z: algebra.
*)
-inline cic:/CoRN/algebra/CFields/div_wd.con.
+inline "cic:/CoRN/algebra/CFields/div_wd.con".
(* UNEXPORTED
Hint Resolve div_wd: algebra_c.
(* UNEXPORTED
Hint Resolve div_wd: algebra_c.
-inline cic:/CoRN/algebra/CFields/div_div.con.
+inline "cic:/CoRN/algebra/CFields/div_div.con".
-inline cic:/CoRN/algebra/CFields/div_resp_ap_zero_rev.con.
+inline "cic:/CoRN/algebra/CFields/div_resp_ap_zero_rev.con".
-inline cic:/CoRN/algebra/CFields/div_resp_ap_zero.con.
+inline "cic:/CoRN/algebra/CFields/div_resp_ap_zero.con".
(*#*
The next lemma says $\frac{x}{\frac{y}{z}} = \frac{x\cdot z}{y}$
#[x/(y/z) = (x.z)/y]#
*)
(*#*
The next lemma says $\frac{x}{\frac{y}{z}} = \frac{x\cdot z}{y}$
#[x/(y/z) = (x.z)/y]#
*)
-inline cic:/CoRN/algebra/CFields/div_div2.con.
+inline "cic:/CoRN/algebra/CFields/div_div2.con".
(*#*
The next lemma says $\frac{x\cdot p}{y\cdot q} = \frac{x}{y}\cdot \frac{p}{q}$
#[(x.p)/(y.q) = (x/y).(p/q)]#
*)
(*#*
The next lemma says $\frac{x\cdot p}{y\cdot q} = \frac{x}{y}\cdot \frac{p}{q}$
#[(x.p)/(y.q) = (x/y).(p/q)]#
*)
-inline cic:/CoRN/algebra/CFields/mult_of_divs.con.
+inline "cic:/CoRN/algebra/CFields/mult_of_divs.con".
-inline cic:/CoRN/algebra/CFields/div_dist.con.
+inline "cic:/CoRN/algebra/CFields/div_dist.con".
-inline cic:/CoRN/algebra/CFields/div_dist'.con.
+inline "cic:/CoRN/algebra/CFields/div_dist'.con".
-inline cic:/CoRN/algebra/CFields/div_semi_sym.con.
+inline "cic:/CoRN/algebra/CFields/div_semi_sym.con".
(* UNEXPORTED
Hint Resolve div_semi_sym: algebra.
*)
(* UNEXPORTED
Hint Resolve div_semi_sym: algebra.
*)
-inline cic:/CoRN/algebra/CFields/eq_div.con.
+inline "cic:/CoRN/algebra/CFields/eq_div.con".
-inline cic:/CoRN/algebra/CFields/div_strext.con.
+inline "cic:/CoRN/algebra/CFields/div_strext.con".
(* UNEXPORTED
End Div_properties.
(* UNEXPORTED
End Div_properties.
Section Mult_Cancel_Ap_Zero.
*)
Section Mult_Cancel_Ap_Zero.
*)
-inline cic:/CoRN/algebra/CFields/F.var.
+inline "cic:/CoRN/algebra/CFields/F.var".
-inline cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con.
+inline "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con".
-inline cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_rht.con.
+inline "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_rht.con".
-inline cic:/CoRN/algebra/CFields/recip_ap_zero.con.
+inline "cic:/CoRN/algebra/CFields/recip_ap_zero.con".
-inline cic:/CoRN/algebra/CFields/recip_resp_ap.con.
+inline "cic:/CoRN/algebra/CFields/recip_resp_ap.con".
(* UNEXPORTED
End Mult_Cancel_Ap_Zero.
(* UNEXPORTED
End Mult_Cancel_Ap_Zero.
-inline cic:/CoRN/algebra/CFields/X.var.
+inline "cic:/CoRN/algebra/CFields/X.var".
-inline cic:/CoRN/algebra/CFields/F.var.
+inline "cic:/CoRN/algebra/CFields/F.var".
-inline cic:/CoRN/algebra/CFields/G.var.
+inline "cic:/CoRN/algebra/CFields/G.var".
-inline cic:/CoRN/algebra/CFields/P.con.
+inline "cic:/CoRN/algebra/CFields/P.con".
-inline cic:/CoRN/algebra/CFields/Q.con.
+inline "cic:/CoRN/algebra/CFields/Q.con".
Some auxiliary notions are helpful in defining the domain.
*)
Some auxiliary notions are helpful in defining the domain.
*)
-inline cic:/CoRN/algebra/CFields/R.con.
+inline "cic:/CoRN/algebra/CFields/R.con".
-inline cic:/CoRN/algebra/CFields/Ext2R.con.
+inline "cic:/CoRN/algebra/CFields/Ext2R.con".
-inline cic:/CoRN/algebra/CFields/part_function_recip_strext.con.
+inline "cic:/CoRN/algebra/CFields/part_function_recip_strext.con".
-inline cic:/CoRN/algebra/CFields/part_function_recip_pred_wd.con.
+inline "cic:/CoRN/algebra/CFields/part_function_recip_pred_wd.con".
-inline cic:/CoRN/algebra/CFields/Frecip.con.
+inline "cic:/CoRN/algebra/CFields/Frecip.con".
(* UNEXPORTED
End Part_Function_Recip.
(* UNEXPORTED
End Part_Function_Recip.
For division things work out almost in the same way.
*)
For division things work out almost in the same way.
*)
-inline cic:/CoRN/algebra/CFields/R.con.
+inline "cic:/CoRN/algebra/CFields/R.con".
-inline cic:/CoRN/algebra/CFields/Ext2R.con.
+inline "cic:/CoRN/algebra/CFields/Ext2R.con".
-inline cic:/CoRN/algebra/CFields/part_function_div_strext.con.
+inline "cic:/CoRN/algebra/CFields/part_function_div_strext.con".
-inline cic:/CoRN/algebra/CFields/part_function_div_pred_wd.con.
+inline "cic:/CoRN/algebra/CFields/part_function_div_pred_wd.con".
-inline cic:/CoRN/algebra/CFields/Fdiv.con.
+inline "cic:/CoRN/algebra/CFields/Fdiv.con".
(* UNEXPORTED
End Part_Function_Div.
(* UNEXPORTED
End Part_Function_Div.
-inline cic:/CoRN/algebra/CFields/R.var.
+inline "cic:/CoRN/algebra/CFields/R.var".
-inline cic:/CoRN/algebra/CFields/included_FRecip.con.
+inline "cic:/CoRN/algebra/CFields/included_FRecip.con".
-inline cic:/CoRN/algebra/CFields/included_FRecip'.con.
+inline "cic:/CoRN/algebra/CFields/included_FRecip'.con".
-inline cic:/CoRN/algebra/CFields/included_FDiv.con.
+inline "cic:/CoRN/algebra/CFields/included_FDiv.con".
-inline cic:/CoRN/algebra/CFields/included_FDiv'.con.
+inline "cic:/CoRN/algebra/CFields/included_FDiv'.con".
-inline cic:/CoRN/algebra/CFields/included_FDiv''.con.
+inline "cic:/CoRN/algebra/CFields/included_FDiv''.con".
(* UNEXPORTED
End CField_Ops.
(* UNEXPORTED
End CField_Ops.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CGroups".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CGroups".
(* $Id: CGroups.v,v 1.9 2004/04/23 10:00:52 lcf Exp $ *)
(*#* printing [-] %\ensuremath-% #−# *)
(* $Id: CGroups.v,v 1.9 2004/04/23 10:00:52 lcf Exp $ *)
(*#* printing [-] %\ensuremath-% #−# *)
(*#* printing {--} %\ensuremath-% #−# *)
(*#* printing {--} %\ensuremath-% #−# *)
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
** Definition of the notion of Group
*)
** Definition of the notion of Group
*)
-inline cic:/CoRN/algebra/CGroups/is_inverse.con.
+inline "cic:/CoRN/algebra/CGroups/is_inverse.con".
(* UNEXPORTED
Implicit Arguments is_inverse [S].
*)
(* UNEXPORTED
Implicit Arguments is_inverse [S].
*)
-inline cic:/CoRN/algebra/CGroups/is_CGroup.con.
+inline "cic:/CoRN/algebra/CGroups/is_CGroup.con".
+
+inline "cic:/CoRN/algebra/CGroups/CGroup.ind".
-inline cic:/CoRN/algebra/CGroups/CGroup.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/CGroups/cg_crr.con" 0 (* compounds *).
Implicit Arguments cg_inv [c].
*)
Implicit Arguments cg_inv [c].
*)
-inline cic:/CoRN/algebra/CGroups/cg_minus.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus.con".
(*#*
%\begin{nameconvention}%
(*#*
%\begin{nameconvention}%
Section CGroup_axioms.
*)
Section CGroup_axioms.
*)
-inline cic:/CoRN/algebra/CGroups/G.var.
+inline "cic:/CoRN/algebra/CGroups/G.var".
-inline cic:/CoRN/algebra/CGroups/cg_inverse.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inverse.con".
(* UNEXPORTED
End CGroup_axioms.
(* UNEXPORTED
End CGroup_axioms.
Section CGroup_basics.
*)
Section CGroup_basics.
*)
-inline cic:/CoRN/algebra/CGroups/G.var.
+inline "cic:/CoRN/algebra/CGroups/G.var".
-inline cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con.
+inline "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con".
-inline cic:/CoRN/algebra/CGroups/cg_lft_inv_unfolded.con.
+inline "cic:/CoRN/algebra/CGroups/cg_lft_inv_unfolded.con".
-inline cic:/CoRN/algebra/CGroups/cg_minus_correct.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_correct.con".
(* UNEXPORTED
Hint Resolve cg_rht_inv_unfolded cg_lft_inv_unfolded cg_minus_correct:
algebra.
*)
(* UNEXPORTED
Hint Resolve cg_rht_inv_unfolded cg_lft_inv_unfolded cg_minus_correct:
algebra.
*)
-inline cic:/CoRN/algebra/CGroups/cg_inverse'.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inverse'.con".
-inline cic:/CoRN/algebra/CGroups/cg_minus_unfolded.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_unfolded.con".
(* UNEXPORTED
Hint Resolve cg_minus_unfolded: algebra.
*)
(* UNEXPORTED
Hint Resolve cg_minus_unfolded: algebra.
*)
-inline cic:/CoRN/algebra/CGroups/cg_minus_wd.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_wd.con".
(* UNEXPORTED
Hint Resolve cg_minus_wd: algebra_c.
*)
(* UNEXPORTED
Hint Resolve cg_minus_wd: algebra_c.
*)
-inline cic:/CoRN/algebra/CGroups/cg_minus_strext.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_strext.con".
-inline cic:/CoRN/algebra/CGroups/cg_minus_is_csetoid_bin_op.con.
+inline "cic:/CoRN/algebra/CGroups/cg_minus_is_csetoid_bin_op.con".
-inline cic:/CoRN/algebra/CGroups/grp_inv_assoc.con.
+inline "cic:/CoRN/algebra/CGroups/grp_inv_assoc.con".
(* UNEXPORTED
Hint Resolve grp_inv_assoc: algebra.
*)
(* UNEXPORTED
Hint Resolve grp_inv_assoc: algebra.
*)
-inline cic:/CoRN/algebra/CGroups/cg_inv_unique.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_unique.con".
-inline cic:/CoRN/algebra/CGroups/cg_inv_inv.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_inv.con".
(* UNEXPORTED
Hint Resolve cg_inv_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve cg_inv_inv: algebra.
*)
-inline cic:/CoRN/algebra/CGroups/cg_cancel_lft.con.
+inline "cic:/CoRN/algebra/CGroups/cg_cancel_lft.con".
-inline cic:/CoRN/algebra/CGroups/cg_cancel_rht.con.
+inline "cic:/CoRN/algebra/CGroups/cg_cancel_rht.con".
-inline cic:/CoRN/algebra/CGroups/cg_inv_unique'.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_unique'.con".
-inline cic:/CoRN/algebra/CGroups/cg_inv_unique_2.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_unique_2.con".
-inline cic:/CoRN/algebra/CGroups/cg_zero_inv.con.
+inline "cic:/CoRN/algebra/CGroups/cg_zero_inv.con".
(* UNEXPORTED
Hint Resolve cg_zero_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve cg_zero_inv: algebra.
*)
-inline cic:/CoRN/algebra/CGroups/cg_inv_zero.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_zero.con".
-inline cic:/CoRN/algebra/CGroups/cg_inv_op.con.
+inline "cic:/CoRN/algebra/CGroups/cg_inv_op.con".
(*#*
Useful for interactive proof development.
*)
(*#*
Useful for interactive proof development.
*)
-inline cic:/CoRN/algebra/CGroups/x_minus_x.con.
+inline "cic:/CoRN/algebra/CGroups/x_minus_x.con".
-inline cic:/CoRN/algebra/CGroups/P.var.
+inline "cic:/CoRN/algebra/CGroups/P.var".
-inline cic:/CoRN/algebra/CGroups/Punit.var.
+inline "cic:/CoRN/algebra/CGroups/Punit.var".
-inline cic:/CoRN/algebra/CGroups/op_pres_P.var.
+inline "cic:/CoRN/algebra/CGroups/op_pres_P.var".
-inline cic:/CoRN/algebra/CGroups/inv_pres_P.var.
+inline "cic:/CoRN/algebra/CGroups/inv_pres_P.var".
-inline cic:/CoRN/algebra/CGroups/subcrr.con.
+inline "cic:/CoRN/algebra/CGroups/subcrr.con".
-inline cic:/CoRN/algebra/CGroups/subinv.con.
+inline "cic:/CoRN/algebra/CGroups/subinv.con".
-inline cic:/CoRN/algebra/CGroups/isgrp_scrr.con.
+inline "cic:/CoRN/algebra/CGroups/isgrp_scrr.con".
-inline cic:/CoRN/algebra/CGroups/Build_SubCGroup.con.
+inline "cic:/CoRN/algebra/CGroups/Build_SubCGroup.con".
(* UNEXPORTED
End SubCGroups.
(* UNEXPORTED
End SubCGroups.
Section Assoc_properties.
*)
Section Assoc_properties.
*)
-inline cic:/CoRN/algebra/CGroups/G.var.
+inline "cic:/CoRN/algebra/CGroups/G.var".
-inline cic:/CoRN/algebra/CGroups/assoc_2.con.
+inline "cic:/CoRN/algebra/CGroups/assoc_2.con".
-inline cic:/CoRN/algebra/CGroups/zero_minus.con.
+inline "cic:/CoRN/algebra/CGroups/zero_minus.con".
-inline cic:/CoRN/algebra/CGroups/cg_cancel_mixed.con.
+inline "cic:/CoRN/algebra/CGroups/cg_cancel_mixed.con".
-inline cic:/CoRN/algebra/CGroups/plus_resp_eq.con.
+inline "cic:/CoRN/algebra/CGroups/plus_resp_eq.con".
(* UNEXPORTED
End Assoc_properties.
(* UNEXPORTED
End Assoc_properties.
Section cgroups_apartness.
*)
Section cgroups_apartness.
*)
-inline cic:/CoRN/algebra/CGroups/G.var.
+inline "cic:/CoRN/algebra/CGroups/G.var".
-inline cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con.
+inline "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con".
-inline cic:/CoRN/algebra/CGroups/op_rht_resp_ap.con.
+inline "cic:/CoRN/algebra/CGroups/op_rht_resp_ap.con".
-inline cic:/CoRN/algebra/CGroups/cg_ap_cancel_rht.con.
+inline "cic:/CoRN/algebra/CGroups/cg_ap_cancel_rht.con".
-inline cic:/CoRN/algebra/CGroups/plus_cancel_ap_rht.con.
+inline "cic:/CoRN/algebra/CGroups/plus_cancel_ap_rht.con".
-inline cic:/CoRN/algebra/CGroups/minus_ap_zero.con.
+inline "cic:/CoRN/algebra/CGroups/minus_ap_zero.con".
-inline cic:/CoRN/algebra/CGroups/zero_minus_apart.con.
+inline "cic:/CoRN/algebra/CGroups/zero_minus_apart.con".
-inline cic:/CoRN/algebra/CGroups/inv_resp_ap_zero.con.
+inline "cic:/CoRN/algebra/CGroups/inv_resp_ap_zero.con".
-inline cic:/CoRN/algebra/CGroups/inv_resp_ap.con.
+inline "cic:/CoRN/algebra/CGroups/inv_resp_ap.con".
-inline cic:/CoRN/algebra/CGroups/minus_resp_ap_rht.con.
+inline "cic:/CoRN/algebra/CGroups/minus_resp_ap_rht.con".
-inline cic:/CoRN/algebra/CGroups/minus_resp_ap_lft.con.
+inline "cic:/CoRN/algebra/CGroups/minus_resp_ap_lft.con".
-inline cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con.
+inline "cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con".
(* UNEXPORTED
End cgroups_apartness.
(* UNEXPORTED
End cgroups_apartness.
-inline cic:/CoRN/algebra/CGroups/G.var.
+inline "cic:/CoRN/algebra/CGroups/G.var".
-inline cic:/CoRN/algebra/CGroups/F.var.
+inline "cic:/CoRN/algebra/CGroups/F.var".
-inline cic:/CoRN/algebra/CGroups/F'.var.
+inline "cic:/CoRN/algebra/CGroups/F'.var".
-inline cic:/CoRN/algebra/CGroups/P.con.
+inline "cic:/CoRN/algebra/CGroups/P.con".
-inline cic:/CoRN/algebra/CGroups/Q.con.
+inline "cic:/CoRN/algebra/CGroups/Q.con".
Section Part_Function_Inv.
*)
Section Part_Function_Inv.
*)
-inline cic:/CoRN/algebra/CGroups/part_function_inv_strext.con.
+inline "cic:/CoRN/algebra/CGroups/part_function_inv_strext.con".
-inline cic:/CoRN/algebra/CGroups/Finv.con.
+inline "cic:/CoRN/algebra/CGroups/Finv.con".
(* UNEXPORTED
End Part_Function_Inv.
(* UNEXPORTED
End Part_Function_Inv.
Section Part_Function_Minus.
*)
Section Part_Function_Minus.
*)
-inline cic:/CoRN/algebra/CGroups/part_function_minus_strext.con.
+inline "cic:/CoRN/algebra/CGroups/part_function_minus_strext.con".
-inline cic:/CoRN/algebra/CGroups/Fminus.con.
+inline "cic:/CoRN/algebra/CGroups/Fminus.con".
(* UNEXPORTED
End Part_Function_Minus.
(* UNEXPORTED
End Part_Function_Minus.
-inline cic:/CoRN/algebra/CGroups/R.var.
+inline "cic:/CoRN/algebra/CGroups/R.var".
-inline cic:/CoRN/algebra/CGroups/included_FInv.con.
+inline "cic:/CoRN/algebra/CGroups/included_FInv.con".
-inline cic:/CoRN/algebra/CGroups/included_FInv'.con.
+inline "cic:/CoRN/algebra/CGroups/included_FInv'.con".
-inline cic:/CoRN/algebra/CGroups/included_FMinus.con.
+inline "cic:/CoRN/algebra/CGroups/included_FMinus.con".
-inline cic:/CoRN/algebra/CGroups/included_FMinus'.con.
+inline "cic:/CoRN/algebra/CGroups/included_FMinus'.con".
-inline cic:/CoRN/algebra/CGroups/included_FMinus''.con.
+inline "cic:/CoRN/algebra/CGroups/included_FMinus''.con".
(* UNEXPORTED
End CGroup_Ops.
(* UNEXPORTED
End CGroup_Ops.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CLogic".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CLogic".
(* $Id: CLogic.v,v 1.10 2004/04/09 15:58:31 lcf Exp $ *)
(*#* printing Not %\ensuremath\neg% #~# *)
(* $Id: CLogic.v,v 1.10 2004/04/09 15:58:31 lcf Exp $ *)
(*#* printing Not %\ensuremath\neg% #~# *)
(*#* printing and %\ensuremath{\mathrel\wedge}% *)
(*#* printing and %\ensuremath{\mathrel\wedge}% *)
-(* INCLUDE
-Compare_dec
-*)
-
-(* INCLUDE
-Basics
-*)
-
-(* INCLUDE
-ZArith
-*)
-
-(* INCLUDE
-ZArithRing
-*)
-
-(* INCLUDE
-Div2
-*)
-
-(* INCLUDE
-Wf_nat
-*)
+include "algebra/Basics.ma".
(*#* *Extending the Coq Logic
Because notions of apartness and order have computational meaning, we
(*#* *Extending the Coq Logic
Because notions of apartness and order have computational meaning, we
-inline cic:/CoRN/algebra/CLogic/CProp.con.
+inline "cic:/CoRN/algebra/CLogic/CProp.con".
(* UNEXPORTED
Section Basics.
(* UNEXPORTED
Section Basics.
and some basic connectives in [CProp].
*)
and some basic connectives in [CProp].
*)
-inline cic:/CoRN/algebra/CLogic/Not.con.
+inline "cic:/CoRN/algebra/CLogic/Not.con".
-inline cic:/CoRN/algebra/CLogic/CAnd.ind.
+inline "cic:/CoRN/algebra/CLogic/CAnd.ind".
-inline cic:/CoRN/algebra/CLogic/Iff.con.
+inline "cic:/CoRN/algebra/CLogic/Iff.con".
-inline cic:/CoRN/algebra/CLogic/CFalse.ind.
+inline "cic:/CoRN/algebra/CLogic/CFalse.ind".
-inline cic:/CoRN/algebra/CLogic/CTrue.ind.
+inline "cic:/CoRN/algebra/CLogic/CTrue.ind".
-inline cic:/CoRN/algebra/CLogic/proj1_sigT.con.
+inline "cic:/CoRN/algebra/CLogic/proj1_sigT.con".
-inline cic:/CoRN/algebra/CLogic/proj2_sigT.con.
+inline "cic:/CoRN/algebra/CLogic/proj2_sigT.con".
-inline cic:/CoRN/algebra/CLogic/sig2T.ind.
+inline "cic:/CoRN/algebra/CLogic/sig2T.ind".
-inline cic:/CoRN/algebra/CLogic/proj1_sig2T.con.
+inline "cic:/CoRN/algebra/CLogic/proj1_sig2T.con".
-inline cic:/CoRN/algebra/CLogic/proj2a_sig2T.con.
+inline "cic:/CoRN/algebra/CLogic/proj2a_sig2T.con".
-inline cic:/CoRN/algebra/CLogic/proj2b_sig2T.con.
+inline "cic:/CoRN/algebra/CLogic/proj2b_sig2T.con".
-inline cic:/CoRN/algebra/CLogic/toCProp.ind.
+inline "cic:/CoRN/algebra/CLogic/toCProp.ind".
-inline cic:/CoRN/algebra/CLogic/toCProp_e.con.
+inline "cic:/CoRN/algebra/CLogic/toCProp_e.con".
-inline cic:/CoRN/algebra/CLogic/CNot.con.
+inline "cic:/CoRN/algebra/CLogic/CNot.con".
-inline cic:/CoRN/algebra/CLogic/Ccontrapos'.con.
+inline "cic:/CoRN/algebra/CLogic/Ccontrapos'.con".
-inline cic:/CoRN/algebra/CLogic/COr.ind.
+inline "cic:/CoRN/algebra/CLogic/COr.ind".
(*#*
Some lemmas to make it possible to use [Step] when reasoning with
biimplications.*)
(*#*
Some lemmas to make it possible to use [Step] when reasoning with
biimplications.*)
-inline cic:/CoRN/algebra/CLogic/Iff_left.con.
+inline "cic:/CoRN/algebra/CLogic/Iff_left.con".
-inline cic:/CoRN/algebra/CLogic/Iff_right.con.
+inline "cic:/CoRN/algebra/CLogic/Iff_right.con".
-inline cic:/CoRN/algebra/CLogic/Iff_refl.con.
+inline "cic:/CoRN/algebra/CLogic/Iff_refl.con".
-inline cic:/CoRN/algebra/CLogic/Iff_sym.con.
+inline "cic:/CoRN/algebra/CLogic/Iff_sym.con".
-inline cic:/CoRN/algebra/CLogic/Iff_trans.con.
+inline "cic:/CoRN/algebra/CLogic/Iff_trans.con".
-inline cic:/CoRN/algebra/CLogic/Iff_imp_imp.con.
+inline "cic:/CoRN/algebra/CLogic/Iff_imp_imp.con".
(* UNEXPORTED
Declare Right Step Iff_right.
(* UNEXPORTED
Declare Right Step Iff_right.
-inline cic:/CoRN/algebra/CLogic/not_r_cor_rect.con.
+inline "cic:/CoRN/algebra/CLogic/not_r_cor_rect.con".
-inline cic:/CoRN/algebra/CLogic/not_l_cor_rect.con.
+inline "cic:/CoRN/algebra/CLogic/not_l_cor_rect.con".
Let [P] be a predicate on $\NN^2$#N times N#.
*)
Let [P] be a predicate on $\NN^2$#N times N#.
*)
-inline cic:/CoRN/algebra/CLogic/P.var.
+inline "cic:/CoRN/algebra/CLogic/P.var".
-inline cic:/CoRN/algebra/CLogic/choice.con.
+inline "cic:/CoRN/algebra/CLogic/choice.con".
(* UNEXPORTED
End Choice.
(* UNEXPORTED
End Choice.
when [A], [B] and [C] are non trivial.
*)
when [A], [B] and [C] are non trivial.
*)
-inline cic:/CoRN/algebra/CLogic/CNot_Not_or.con.
+inline "cic:/CoRN/algebra/CLogic/CNot_Not_or.con".
-inline cic:/CoRN/algebra/CLogic/CdeMorgan_ex_all.con.
+inline "cic:/CoRN/algebra/CLogic/CdeMorgan_ex_all.con".
(* UNEXPORTED
End Logical_Remarks.
(* UNEXPORTED
End Logical_Remarks.
-inline cic:/CoRN/algebra/CLogic/A.var.
+inline "cic:/CoRN/algebra/CLogic/A.var".
-inline cic:/CoRN/algebra/CLogic/Crelation.con.
+inline "cic:/CoRN/algebra/CLogic/Crelation.con".
-inline cic:/CoRN/algebra/CLogic/R.var.
+inline "cic:/CoRN/algebra/CLogic/R.var".
-inline cic:/CoRN/algebra/CLogic/Creflexive.con.
+inline "cic:/CoRN/algebra/CLogic/Creflexive.con".
-inline cic:/CoRN/algebra/CLogic/Ctransitive.con.
+inline "cic:/CoRN/algebra/CLogic/Ctransitive.con".
-inline cic:/CoRN/algebra/CLogic/Csymmetric.con.
+inline "cic:/CoRN/algebra/CLogic/Csymmetric.con".
-inline cic:/CoRN/algebra/CLogic/Cequiv.con.
+inline "cic:/CoRN/algebra/CLogic/Cequiv.con".
(* UNEXPORTED
End CRelation_Definition.
(* UNEXPORTED
End CRelation_Definition.
-inline cic:/CoRN/algebra/CLogic/A.var.
+inline "cic:/CoRN/algebra/CLogic/A.var".
-inline cic:/CoRN/algebra/CLogic/Trelation.con.
+inline "cic:/CoRN/algebra/CLogic/Trelation.con".
-inline cic:/CoRN/algebra/CLogic/R.var.
+inline "cic:/CoRN/algebra/CLogic/R.var".
-inline cic:/CoRN/algebra/CLogic/Treflexive.con.
+inline "cic:/CoRN/algebra/CLogic/Treflexive.con".
-inline cic:/CoRN/algebra/CLogic/Ttransitive.con.
+inline "cic:/CoRN/algebra/CLogic/Ttransitive.con".
-inline cic:/CoRN/algebra/CLogic/Tsymmetric.con.
+inline "cic:/CoRN/algebra/CLogic/Tsymmetric.con".
-inline cic:/CoRN/algebra/CLogic/Tequiv.con.
+inline "cic:/CoRN/algebra/CLogic/Tequiv.con".
(* UNEXPORTED
End TRelation_Definition.
*)
(* UNEXPORTED
End TRelation_Definition.
*)
-inline cic:/CoRN/algebra/CLogic/eqs.ind.
+inline "cic:/CoRN/algebra/CLogic/eqs.ind".
(* UNEXPORTED
Section le_odd.
(* UNEXPORTED
Section le_odd.
(*#* ** The relation [le], [lt], [odd] and [even] in [CProp]
*)
(*#* ** The relation [le], [lt], [odd] and [even] in [CProp]
*)
-inline cic:/CoRN/algebra/CLogic/Cle.ind.
+inline "cic:/CoRN/algebra/CLogic/Cle.ind".
-inline cic:/CoRN/algebra/CLogic/Cnat_double_ind.con.
+inline "cic:/CoRN/algebra/CLogic/Cnat_double_ind.con".
-inline cic:/CoRN/algebra/CLogic/my_Cle_ind.con.
+inline "cic:/CoRN/algebra/CLogic/my_Cle_ind.con".
-inline cic:/CoRN/algebra/CLogic/Cle_n_S.con.
+inline "cic:/CoRN/algebra/CLogic/Cle_n_S.con".
-inline cic:/CoRN/algebra/CLogic/toCle.con.
+inline "cic:/CoRN/algebra/CLogic/toCle.con".
(* UNEXPORTED
Hint Resolve toCle.
*)
(* UNEXPORTED
Hint Resolve toCle.
*)
-inline cic:/CoRN/algebra/CLogic/Cle_to.con.
+inline "cic:/CoRN/algebra/CLogic/Cle_to.con".
-inline cic:/CoRN/algebra/CLogic/Clt.con.
+inline "cic:/CoRN/algebra/CLogic/Clt.con".
-inline cic:/CoRN/algebra/CLogic/toCProp_lt.con.
+inline "cic:/CoRN/algebra/CLogic/toCProp_lt.con".
-inline cic:/CoRN/algebra/CLogic/Clt_to.con.
+inline "cic:/CoRN/algebra/CLogic/Clt_to.con".
-inline cic:/CoRN/algebra/CLogic/Cle_le_S_eq.con.
+inline "cic:/CoRN/algebra/CLogic/Cle_le_S_eq.con".
-inline cic:/CoRN/algebra/CLogic/Cnat_total_order.con.
+inline "cic:/CoRN/algebra/CLogic/Cnat_total_order.con".
-inline cic:/CoRN/algebra/CLogic/Codd.ind.
+inline "cic:/CoRN/algebra/CLogic/Codd.ind".
-inline cic:/CoRN/algebra/CLogic/Codd_even_to.con.
+inline "cic:/CoRN/algebra/CLogic/Codd_even_to.con".
-inline cic:/CoRN/algebra/CLogic/Codd_to.con.
+inline "cic:/CoRN/algebra/CLogic/Codd_to.con".
-inline cic:/CoRN/algebra/CLogic/Ceven_to.con.
+inline "cic:/CoRN/algebra/CLogic/Ceven_to.con".
-inline cic:/CoRN/algebra/CLogic/to_Codd_even.con.
+inline "cic:/CoRN/algebra/CLogic/to_Codd_even.con".
-inline cic:/CoRN/algebra/CLogic/to_Codd.con.
+inline "cic:/CoRN/algebra/CLogic/to_Codd.con".
-inline cic:/CoRN/algebra/CLogic/to_Ceven.con.
+inline "cic:/CoRN/algebra/CLogic/to_Ceven.con".
(* UNEXPORTED
End le_odd.
(* UNEXPORTED
End le_odd.
-inline cic:/CoRN/algebra/CLogic/CZ_exh.con.
+inline "cic:/CoRN/algebra/CLogic/CZ_exh.con".
-inline cic:/CoRN/algebra/CLogic/Cnats_Z_ind.con.
+inline "cic:/CoRN/algebra/CLogic/Cnats_Z_ind.con".
-inline cic:/CoRN/algebra/CLogic/Cdiff_Z_ind.con.
+inline "cic:/CoRN/algebra/CLogic/Cdiff_Z_ind.con".
-inline cic:/CoRN/algebra/CLogic/Cpred_succ_Z_ind.con.
+inline "cic:/CoRN/algebra/CLogic/Cpred_succ_Z_ind.con".
-inline cic:/CoRN/algebra/CLogic/not_r_sum_rec.con.
+inline "cic:/CoRN/algebra/CLogic/not_r_sum_rec.con".
-inline cic:/CoRN/algebra/CLogic/not_l_sum_rec.con.
+inline "cic:/CoRN/algebra/CLogic/not_l_sum_rec.con".
-inline cic:/CoRN/algebra/CLogic/nat_less_n_pred.con.
+inline "cic:/CoRN/algebra/CLogic/nat_less_n_pred.con".
-inline cic:/CoRN/algebra/CLogic/nat_less_n_pred'.con.
+inline "cic:/CoRN/algebra/CLogic/nat_less_n_pred'.con".
(* UNEXPORTED
Implicit Arguments nat_less_n_pred [n].
(* UNEXPORTED
Implicit Arguments nat_less_n_pred [n].
Next, we prove the usual results about sums of even and odd numbers:
*)
Next, we prove the usual results about sums of even and odd numbers:
*)
-inline cic:/CoRN/algebra/CLogic/even_plus_n_n.con.
+inline "cic:/CoRN/algebra/CLogic/even_plus_n_n.con".
-inline cic:/CoRN/algebra/CLogic/even_or_odd_plus.con.
+inline "cic:/CoRN/algebra/CLogic/even_or_odd_plus.con".
(*#* Finally, we prove that an arbitrary natural number can be written in some canonical way.
*)
(*#* Finally, we prove that an arbitrary natural number can be written in some canonical way.
*)
-inline cic:/CoRN/algebra/CLogic/even_or_odd_plus_gt.con.
+inline "cic:/CoRN/algebra/CLogic/even_or_odd_plus_gt.con".
(* UNEXPORTED
End Odd_and_Even.
(* UNEXPORTED
End Odd_and_Even.
definitions keeping conciseness.
*)
definitions keeping conciseness.
*)
-inline cic:/CoRN/algebra/CLogic/Clt_le_weak.con.
+inline "cic:/CoRN/algebra/CLogic/Clt_le_weak.con".
-inline cic:/CoRN/algebra/CLogic/lt_5.con.
+inline "cic:/CoRN/algebra/CLogic/lt_5.con".
-inline cic:/CoRN/algebra/CLogic/lt_8.con.
+inline "cic:/CoRN/algebra/CLogic/lt_8.con".
-inline cic:/CoRN/algebra/CLogic/pred_lt.con.
+inline "cic:/CoRN/algebra/CLogic/pred_lt.con".
-inline cic:/CoRN/algebra/CLogic/lt_10.con.
+inline "cic:/CoRN/algebra/CLogic/lt_10.con".
-inline cic:/CoRN/algebra/CLogic/lt_pred'.con.
+inline "cic:/CoRN/algebra/CLogic/lt_pred'.con".
-inline cic:/CoRN/algebra/CLogic/le_1.con.
+inline "cic:/CoRN/algebra/CLogic/le_1.con".
-inline cic:/CoRN/algebra/CLogic/le_2.con.
+inline "cic:/CoRN/algebra/CLogic/le_2.con".
-inline cic:/CoRN/algebra/CLogic/plus_eq_one_imp_eq_zero.con.
+inline "cic:/CoRN/algebra/CLogic/plus_eq_one_imp_eq_zero.con".
-inline cic:/CoRN/algebra/CLogic/not_not_lt.con.
+inline "cic:/CoRN/algebra/CLogic/not_not_lt.con".
-inline cic:/CoRN/algebra/CLogic/plus_pred_pred_plus.con.
+inline "cic:/CoRN/algebra/CLogic/plus_pred_pred_plus.con".
(*#* We now prove some properties of functions on the natural numbers.
(*#* We now prove some properties of functions on the natural numbers.
-inline cic:/CoRN/algebra/CLogic/h.var.
+inline "cic:/CoRN/algebra/CLogic/h.var".
(*#*
First we characterize monotonicity by a local condition: if [h(n) < h(n+1)]
(*#*
First we characterize monotonicity by a local condition: if [h(n) < h(n+1)]
holds for weak monotonicity.
*)
holds for weak monotonicity.
*)
-inline cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon.con.
+inline "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon.con".
-inline cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon_le.con.
+inline "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon_le.con".
(*#* A strictly increasing function is injective: *)
(*#* A strictly increasing function is injective: *)
-inline cic:/CoRN/algebra/CLogic/nat_mon_imp_inj.con.
+inline "cic:/CoRN/algebra/CLogic/nat_mon_imp_inj.con".
(*#* And (not completely trivial) a function that preserves [lt] also preserves [le]. *)
(*#* And (not completely trivial) a function that preserves [lt] also preserves [le]. *)
-inline cic:/CoRN/algebra/CLogic/nat_mon_imp_mon'.con.
+inline "cic:/CoRN/algebra/CLogic/nat_mon_imp_mon'.con".
(*#*
The last lemmas in this section state that a monotonous function in the
(*#*
The last lemmas in this section state that a monotonous function in the
These are useful for integration.
*)
These are useful for integration.
*)
-inline cic:/CoRN/algebra/CLogic/mon_fun_covers.con.
+inline "cic:/CoRN/algebra/CLogic/mon_fun_covers.con".
-inline cic:/CoRN/algebra/CLogic/weird_mon_covers.con.
+inline "cic:/CoRN/algebra/CLogic/weird_mon_covers.con".
(* UNEXPORTED
End Natural_Numbers.
(* UNEXPORTED
End Natural_Numbers.
Useful for the Fundamental Theorem of Algebra.
*)
Useful for the Fundamental Theorem of Algebra.
*)
-inline cic:/CoRN/algebra/CLogic/kseq_prop.con.
+inline "cic:/CoRN/algebra/CLogic/kseq_prop.con".
(* UNEXPORTED
Section Predicates_to_CProp.
(* UNEXPORTED
Section Predicates_to_CProp.
results for [CProp]-valued predicates:
*)
results for [CProp]-valued predicates:
*)
-inline cic:/CoRN/algebra/CLogic/even_induction.con.
+inline "cic:/CoRN/algebra/CLogic/even_induction.con".
-inline cic:/CoRN/algebra/CLogic/odd_induction.con.
+inline "cic:/CoRN/algebra/CLogic/odd_induction.con".
-inline cic:/CoRN/algebra/CLogic/four_induction.con.
+inline "cic:/CoRN/algebra/CLogic/four_induction.con".
-inline cic:/CoRN/algebra/CLogic/nat_complete_double_induction.con.
+inline "cic:/CoRN/algebra/CLogic/nat_complete_double_induction.con".
-inline cic:/CoRN/algebra/CLogic/odd_double_ind.con.
+inline "cic:/CoRN/algebra/CLogic/odd_double_ind.con".
(*#* For subsetoid predicates in the natural numbers we can eliminate
disjunction (and existential quantification) as follows.
*)
(*#* For subsetoid predicates in the natural numbers we can eliminate
disjunction (and existential quantification) as follows.
*)
-inline cic:/CoRN/algebra/CLogic/finite_or_elim.con.
+inline "cic:/CoRN/algebra/CLogic/finite_or_elim.con".
-inline cic:/CoRN/algebra/CLogic/str_finite_or_elim.con.
+inline "cic:/CoRN/algebra/CLogic/str_finite_or_elim.con".
(* UNEXPORTED
End Predicates_to_CProp.
(* UNEXPORTED
End Predicates_to_CProp.
-inline cic:/CoRN/algebra/CLogic/even_ind.con.
+inline "cic:/CoRN/algebra/CLogic/even_ind.con".
-inline cic:/CoRN/algebra/CLogic/odd_ind.con.
+inline "cic:/CoRN/algebra/CLogic/odd_ind.con".
-inline cic:/CoRN/algebra/CLogic/nat_complete_double_ind.con.
+inline "cic:/CoRN/algebra/CLogic/nat_complete_double_ind.con".
-inline cic:/CoRN/algebra/CLogic/four_ind.con.
+inline "cic:/CoRN/algebra/CLogic/four_ind.con".
(* UNEXPORTED
End Predicates_to_Prop.
(* UNEXPORTED
End Predicates_to_Prop.
-inline cic:/CoRN/algebra/CLogic/Zlts.con.
+inline "cic:/CoRN/algebra/CLogic/Zlts.con".
-inline cic:/CoRN/algebra/CLogic/toCProp_Zlt.con.
+inline "cic:/CoRN/algebra/CLogic/toCProp_Zlt.con".
-inline cic:/CoRN/algebra/CLogic/CZlt_to.con.
+inline "cic:/CoRN/algebra/CLogic/CZlt_to.con".
-inline cic:/CoRN/algebra/CLogic/Zsgn_1.con.
+inline "cic:/CoRN/algebra/CLogic/Zsgn_1.con".
-inline cic:/CoRN/algebra/CLogic/Zsgn_2.con.
+inline "cic:/CoRN/algebra/CLogic/Zsgn_2.con".
-inline cic:/CoRN/algebra/CLogic/Zsgn_3.con.
+inline "cic:/CoRN/algebra/CLogic/Zsgn_3.con".
(*#* The following have unusual names, in line with the series of lemmata in
fast_integers.v.
*)
(*#* The following have unusual names, in line with the series of lemmata in
fast_integers.v.
*)
-inline cic:/CoRN/algebra/CLogic/ZL4'.con.
+inline "cic:/CoRN/algebra/CLogic/ZL4'.con".
-inline cic:/CoRN/algebra/CLogic/ZL9.con.
+inline "cic:/CoRN/algebra/CLogic/ZL9.con".
-inline cic:/CoRN/algebra/CLogic/Zsgn_4.con.
+inline "cic:/CoRN/algebra/CLogic/Zsgn_4.con".
-inline cic:/CoRN/algebra/CLogic/Zsgn_5.con.
+inline "cic:/CoRN/algebra/CLogic/Zsgn_5.con".
-inline cic:/CoRN/algebra/CLogic/nat_nat_pos.con.
+inline "cic:/CoRN/algebra/CLogic/nat_nat_pos.con".
-inline cic:/CoRN/algebra/CLogic/S_predn.con.
+inline "cic:/CoRN/algebra/CLogic/S_predn.con".
-inline cic:/CoRN/algebra/CLogic/absolu_1.con.
+inline "cic:/CoRN/algebra/CLogic/absolu_1.con".
-inline cic:/CoRN/algebra/CLogic/absolu_2.con.
+inline "cic:/CoRN/algebra/CLogic/absolu_2.con".
-inline cic:/CoRN/algebra/CLogic/Zgt_mult_conv_absorb_l.con.
+inline "cic:/CoRN/algebra/CLogic/Zgt_mult_conv_absorb_l.con".
-inline cic:/CoRN/algebra/CLogic/Zgt_mult_reg_absorb_l.con.
+inline "cic:/CoRN/algebra/CLogic/Zgt_mult_reg_absorb_l.con".
-inline cic:/CoRN/algebra/CLogic/Zmult_Sm_Sn.con.
+inline "cic:/CoRN/algebra/CLogic/Zmult_Sm_Sn.con".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CMonoids".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CMonoids".
(* $Id: CMonoids.v,v 1.3 2004/04/07 15:07:57 lcf Exp $ *)
(*#* printing Zero %\ensuremath{\mathbf0}% #0# *)
(* $Id: CMonoids.v,v 1.3 2004/04/07 15:07:57 lcf Exp $ *)
(*#* printing Zero %\ensuremath{\mathbf0}% #0# *)
-(* INCLUDE
-CSemiGroups
-*)
+include "algebra/CSemiGroups.ma".
** Definition of monoids
*)
** Definition of monoids
*)
-inline cic:/CoRN/algebra/CMonoids/is_rht_unit.con.
+inline "cic:/CoRN/algebra/CMonoids/is_rht_unit.con".
-inline cic:/CoRN/algebra/CMonoids/is_lft_unit.con.
+inline "cic:/CoRN/algebra/CMonoids/is_lft_unit.con".
(* UNEXPORTED
Implicit Arguments is_lft_unit [S].
(* UNEXPORTED
Implicit Arguments is_lft_unit [S].
Implicit Arguments is_rht_unit [S].
*)
Implicit Arguments is_rht_unit [S].
*)
-inline cic:/CoRN/algebra/CMonoids/is_CMonoid.ind.
+inline "cic:/CoRN/algebra/CMonoids/is_CMonoid.ind".
+
+inline "cic:/CoRN/algebra/CMonoids/CMonoid.ind".
-inline cic:/CoRN/algebra/CMonoids/CMonoid.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/CMonoids/cm_crr.con" 0 (* compounds *).
(*#*
%\begin{nameconvention}%
(*#*
%\begin{nameconvention}%
e.g. for the setoid of non-zeros.
*)
e.g. for the setoid of non-zeros.
*)
-inline cic:/CoRN/algebra/CMonoids/nonZeroP.con.
+inline "cic:/CoRN/algebra/CMonoids/nonZeroP.con".
Section CMonoid_axioms.
*)
Section CMonoid_axioms.
*)
-inline cic:/CoRN/algebra/CMonoids/M.var.
+inline "cic:/CoRN/algebra/CMonoids/M.var".
-inline cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con.
+inline "cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con".
-inline cic:/CoRN/algebra/CMonoids/cm_rht_unit.con.
+inline "cic:/CoRN/algebra/CMonoids/cm_rht_unit.con".
-inline cic:/CoRN/algebra/CMonoids/cm_lft_unit.con.
+inline "cic:/CoRN/algebra/CMonoids/cm_lft_unit.con".
(* UNEXPORTED
End CMonoid_axioms.
(* UNEXPORTED
End CMonoid_axioms.
Section CMonoid_basics.
*)
Section CMonoid_basics.
*)
-inline cic:/CoRN/algebra/CMonoids/M.var.
+inline "cic:/CoRN/algebra/CMonoids/M.var".
-inline cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con.
+inline "cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con".
-inline cic:/CoRN/algebra/CMonoids/cm_lft_unit_unfolded.con.
+inline "cic:/CoRN/algebra/CMonoids/cm_lft_unit_unfolded.con".
(* UNEXPORTED
Hint Resolve cm_rht_unit_unfolded cm_lft_unit_unfolded: algebra.
*)
(* UNEXPORTED
Hint Resolve cm_rht_unit_unfolded cm_lft_unit_unfolded: algebra.
*)
-inline cic:/CoRN/algebra/CMonoids/cm_unit_unique_lft.con.
+inline "cic:/CoRN/algebra/CMonoids/cm_unit_unique_lft.con".
-inline cic:/CoRN/algebra/CMonoids/cm_unit_unique_rht.con.
+inline "cic:/CoRN/algebra/CMonoids/cm_unit_unique_rht.con".
The proof component of the monoid is irrelevant.
*)
The proof component of the monoid is irrelevant.
*)
-inline cic:/CoRN/algebra/CMonoids/is_CMonoid_proof_irr.con.
+inline "cic:/CoRN/algebra/CMonoids/is_CMonoid_proof_irr.con".
-inline cic:/CoRN/algebra/CMonoids/P.var.
+inline "cic:/CoRN/algebra/CMonoids/P.var".
-inline cic:/CoRN/algebra/CMonoids/Punit.var.
+inline "cic:/CoRN/algebra/CMonoids/Punit.var".
-inline cic:/CoRN/algebra/CMonoids/op_pres_P.var.
+inline "cic:/CoRN/algebra/CMonoids/op_pres_P.var".
-inline cic:/CoRN/algebra/CMonoids/subcrr.con.
+inline "cic:/CoRN/algebra/CMonoids/subcrr.con".
-inline cic:/CoRN/algebra/CMonoids/ismon_scrr.con.
+inline "cic:/CoRN/algebra/CMonoids/ismon_scrr.con".
-inline cic:/CoRN/algebra/CMonoids/Build_SubCMonoid.con.
+inline "cic:/CoRN/algebra/CMonoids/Build_SubCMonoid.con".
(* UNEXPORTED
End SubCMonoids.
(* UNEXPORTED
End SubCMonoids.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdAbs".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdAbs".
-(* INCLUDE
-COrdFields2
-*)
+include "CoRN.ma".
+
+include "algebra/COrdFields2.ma".
(*#*
** Properties of [AbsSmall]
(*#*
** Properties of [AbsSmall]
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall.con".
(* UNEXPORTED
Implicit Arguments AbsSmall [R].
(* UNEXPORTED
Implicit Arguments AbsSmall [R].
-inline cic:/CoRN/algebra/COrdAbs/R.var.
+inline "cic:/CoRN/algebra/COrdAbs/R.var".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr_unfolded.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr_unfolded.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl_unfolded.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl_unfolded.con".
(* UNEXPORTED
Declare Left Step AbsSmall_wdl_unfolded.
(* UNEXPORTED
Declare Left Step AbsSmall_wdl_unfolded.
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_leEq_trans.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_leEq_trans.con".
-inline cic:/CoRN/algebra/COrdAbs/zero_AbsSmall.con.
+inline "cic:/CoRN/algebra/COrdAbs/zero_AbsSmall.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_trans.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_trans.con".
-inline cic:/CoRN/algebra/COrdAbs/leEq_imp_AbsSmall.con.
+inline "cic:/CoRN/algebra/COrdAbs/leEq_imp_AbsSmall.con".
-inline cic:/CoRN/algebra/COrdAbs/inv_resp_AbsSmall.con.
+inline "cic:/CoRN/algebra/COrdAbs/inv_resp_AbsSmall.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_minus.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_minus.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_plus.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_plus.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div_two.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div_two.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_delta.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_delta.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_delta.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_delta.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_eps_div2.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_eps_div2.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_eps_div2.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_eps_div2.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_intermediate.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_intermediate.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div2.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div2.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_nonneg.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_nonneg.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_mult.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_mult.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_cancel_mult.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_cancel_mult.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con".
(* UNEXPORTED
End AbsSmall_properties.
(* UNEXPORTED
End AbsSmall_properties.
(*#* ** Properties of [AbsBig] *)
(*#* ** Properties of [AbsBig] *)
-inline cic:/CoRN/algebra/COrdAbs/absBig.con.
+inline "cic:/CoRN/algebra/COrdAbs/absBig.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con".
(* UNEXPORTED
Section absBig_wd_properties.
(* UNEXPORTED
Section absBig_wd_properties.
-inline cic:/CoRN/algebra/COrdAbs/R.var.
+inline "cic:/CoRN/algebra/COrdAbs/R.var".
-inline cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsBig_wdl.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsBig_wdr_unfolded.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr_unfolded.con".
-inline cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con.
+inline "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con".
(* UNEXPORTED
End absBig_wd_properties.
(* UNEXPORTED
End absBig_wd_properties.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdCauchy".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdCauchy".
+include "CoRN.ma".
+
+include "algebra/COrdAbs.ma".
-inline cic:/CoRN/algebra/COrdCauchy/R.var.
+inline "cic:/CoRN/algebra/COrdCauchy/R.var".
-inline cic:/CoRN/algebra/COrdCauchy/Cauchy_prop.con.
+inline "cic:/CoRN/algebra/COrdCauchy/Cauchy_prop.con".
-inline cic:/CoRN/algebra/COrdCauchy/CauchySeq.ind.
+inline "cic:/CoRN/algebra/COrdCauchy/CauchySeq.ind".
+
+coercion "cic:/matita/CoRN-Decl/algebra/COrdCauchy/CS_seq.con" 0 (* compounds *).
-inline cic:/CoRN/algebra/COrdCauchy/SeqLimit.con.
+inline "cic:/CoRN/algebra/COrdCauchy/SeqLimit.con".
-inline cic:/CoRN/algebra/COrdCauchy/CS_seq_bounded.con.
+inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_bounded.con".
-inline cic:/CoRN/algebra/COrdCauchy/CS_seq_const.con.
+inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_const.con".
(*#*
%\begin{convention}% Assume [f] and [g] are Cauchy sequences on [R].
%\end{convention}%
*)
(*#*
%\begin{convention}% Assume [f] and [g] are Cauchy sequences on [R].
%\end{convention}%
*)
-inline cic:/CoRN/algebra/COrdCauchy/f.var.
+inline "cic:/CoRN/algebra/COrdCauchy/f.var".
-inline cic:/CoRN/algebra/COrdCauchy/g.var.
+inline "cic:/CoRN/algebra/COrdCauchy/g.var".
-inline cic:/CoRN/algebra/COrdCauchy/Hf.var.
+inline "cic:/CoRN/algebra/COrdCauchy/Hf.var".
-inline cic:/CoRN/algebra/COrdCauchy/Hg.var.
+inline "cic:/CoRN/algebra/COrdCauchy/Hg.var".
-inline cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con.
+inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con".
-inline cic:/CoRN/algebra/COrdCauchy/CS_seq_inv.con.
+inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_inv.con".
-inline cic:/CoRN/algebra/COrdCauchy/CS_seq_mult.con.
+inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_mult.con".
(*#*
We now assume that [f] is, from some point onwards, greater than
(*#*
We now assume that [f] is, from some point onwards, greater than
-inline cic:/CoRN/algebra/COrdCauchy/e.var.
+inline "cic:/CoRN/algebra/COrdCauchy/e.var".
-inline cic:/CoRN/algebra/COrdCauchy/He.var.
+inline "cic:/CoRN/algebra/COrdCauchy/He.var".
-inline cic:/CoRN/algebra/COrdCauchy/N.var.
+inline "cic:/CoRN/algebra/COrdCauchy/N.var".
-inline cic:/CoRN/algebra/COrdCauchy/f_bnd.var.
+inline "cic:/CoRN/algebra/COrdCauchy/f_bnd.var".
-inline cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con.
+inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con".
-inline cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_seq.con.
+inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_seq.con".
-inline cic:/CoRN/algebra/COrdCauchy/CS_seq_recip.con.
+inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip.con".
(* UNEXPORTED
End OrdField_Cauchy.
(* UNEXPORTED
End OrdField_Cauchy.
-inline cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con.
+inline "cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con".
(* UNEXPORTED
Section Mult_AbsSmall.
*)
(* UNEXPORTED
Section Mult_AbsSmall.
*)
-inline cic:/CoRN/algebra/COrdCauchy/R.var.
+inline "cic:/CoRN/algebra/COrdCauchy/R.var".
(*#*
** [AbsSmall] revisited
(*#*
** [AbsSmall] revisited
-inline cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall'_rht.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall'_rht.con".
-inline cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_rht.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_rht.con".
-inline cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_lft.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_lft.con".
-inline cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall.con".
(* UNEXPORTED
End Mult_AbsSmall.
(* UNEXPORTED
End Mult_AbsSmall.
Section Mult_Continuous.
*)
Section Mult_Continuous.
*)
-inline cic:/CoRN/algebra/COrdCauchy/R.var.
+inline "cic:/CoRN/algebra/COrdCauchy/R.var".
(*#*
** Multiplication is continuous
(*#*
** Multiplication is continuous
-inline cic:/CoRN/algebra/COrdCauchy/smaller.con.
+inline "cic:/CoRN/algebra/COrdCauchy/smaller.con".
-inline cic:/CoRN/algebra/COrdCauchy/estimate_abs.con.
+inline "cic:/CoRN/algebra/COrdCauchy/estimate_abs.con".
-inline cic:/CoRN/algebra/COrdCauchy/mult_contin.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mult_contin.con".
(*#* Addition is also continuous. *)
(*#* Addition is also continuous. *)
-inline cic:/CoRN/algebra/COrdCauchy/plus_contin.con.
+inline "cic:/CoRN/algebra/COrdCauchy/plus_contin.con".
(* UNEXPORTED
End Mult_Continuous.
(* UNEXPORTED
End Mult_Continuous.
-inline cic:/CoRN/algebra/COrdCauchy/R.var.
+inline "cic:/CoRN/algebra/COrdCauchy/R.var".
(*#*
We begin by characterizing the preservation of less (less or equal)
in terms of preservation of less or equal (less).
*)
(*#*
We begin by characterizing the preservation of less (less or equal)
in terms of preservation of less or equal (less).
*)
-inline cic:/CoRN/algebra/COrdCauchy/resp_less_char'.con.
+inline "cic:/CoRN/algebra/COrdCauchy/resp_less_char'.con".
-inline cic:/CoRN/algebra/COrdCauchy/resp_less_char.con.
+inline "cic:/CoRN/algebra/COrdCauchy/resp_less_char.con".
-inline cic:/CoRN/algebra/COrdCauchy/resp_leEq_char'.con.
+inline "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char'.con".
-inline cic:/CoRN/algebra/COrdCauchy/resp_leEq_char.con.
+inline "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char.con".
(*#*
Next, we see different characterizations of monotonous functions from
(*#*
Next, we see different characterizations of monotonous functions from
Also, strictly monotonous functions are injective.
*)
Also, strictly monotonous functions are injective.
*)
-inline cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'.con".
-inline cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'.con".
-inline cic:/CoRN/algebra/COrdCauchy/mon_imp_inj.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_lt.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_lt.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_lt.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_lt.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_lt.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_lt.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_lt.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_lt.con".
-inline cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_lt.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_lt.con".
-inline cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_lt.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_lt.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_le.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_le.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_le.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_le.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_le.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_le.con".
-inline cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_le.con.
+inline "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_le.con".
-inline cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_le.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_le.con".
-inline cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_le.con.
+inline "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_le.con".
(*#*
A similar result for %{\em %partial%}% functions.
*)
(*#*
A similar result for %{\em %partial%}% functions.
*)
-inline cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con.
+inline "cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con".
(* UNEXPORTED
End Monotonous_functions.
(* UNEXPORTED
End Monotonous_functions.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdFields".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdFields".
(* $Id: COrdFields.v,v 1.6 2004/04/23 10:00:52 lcf Exp $ *)
(*#* printing [<] %\ensuremath<% #<# *)
(* $Id: COrdFields.v,v 1.6 2004/04/23 10:00:52 lcf Exp $ *)
(*#* printing [<] %\ensuremath<% #<# *)
(*#* printing FortyEightNZ %\ensuremath{\mathbf{48}}% #48# *)
(*#* printing FortyEightNZ %\ensuremath{\mathbf{48}}% #48# *)
-(* INCLUDE
-FieldReflection
-*)
+include "tactics/FieldReflection.ma".
-inline cic:/CoRN/algebra/COrdFields/strictorder.ind.
+inline "cic:/CoRN/algebra/COrdFields/strictorder.ind".
(* UNEXPORTED
Implicit Arguments strictorder [A].
(* UNEXPORTED
Implicit Arguments strictorder [A].
Implicit Arguments so_asym [A R].
*)
Implicit Arguments so_asym [A R].
*)
-inline cic:/CoRN/algebra/COrdFields/is_COrdField.ind.
+inline "cic:/CoRN/algebra/COrdFields/is_COrdField.ind".
+
+inline "cic:/CoRN/algebra/COrdFields/COrdField.ind".
-inline cic:/CoRN/algebra/COrdFields/COrdField.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/COrdFields/cof_crr.con" 0 (* compounds *).
(*#*
%\begin{nameconvention}%
(*#*
%\begin{nameconvention}%
Implicit Arguments cof_less [c].
*)
Implicit Arguments cof_less [c].
*)
-inline cic:/CoRN/algebra/COrdFields/greater.con.
+inline "cic:/CoRN/algebra/COrdFields/greater.con".
(* UNEXPORTED
Implicit Arguments greater [F].
(* UNEXPORTED
Implicit Arguments greater [F].
Less or equal is defined as ``not greater than''.
*)
Less or equal is defined as ``not greater than''.
*)
-inline cic:/CoRN/algebra/COrdFields/leEq.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq.con".
(*#*
%\begin{nameconvention}%
(*#*
%\begin{nameconvention}%
-inline cic:/CoRN/algebra/COrdFields/F.var.
+inline "cic:/CoRN/algebra/COrdFields/F.var".
-inline cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con.
+inline "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con".
-inline cic:/CoRN/algebra/COrdFields/less_strorder.con.
+inline "cic:/CoRN/algebra/COrdFields/less_strorder.con".
-inline cic:/CoRN/algebra/COrdFields/less_transitive_unfolded.con.
+inline "cic:/CoRN/algebra/COrdFields/less_transitive_unfolded.con".
-inline cic:/CoRN/algebra/COrdFields/less_antisymmetric_unfolded.con.
+inline "cic:/CoRN/algebra/COrdFields/less_antisymmetric_unfolded.con".
-inline cic:/CoRN/algebra/COrdFields/less_irreflexive.con.
+inline "cic:/CoRN/algebra/COrdFields/less_irreflexive.con".
-inline cic:/CoRN/algebra/COrdFields/less_irreflexive_unfolded.con.
+inline "cic:/CoRN/algebra/COrdFields/less_irreflexive_unfolded.con".
-inline cic:/CoRN/algebra/COrdFields/plus_resp_less_rht.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_resp_less_rht.con".
-inline cic:/CoRN/algebra/COrdFields/mult_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_resp_pos.con".
-inline cic:/CoRN/algebra/COrdFields/less_conf_ap.con.
+inline "cic:/CoRN/algebra/COrdFields/less_conf_ap.con".
-inline cic:/CoRN/algebra/COrdFields/less_wdr.con.
+inline "cic:/CoRN/algebra/COrdFields/less_wdr.con".
-inline cic:/CoRN/algebra/COrdFields/less_wdl.con.
+inline "cic:/CoRN/algebra/COrdFields/less_wdl.con".
(* UNEXPORTED
End COrdField_axioms.
(* UNEXPORTED
End COrdField_axioms.
-inline cic:/CoRN/algebra/COrdFields/R.var.
+inline "cic:/CoRN/algebra/COrdFields/R.var".
-inline cic:/CoRN/algebra/COrdFields/less_imp_ap.con.
+inline "cic:/CoRN/algebra/COrdFields/less_imp_ap.con".
-inline cic:/CoRN/algebra/COrdFields/Greater_imp_ap.con.
+inline "cic:/CoRN/algebra/COrdFields/Greater_imp_ap.con".
-inline cic:/CoRN/algebra/COrdFields/ap_imp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/ap_imp_less.con".
(*#*
Now properties which can be derived.
*)
(*#*
Now properties which can be derived.
*)
-inline cic:/CoRN/algebra/COrdFields/less_cotransitive.con.
+inline "cic:/CoRN/algebra/COrdFields/less_cotransitive.con".
-inline cic:/CoRN/algebra/COrdFields/less_cotransitive_unfolded.con.
+inline "cic:/CoRN/algebra/COrdFields/less_cotransitive_unfolded.con".
-inline cic:/CoRN/algebra/COrdFields/pos_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_ap_zero.con".
(* Main characterization of less *)
(* Main characterization of less *)
-inline cic:/CoRN/algebra/COrdFields/leEq_not_eq.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_not_eq.con".
(* UNEXPORTED
End OrdField_basics.
(* UNEXPORTED
End OrdField_basics.
(*#* ** Basic properties of [ [<=] ]
*)
(*#* ** Basic properties of [ [<=] ]
*)
-inline cic:/CoRN/algebra/COrdFields/R.var.
+inline "cic:/CoRN/algebra/COrdFields/R.var".
-inline cic:/CoRN/algebra/COrdFields/leEq_wdr.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_wdr.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_wdl.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_wdl.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_reflexive.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_reflexive.con".
(* UNEXPORTED
Declare Left Step leEq_wdl.
(* UNEXPORTED
Declare Left Step leEq_wdl.
Declare Right Step leEq_wdr.
*)
Declare Right Step leEq_wdr.
*)
-inline cic:/CoRN/algebra/COrdFields/eq_imp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields/eq_imp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_imp_eq.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_imp_eq.con".
-inline cic:/CoRN/algebra/COrdFields/lt_equiv_imp_eq.con.
+inline "cic:/CoRN/algebra/COrdFields/lt_equiv_imp_eq.con".
-inline cic:/CoRN/algebra/COrdFields/less_leEq_trans.con.
+inline "cic:/CoRN/algebra/COrdFields/less_leEq_trans.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_less_trans.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_less_trans.con".
-inline cic:/CoRN/algebra/COrdFields/leEq_transitive.con.
+inline "cic:/CoRN/algebra/COrdFields/leEq_transitive.con".
-inline cic:/CoRN/algebra/COrdFields/less_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields/less_leEq.con".
(* UNEXPORTED
End Basic_Properties_of_leEq.
(* UNEXPORTED
End Basic_Properties_of_leEq.
-inline cic:/CoRN/algebra/COrdFields/R.var.
+inline "cic:/CoRN/algebra/COrdFields/R.var".
-inline cic:/CoRN/algebra/COrdFields/pos_one.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_one.con".
-inline cic:/CoRN/algebra/COrdFields/nring_less_succ.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_less_succ.con".
-inline cic:/CoRN/algebra/COrdFields/nring_less.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_less.con".
-inline cic:/CoRN/algebra/COrdFields/nring_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_leEq.con".
-inline cic:/CoRN/algebra/COrdFields/nring_apart.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_apart.con".
-inline cic:/CoRN/algebra/COrdFields/nring_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/nring_ap_zero'.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_ap_zero'.con".
-inline cic:/CoRN/algebra/COrdFields/nring_ap_zero_imp.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_ap_zero_imp.con".
-inline cic:/CoRN/algebra/COrdFields/Snring.con.
+inline "cic:/CoRN/algebra/COrdFields/Snring.con".
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
-inline cic:/CoRN/algebra/COrdFields/pos_Snring.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_Snring.con".
-inline cic:/CoRN/algebra/COrdFields/nringS_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/nringS_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/nring_fac_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_fac_ap_zero.con".
-(* INCLUDE
-Opaque_algebra
-*)
+include "tactics/Opaque_algebra.ma".
(* UNEXPORTED
Section up_to_four.
(* UNEXPORTED
Section up_to_four.
%\end{nameconvention}%
*)
%\end{nameconvention}%
*)
-inline cic:/CoRN/algebra/COrdFields/less_plusOne.con.
+inline "cic:/CoRN/algebra/COrdFields/less_plusOne.con".
-inline cic:/CoRN/algebra/COrdFields/zero_lt_posplus1.con.
+inline "cic:/CoRN/algebra/COrdFields/zero_lt_posplus1.con".
-inline cic:/CoRN/algebra/COrdFields/plus_one_ext_less.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_one_ext_less.con".
-inline cic:/CoRN/algebra/COrdFields/one_less_two.con.
+inline "cic:/CoRN/algebra/COrdFields/one_less_two.con".
-inline cic:/CoRN/algebra/COrdFields/two_less_three.con.
+inline "cic:/CoRN/algebra/COrdFields/two_less_three.con".
-inline cic:/CoRN/algebra/COrdFields/three_less_four.con.
+inline "cic:/CoRN/algebra/COrdFields/three_less_four.con".
-inline cic:/CoRN/algebra/COrdFields/pos_two.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_two.con".
-inline cic:/CoRN/algebra/COrdFields/one_less_three.con.
+inline "cic:/CoRN/algebra/COrdFields/one_less_three.con".
-inline cic:/CoRN/algebra/COrdFields/two_less_four.con.
+inline "cic:/CoRN/algebra/COrdFields/two_less_four.con".
-inline cic:/CoRN/algebra/COrdFields/pos_three.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_three.con".
-inline cic:/CoRN/algebra/COrdFields/one_less_four.con.
+inline "cic:/CoRN/algebra/COrdFields/one_less_four.con".
-inline cic:/CoRN/algebra/COrdFields/pos_four.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_four.con".
-inline cic:/CoRN/algebra/COrdFields/two_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/two_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/three_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/three_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/four_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/four_ap_zero.con".
(* UNEXPORTED
End up_to_four.
(* UNEXPORTED
End up_to_four.
(*#* *** Properties of some other numbers *)
(*#* *** Properties of some other numbers *)
-inline cic:/CoRN/algebra/COrdFields/pos_six.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_six.con".
-inline cic:/CoRN/algebra/COrdFields/pos_eight.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_eight.con".
-inline cic:/CoRN/algebra/COrdFields/pos_nine.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_nine.con".
-inline cic:/CoRN/algebra/COrdFields/pos_twelve.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_twelve.con".
-inline cic:/CoRN/algebra/COrdFields/pos_sixteen.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_sixteen.con".
-inline cic:/CoRN/algebra/COrdFields/pos_eighteen.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_eighteen.con".
-inline cic:/CoRN/algebra/COrdFields/pos_twentyfour.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_twentyfour.con".
-inline cic:/CoRN/algebra/COrdFields/pos_fortyeight.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_fortyeight.con".
-inline cic:/CoRN/algebra/COrdFields/six_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/six_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/eight_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/eight_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/nine_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/nine_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/twelve_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/twelve_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/sixteen_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/sixteen_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/eighteen_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/eighteen_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/twentyfour_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/twentyfour_ap_zero.con".
-inline cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con.
+inline "cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con".
(* UNEXPORTED
End More_than_four.
(* UNEXPORTED
End More_than_four.
*** Consequences of infinity
*)
*** Consequences of infinity
*)
-inline cic:/CoRN/algebra/COrdFields/F.var.
+inline "cic:/CoRN/algebra/COrdFields/F.var".
-inline cic:/CoRN/algebra/COrdFields/square_eq.con.
+inline "cic:/CoRN/algebra/COrdFields/square_eq.con".
(*#*
Ordered fields have characteristic zero.
*)
(*#*
Ordered fields have characteristic zero.
*)
-inline cic:/CoRN/algebra/COrdFields/char0_OrdField.con.
+inline "cic:/CoRN/algebra/COrdFields/char0_OrdField.con".
(* UNEXPORTED
End consequences_of_infinity.
(* UNEXPORTED
End consequences_of_infinity.
** Properties of [[<]]
*)
** Properties of [[<]]
*)
-inline cic:/CoRN/algebra/COrdFields/R.var.
+inline "cic:/CoRN/algebra/COrdFields/R.var".
(*#*
We do not use a special predicate for positivity,
(*#*
We do not use a special predicate for positivity,
-inline cic:/CoRN/algebra/COrdFields/plus_resp_less_lft.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_resp_less_lft.con".
-inline cic:/CoRN/algebra/COrdFields/inv_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/inv_resp_less.con".
(* UNEXPORTED
Transparent cg_minus.
*)
(* UNEXPORTED
Transparent cg_minus.
*)
-inline cic:/CoRN/algebra/COrdFields/minus_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/minus_resp_less.con".
(* UNEXPORTED
Transparent cg_minus.
*)
(* UNEXPORTED
Transparent cg_minus.
*)
-inline cic:/CoRN/algebra/COrdFields/minus_resp_less_rht.con.
+inline "cic:/CoRN/algebra/COrdFields/minus_resp_less_rht.con".
-inline cic:/CoRN/algebra/COrdFields/plus_resp_less_both.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_resp_less_both.con".
(*#*
For versions of [plus_resp_less_both] where one [ [<] ] in the
(*#*
For versions of [plus_resp_less_both] where one [ [<] ] in the
-inline cic:/CoRN/algebra/COrdFields/plus_cancel_less.con.
+inline "cic:/CoRN/algebra/COrdFields/plus_cancel_less.con".
-inline cic:/CoRN/algebra/COrdFields/inv_cancel_less.con.
+inline "cic:/CoRN/algebra/COrdFields/inv_cancel_less.con".
Coq%(see the Coq shortcoming in Section~\ref{section:setoid-basics})%.
*)
Coq%(see the Coq shortcoming in Section~\ref{section:setoid-basics})%.
*)
-inline cic:/CoRN/algebra/COrdFields/shift_less_plus.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_plus.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_plus'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_plus'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_minus.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_minus.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_minus'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_minus'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_plus_less.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_plus_less.con".
-inline cic:/CoRN/algebra/COrdFields/shift_plus_less'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_plus_less'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_minus_less.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_minus_less.con".
-inline cic:/CoRN/algebra/COrdFields/shift_minus_less'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_minus_less'.con".
(*#*
Some special cases of laws for shifting.
*)
(*#*
Some special cases of laws for shifting.
*)
-inline cic:/CoRN/algebra/COrdFields/shift_zero_less_minus.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus.con".
-inline cic:/CoRN/algebra/COrdFields/shift_zero_less_minus'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus'.con".
-inline cic:/CoRN/algebra/COrdFields/qltone.con.
+inline "cic:/CoRN/algebra/COrdFields/qltone.con".
(* UNEXPORTED
End addition.
(* UNEXPORTED
End addition.
-inline cic:/CoRN/algebra/COrdFields/mult_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields/recip_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields/recip_resp_pos.con".
-inline cic:/CoRN/algebra/COrdFields/div_resp_less_rht.con.
+inline "cic:/CoRN/algebra/COrdFields/div_resp_less_rht.con".
-inline cic:/CoRN/algebra/COrdFields/div_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields/div_resp_pos.con".
-inline cic:/CoRN/algebra/COrdFields/mult_resp_less_lft.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_resp_less_lft.con".
-inline cic:/CoRN/algebra/COrdFields/mult_resp_less_both.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_resp_less_both.con".
-inline cic:/CoRN/algebra/COrdFields/recip_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/recip_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields/div_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/div_resp_less.con".
(*#* Cancellation laws
*)
(*#* Cancellation laws
*)
-inline cic:/CoRN/algebra/COrdFields/mult_cancel_less.con.
+inline "cic:/CoRN/algebra/COrdFields/mult_cancel_less.con".
-inline cic:/CoRN/algebra/COrdFields/shift_div_less.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_div_less.con".
-inline cic:/CoRN/algebra/COrdFields/shift_div_less'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_div_less'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_div.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_div.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_mult.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_mult.con".
-inline cic:/CoRN/algebra/COrdFields/shift_less_mult'.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_less_mult'.con".
-inline cic:/CoRN/algebra/COrdFields/shift_mult_less.con.
+inline "cic:/CoRN/algebra/COrdFields/shift_mult_less.con".
(*#* Other properties of multiplication and division
*)
(*#* Other properties of multiplication and division
*)
-inline cic:/CoRN/algebra/COrdFields/minusOne_less.con.
+inline "cic:/CoRN/algebra/COrdFields/minusOne_less.con".
-inline cic:/CoRN/algebra/COrdFields/swap_div.con.
+inline "cic:/CoRN/algebra/COrdFields/swap_div.con".
-inline cic:/CoRN/algebra/COrdFields/eps_div_less_eps.con.
+inline "cic:/CoRN/algebra/COrdFields/eps_div_less_eps.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_two.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_two.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_two'.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_two'.con".
(*
Apply mult_cancel_less with (Two::R).
(*
Apply mult_cancel_less with (Two::R).
-inline cic:/CoRN/algebra/COrdFields/pos_div_three.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_three.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_three'.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_three'.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_four.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_four.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_four'.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_four'.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_six.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_six.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_eight.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_eight.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_nine.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_nine.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_twelve.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_twelve.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_sixteen.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_sixteen.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_eighteen.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_eighteen.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_twentyfour.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_twentyfour.con".
-inline cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con".
(* UNEXPORTED
End multiplication.
(* UNEXPORTED
End multiplication.
*** Miscellaneous properties
*)
*** Miscellaneous properties
*)
-inline cic:/CoRN/algebra/COrdFields/nring_pos.con.
+inline "cic:/CoRN/algebra/COrdFields/nring_pos.con".
-inline cic:/CoRN/algebra/COrdFields/less_nring.con.
+inline "cic:/CoRN/algebra/COrdFields/less_nring.con".
-inline cic:/CoRN/algebra/COrdFields/pos_nring_fac.con.
+inline "cic:/CoRN/algebra/COrdFields/pos_nring_fac.con".
-inline cic:/CoRN/algebra/COrdFields/Smallest_less_Average.con.
+inline "cic:/CoRN/algebra/COrdFields/Smallest_less_Average.con".
-inline cic:/CoRN/algebra/COrdFields/Average_less_Greatest.con.
+inline "cic:/CoRN/algebra/COrdFields/Average_less_Greatest.con".
-inline cic:/CoRN/algebra/COrdFields/Sum_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/Sum_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields/Sumx_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields/Sumx_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields/positive_Sum_two.con.
+inline "cic:/CoRN/algebra/COrdFields/positive_Sum_two.con".
-inline cic:/CoRN/algebra/COrdFields/positive_Sumx.con.
+inline "cic:/CoRN/algebra/COrdFields/positive_Sumx.con".
-inline cic:/CoRN/algebra/COrdFields/negative_Sumx.con.
+inline "cic:/CoRN/algebra/COrdFields/negative_Sumx.con".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdFields2".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdFields2".
-(* INCLUDE
-COrdFields
-*)
+include "CoRN.ma".
+
+include "algebra/COrdFields.ma".
(*#* printing one_div_succ %\ensuremath{\frac1{\cdot+1}}% *)
(*#* printing one_div_succ %\ensuremath{\frac1{\cdot+1}}% *)
-inline cic:/CoRN/algebra/COrdFields2/R.var.
+inline "cic:/CoRN/algebra/COrdFields2/R.var".
(* UNEXPORTED
Section addition.
(* UNEXPORTED
Section addition.
*** Addition and subtraction%\label{section:leEq-plus-minus}%
*)
*** Addition and subtraction%\label{section:leEq-plus-minus}%
*)
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_lft.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_lft.con".
-inline cic:/CoRN/algebra/COrdFields2/minus_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/inv_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/inv_resp_leEq.con".
(* UNEXPORTED
Transparent cg_minus.
*)
(* UNEXPORTED
Transparent cg_minus.
*)
-inline cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_both.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_both.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_less_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_less_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_less.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_less.con".
-inline cic:/CoRN/algebra/COrdFields2/minus_resp_less_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/minus_resp_less_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_both.con.
+inline "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_both.con".
(*#* Cancellation properties
*)
(*#* Cancellation properties
*)
-inline cic:/CoRN/algebra/COrdFields2/plus_cancel_leEq_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_cancel_leEq_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/inv_cancel_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/inv_cancel_leEq.con".
(*#* Laws for shifting
*)
(*#* Laws for shifting
*)
-inline cic:/CoRN/algebra/COrdFields2/shift_plus_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_plus.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_plus_leEq'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_plus'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_lft.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_lft.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_minus_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_minus_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_minus.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_minus'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con".
(* UNEXPORTED
End addition.
(* UNEXPORTED
End addition.
Multiplication and division respect [[<=]]
*)
Multiplication and division respect [[<=]]
*)
-inline cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_lft.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_lft.con".
-inline cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_both.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_both.con".
-inline cic:/CoRN/algebra/COrdFields2/recip_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/recip_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/div_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/div_resp_leEq.con".
(* UNEXPORTED
Hint Resolve recip_resp_leEq: algebra.
(* UNEXPORTED
Hint Resolve recip_resp_leEq: algebra.
(*#* Cancellation properties
*)
(*#* Cancellation properties
*)
-inline cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con".
(*#* Laws for shifting
*)
(*#* Laws for shifting
*)
-inline cic:/CoRN/algebra/COrdFields2/shift_mult_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_mult_leEq'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_mult'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_mult'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_div_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_div_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_div_leEq'.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_div_leEq'.con".
-inline cic:/CoRN/algebra/COrdFields2/shift_leEq_div.con.
+inline "cic:/CoRN/algebra/COrdFields2/shift_leEq_div.con".
(* UNEXPORTED
Hint Resolve shift_leEq_div: algebra.
*)
(* UNEXPORTED
Hint Resolve shift_leEq_div: algebra.
*)
-inline cic:/CoRN/algebra/COrdFields2/eps_div_leEq_eps.con.
+inline "cic:/CoRN/algebra/COrdFields2/eps_div_leEq_eps.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_two.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_two.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_two'.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_two'.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_three.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_three.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_three'.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_three'.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_four.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_four.con".
-inline cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con.
+inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con".
(* UNEXPORTED
End multiplication.
(* UNEXPORTED
End multiplication.
*** Miscellaneous Properties
*)
*** Miscellaneous Properties
*)
-inline cic:/CoRN/algebra/COrdFields2/sqr_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/sqr_nonneg.con".
-inline cic:/CoRN/algebra/COrdFields2/nring_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/nring_nonneg.con".
-inline cic:/CoRN/algebra/COrdFields2/suc_leEq_dub.con.
+inline "cic:/CoRN/algebra/COrdFields2/suc_leEq_dub.con".
-inline cic:/CoRN/algebra/COrdFields2/leEq_nring.con.
+inline "cic:/CoRN/algebra/COrdFields2/leEq_nring.con".
-inline cic:/CoRN/algebra/COrdFields2/cc_abs_aid.con.
+inline "cic:/CoRN/algebra/COrdFields2/cc_abs_aid.con".
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
-inline cic:/CoRN/algebra/COrdFields2/nexp_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/nexp_resp_pos.con".
-(* INCLUDE
-Opaque_algebra
-*)
+include "tactics/Opaque_algebra.ma".
-inline cic:/CoRN/algebra/COrdFields2/mult_resp_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_resp_nonneg.con".
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
-inline cic:/CoRN/algebra/COrdFields2/nexp_resp_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/nexp_resp_nonneg.con".
-inline cic:/CoRN/algebra/COrdFields2/power_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/power_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/nexp_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields2/nexp_resp_less.con".
-inline cic:/CoRN/algebra/COrdFields2/power_cancel_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/power_cancel_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/power_cancel_less.con.
+inline "cic:/CoRN/algebra/COrdFields2/power_cancel_less.con".
-inline cic:/CoRN/algebra/COrdFields2/nat_less_bin_nexp.con.
+inline "cic:/CoRN/algebra/COrdFields2/nat_less_bin_nexp.con".
-inline cic:/CoRN/algebra/COrdFields2/Sum_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/Sum_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/Sumx_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/Sumx_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/Sum2_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/Sum2_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/approach_zero.con.
+inline "cic:/CoRN/algebra/COrdFields2/approach_zero.con".
-inline cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con.
+inline "cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con".
(* UNEXPORTED
End misc.
*)
(* UNEXPORTED
End misc.
*)
-inline cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con".
(* UNEXPORTED
End Properties_of_leEq.
(* UNEXPORTED
End Properties_of_leEq.
-inline cic:/CoRN/algebra/COrdFields2/R.var.
+inline "cic:/CoRN/algebra/COrdFields2/R.var".
(* begin hide *)
(* end hide *)
(* begin hide *)
(* end hide *)
-inline cic:/CoRN/algebra/COrdFields2/mult_pos_imp.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_pos_imp.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_pos_nonneg.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_pos_nonneg.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_nonneg_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_nonneg_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/pos_square.con.
+inline "cic:/CoRN/algebra/COrdFields2/pos_square.con".
-inline cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_rht.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_rht.con".
-inline cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_lft.con.
+inline "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_lft.con".
-inline cic:/CoRN/algebra/COrdFields2/pos_wd.con.
+inline "cic:/CoRN/algebra/COrdFields2/pos_wd.con".
-inline cic:/CoRN/algebra/COrdFields2/even_power_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/even_power_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/odd_power_cancel_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/odd_power_cancel_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/plus_resp_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/plus_resp_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/pos_nring_S.con.
+inline "cic:/CoRN/algebra/COrdFields2/pos_nring_S.con".
-inline cic:/CoRN/algebra/COrdFields2/square_eq_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/square_eq_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/square_eq_neg.con.
+inline "cic:/CoRN/algebra/COrdFields2/square_eq_neg.con".
(* UNEXPORTED
End PosP_properties.
(* UNEXPORTED
End PosP_properties.
-inline cic:/CoRN/algebra/COrdFields2/one_div_succ.con.
+inline "cic:/CoRN/algebra/COrdFields2/one_div_succ.con".
(* UNEXPORTED
Implicit Arguments one_div_succ [R].
(* UNEXPORTED
Implicit Arguments one_div_succ [R].
Section One_div_succ_properties.
*)
Section One_div_succ_properties.
*)
-inline cic:/CoRN/algebra/COrdFields2/R.var.
+inline "cic:/CoRN/algebra/COrdFields2/R.var".
-inline cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con.
+inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con".
-inline cic:/CoRN/algebra/COrdFields2/one_div_succ_pos.con.
+inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_pos.con".
-inline cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con.
+inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con".
(* UNEXPORTED
End One_div_succ_properties.
(* UNEXPORTED
End One_div_succ_properties.
** Properties of [Half]
*)
** Properties of [Half]
*)
-inline cic:/CoRN/algebra/COrdFields2/Half.con.
+inline "cic:/CoRN/algebra/COrdFields2/Half.con".
(* UNEXPORTED
Implicit Arguments Half [R].
(* UNEXPORTED
Implicit Arguments Half [R].
-inline cic:/CoRN/algebra/COrdFields2/R.var.
+inline "cic:/CoRN/algebra/COrdFields2/R.var".
-inline cic:/CoRN/algebra/COrdFields2/half_1.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_1.con".
(* UNEXPORTED
Hint Resolve half_1: algebra.
*)
(* UNEXPORTED
Hint Resolve half_1: algebra.
*)
-inline cic:/CoRN/algebra/COrdFields2/pos_half.con.
+inline "cic:/CoRN/algebra/COrdFields2/pos_half.con".
-inline cic:/CoRN/algebra/COrdFields2/half_1'.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_1'.con".
-inline cic:/CoRN/algebra/COrdFields2/half_2.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_2.con".
-inline cic:/CoRN/algebra/COrdFields2/half_lt1.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_lt1.con".
-inline cic:/CoRN/algebra/COrdFields2/half_3.con.
+inline "cic:/CoRN/algebra/COrdFields2/half_3.con".
(* UNEXPORTED
End Half_properties.
(* UNEXPORTED
End Half_properties.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_ApZero".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_ApZero".
(* $Id: CPoly_ApZero.v,v 1.3 2004/04/23 10:00:53 lcf Exp $ *)
(* $Id: CPoly_ApZero.v,v 1.3 2004/04/23 10:00:53 lcf Exp $ *)
-(* INCLUDE
-CPoly_Degree
-*)
+include "algebra/CPoly_Degree.ma".
-(* INCLUDE
-COrdFields2
-*)
+include "algebra/COrdFields2.ma".
(*#* * Polynomials apart from zero *)
(*#* * Polynomials apart from zero *)
-inline cic:/CoRN/algebra/CPoly_ApZero/distinct1.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/distinct1.con".
(* UNEXPORTED
Implicit Arguments distinct1 [A].
(* UNEXPORTED
Implicit Arguments distinct1 [A].
-inline cic:/CoRN/algebra/CPoly_ApZero/R.var.
+inline "cic:/CoRN/algebra/CPoly_ApZero/R.var".
-inline cic:/CoRN/algebra/CPoly_ApZero/a_.var.
+inline "cic:/CoRN/algebra/CPoly_ApZero/a_.var".
-inline cic:/CoRN/algebra/CPoly_ApZero/distinct_a_.var.
+inline "cic:/CoRN/algebra/CPoly_ApZero/distinct_a_.var".
-inline cic:/CoRN/algebra/CPoly_ApZero/f.var.
+inline "cic:/CoRN/algebra/CPoly_ApZero/f.var".
-inline cic:/CoRN/algebra/CPoly_ApZero/n.var.
+inline "cic:/CoRN/algebra/CPoly_ApZero/n.var".
-inline cic:/CoRN/algebra/CPoly_ApZero/degree_f.var.
+inline "cic:/CoRN/algebra/CPoly_ApZero/degree_f.var".
(* begin hide *)
(* end hide *)
(* begin hide *)
(* end hide *)
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_linear_shifted.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_shifted.con".
-(* INCLUDE
-Opaque_algebra
-*)
+include "tactics/Opaque_algebra.ma".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_linear_factor.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_factor.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/zero_poly.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/zero_poly.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/identical_poly.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/identical_poly.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_degree.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_degree.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_zero.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_zero.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_apzero.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_apzero.con".
(* UNEXPORTED
Hint Resolve poly_01_factor'_zero.
*)
(* UNEXPORTED
Hint Resolve poly_01_factor'_zero.
*)
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_degree.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_degree.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_zero.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_zero.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_one.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_one.con".
(* UNEXPORTED
Hint Resolve poly_01_factor_zero poly_01_factor_one: algebra.
*)
(* UNEXPORTED
Hint Resolve poly_01_factor_zero poly_01_factor_one: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree'.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree'.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_zero.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_zero.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_01_one.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_one.con".
(* UNEXPORTED
Hint Resolve poly_01_zero poly_01_one: algebra.
*)
(* UNEXPORTED
Hint Resolve poly_01_zero poly_01_one: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_representation''.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_representation''.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_representation'.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_representation'.con".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_representation.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_representation.con".
(* UNEXPORTED
Hint Resolve poly_representation: algebra.
*)
(* UNEXPORTED
Hint Resolve poly_representation: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con".
(* UNEXPORTED
End Poly_Representation.
(* UNEXPORTED
End Poly_Representation.
-inline cic:/CoRN/algebra/CPoly_ApZero/R.var.
+inline "cic:/CoRN/algebra/CPoly_ApZero/R.var".
-inline cic:/CoRN/algebra/CPoly_ApZero/H.var.
+inline "cic:/CoRN/algebra/CPoly_ApZero/H.var".
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_apzero.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_apzero.con".
(*#*
Also, in this situation polynomials are extensional functions.
*)
(*#*
Also, in this situation polynomials are extensional functions.
*)
-inline cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con".
(* UNEXPORTED
End Characteristic_zero.
(* UNEXPORTED
End Characteristic_zero.
Section Poly_ApZero_Interval.
*)
Section Poly_ApZero_Interval.
*)
-inline cic:/CoRN/algebra/CPoly_ApZero/R.var.
+inline "cic:/CoRN/algebra/CPoly_ApZero/R.var".
(* begin hide *)
(* end hide *)
(* begin hide *)
(* end hide *)
-inline cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con.
+inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con".
(* UNEXPORTED
End Poly_ApZero_Interval.
(* UNEXPORTED
End Poly_ApZero_Interval.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_Degree".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_Degree".
(* $Id: CPoly_Degree.v,v 1.5 2004/04/23 10:00:53 lcf Exp $ *)
(* $Id: CPoly_Degree.v,v 1.5 2004/04/23 10:00:53 lcf Exp $ *)
-(* INCLUDE
-CPoly_NthCoeff
-*)
+include "algebra/CPoly_NthCoeff.ma".
+include "algebra/CFields.ma".
(*#* *Degrees of Polynomials
** Degrees of polynomials over a ring
(*#* *Degrees of Polynomials
** Degrees of polynomials over a ring
-inline cic:/CoRN/algebra/CPoly_Degree/R.var.
+inline "cic:/CoRN/algebra/CPoly_Degree/R.var".
coefficient is [[#]Zero])!
*)
coefficient is [[#]Zero])!
*)
-inline cic:/CoRN/algebra/CPoly_Degree/lth_of_poly.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/lth_of_poly.con".
(*#*
When dealing with constructive polynomials, notably over the reals or
(*#*
When dealing with constructive polynomials, notably over the reals or
that the `degree is at most [j]'.
*)
that the `degree is at most [j]'.
*)
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic.con".
-inline cic:/CoRN/algebra/CPoly_Degree/odd_cpoly.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/odd_cpoly.con".
-inline cic:/CoRN/algebra/CPoly_Degree/even_cpoly.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/even_cpoly.con".
-inline cic:/CoRN/algebra/CPoly_Degree/regular.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/regular.con".
(* UNEXPORTED
End Degree_def.
(* UNEXPORTED
End Degree_def.
-inline cic:/CoRN/algebra/CPoly_Degree/R.var.
+inline "cic:/CoRN/algebra/CPoly_Degree/R.var".
(* begin hide *)
(* end hide *)
(* begin hide *)
(* end hide *)
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_wd.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_wd.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_wd.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_wd.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_wd.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_wd.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_imp_degree_le.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_imp_degree_le.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_c_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_c_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_c_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_c_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_c_one.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_c_one.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_x_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_x_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_x_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_x_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_x_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_x_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_mon.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_mon.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_inv.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_inv.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_plus.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_plus.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_minus.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_minus.con".
-inline cic:/CoRN/algebra/CPoly_Degree/Sum_degree_le.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/Sum_degree_le.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_inv.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_inv.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_plus_rht.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_plus_rht.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_minus_lft.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_minus_lft.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_plus.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_plus.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_minus.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_minus.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_mult.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_mult_aux.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_mult_aux.con".
(* UNEXPORTED
Hint Resolve degree_mult_aux: algebra.
*)
(* UNEXPORTED
Hint Resolve degree_mult_aux: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_Degree/monic_mult.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_mult.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_nexp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_nexp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_nexp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_nexp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/lt_i_lth_of_poly.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/lt_i_lth_of_poly.con".
-inline cic:/CoRN/algebra/CPoly_Degree/poly_degree_lth.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/poly_degree_lth.con".
-inline cic:/CoRN/algebra/CPoly_Degree/Cpoly_ex_degree.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/Cpoly_ex_degree.con".
-inline cic:/CoRN/algebra/CPoly_Degree/poly_as_sum''.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum''.con".
(* UNEXPORTED
Hint Resolve poly_as_sum'': algebra.
*)
(* UNEXPORTED
Hint Resolve poly_as_sum'': algebra.
*)
-inline cic:/CoRN/algebra/CPoly_Degree/poly_as_sum'.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum'.con".
-inline cic:/CoRN/algebra/CPoly_Degree/poly_as_sum.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_zero.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_zero.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_1_imp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_1_imp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_cpoly_linear.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_cpoly_linear.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_cpoly_linear.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_cpoly_linear.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_one.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_one.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con".
(* UNEXPORTED
End Degree_props.
(* UNEXPORTED
End Degree_props.
-inline cic:/CoRN/algebra/CPoly_Degree/F.var.
+inline "cic:/CoRN/algebra/CPoly_Degree/F.var".
(* begin hide *)
(* end hide *)
(* begin hide *)
(* end hide *)
-inline cic:/CoRN/algebra/CPoly_Degree/degree_mult.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_mult.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_nexp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_nexp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_mult_imp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult_imp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con".
(* UNEXPORTED
End degree_props_Field.
(* UNEXPORTED
End degree_props_Field.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_NthCoeff".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_NthCoeff".
(* $Id: CPoly_NthCoeff.v,v 1.6 2004/04/23 10:00:53 lcf Exp $ *)
(* $Id: CPoly_NthCoeff.v,v 1.6 2004/04/23 10:00:53 lcf Exp $ *)
-(* INCLUDE
-CPolynomials
-*)
+include "algebra/CPolynomials.ma".
(*#*
* Polynomials: Nth Coefficient
(*#*
* Polynomials: Nth Coefficient
-inline cic:/CoRN/algebra/CPoly_NthCoeff/R.var.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/R.var".
+ ... + an X^n#, the [Zero]-th coefficient is $a_0$#a0#, the first
is $a_1$#a1# etcetera. *)
+ ... + an X^n#, the [Zero]-th coefficient is $a_0$#a0#, the first
is $a_1$#a1# etcetera. *)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_strext.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_strext.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_wd.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_wd.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_fun.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_fun.con".
(*#*
%\begin{shortcoming}%
(*#*
%\begin{shortcoming}%
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nonConst.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nonConst.con".
(*#*
The following is probably NOT needed. These functions are
NOT extensional, that is, they are not CSetoid functions.
*)
(*#*
The following is probably NOT needed. These functions are
NOT extensional, that is, they are not CSetoid functions.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con".
(* The in_coeff predicate*)
(* The in_coeff predicate*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/in_coeff.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/in_coeff.con".
(*#*
The [cpoly_zero] case should be [c [=] Zero] in order to be extensional.
*)
(*#*
The [cpoly_zero] case should be [c [=] Zero] in order to be extensional.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con".
(* UNEXPORTED
End NthCoeff_def.
(* UNEXPORTED
End NthCoeff_def.
(*#* ** Properties of [nth_coeff] *)
(*#* ** Properties of [nth_coeff] *)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/R.var.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/R.var".
(* begin hide *)
(* end hide *)
(* begin hide *)
(* end hide *)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_zero.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_zero.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_lin.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_lin.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_lin.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_lin.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_c_.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_c_.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_x_mult.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_x_mult.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_x_mult.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_x_mult.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_mult_x_.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_mult_x_.con".
(* UNEXPORTED
Hint Resolve nth_coeff_zero coeff_O_lin coeff_Sm_lin coeff_O_c_
coeff_O_x_mult coeff_Sm_x_mult coeff_Sm_mult_x_: algebra.
*)
(* UNEXPORTED
Hint Resolve nth_coeff_zero coeff_O_lin coeff_Sm_lin coeff_O_c_
coeff_O_x_mult coeff_Sm_x_mult coeff_Sm_mult_x_: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ap_zero_imp.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ap_zero_imp.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_plus.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_plus.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv.con".
(* UNEXPORTED
Hint Resolve nth_coeff_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve nth_coeff_inv: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_c_mult_p.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_c_mult_p.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_p_mult_c_.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_p_mult_c_.con".
(* UNEXPORTED
Hint Resolve nth_coeff_c_mult_p nth_coeff_p_mult_c_ nth_coeff_plus: algebra.
*)
(* UNEXPORTED
Hint Resolve nth_coeff_c_mult_p nth_coeff_p_mult_c_ nth_coeff_plus: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_complicated.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_complicated.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/all_nth_coeff_eq_imp.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/all_nth_coeff_eq_imp.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/poly_at_zero.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/poly_at_zero.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv'.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv'.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_minus.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_minus.con".
(* UNEXPORTED
Hint Resolve nth_coeff_minus: algebra.
*)
(* UNEXPORTED
Hint Resolve nth_coeff_minus: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum0.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum0.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_eq.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_eq.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_neq.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_neq.con".
-inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con.
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con".
(* UNEXPORTED
End NthCoeff_props.
(* UNEXPORTED
End NthCoeff_props.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPolynomials".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPolynomials".
(* $Id: CPolynomials.v,v 1.9 2004/04/23 10:00:53 lcf Exp $ *)
(*#* printing _X_ %\ensuremath{x}% *)
(* $Id: CPolynomials.v,v 1.9 2004/04/23 10:00:53 lcf Exp $ *)
(*#* printing _X_ %\ensuremath{x}% *)
(*#* printing FX %\ensuremath{F[x]}% #F[x]# *)
(*#* printing FX %\ensuremath{F[x]}% #F[x]# *)
-(* INCLUDE
-RingReflection
-*)
+include "tactics/RingReflection.ma".
(*#* * Polynomials
The first section only proves the polynomials form a ring, and nothing more
(*#* * Polynomials
The first section only proves the polynomials form a ring, and nothing more
-inline cic:/CoRN/algebra/CPolynomials/CR.var.
+inline "cic:/CoRN/algebra/CPolynomials/CR.var".
(*#*
The intuition behind the type [cpoly] is the following
(*#*
The intuition behind the type [cpoly] is the following
-inline cic:/CoRN/algebra/CPolynomials/cpoly.ind.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly.ind".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_constant.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_constant.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_one.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_one.con".
(*#*
Some useful induction lemmas for doubly quantified propositions.
*)
(*#*
Some useful induction lemmas for doubly quantified propositions.
*)
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0.con".
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0.con".
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0'.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0'.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0'.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0'.con".
(*#* *** The polynomials form a setoid
*)
(*#* *** The polynomials form a setoid
*)
-inline cic:/CoRN/algebra/CPolynomials/cpoly_eq_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_eq_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_eq.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_eq.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_eq_p_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_eq_p_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_ap.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_ap.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_ap_p_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_ap_p_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/irreflexive_cpoly_ap.con.
+inline "cic:/CoRN/algebra/CPolynomials/irreflexive_cpoly_ap.con".
-inline cic:/CoRN/algebra/CPolynomials/symmetric_cpoly_ap.con.
+inline "cic:/CoRN/algebra/CPolynomials/symmetric_cpoly_ap.con".
-inline cic:/CoRN/algebra/CPolynomials/cotransitive_cpoly_ap.con.
+inline "cic:/CoRN/algebra/CPolynomials/cotransitive_cpoly_ap.con".
-inline cic:/CoRN/algebra/CPolynomials/tight_apart_cpoly_ap.con.
+inline "cic:/CoRN/algebra/CPolynomials/tight_apart_cpoly_ap.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_is_CSetoid.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_is_CSetoid.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_csetoid.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid.con".
(*#*
Now that we know that the polynomials form a setoid, we can use the
(*#*
Now that we know that the polynomials form a setoid, we can use the
in terms of these generators.
*)
in terms of these generators.
*)
-inline cic:/CoRN/algebra/CPolynomials/cpoly_zero_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_zero_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_linear_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_linear_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_ind_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_ind_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_ind_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_ind_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_zero_.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_zero_.con".
-inline cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_zero_eq_lin_.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_zero_eq_lin_.con".
-inline cic:/CoRN/algebra/CPolynomials/_cpoly_zero_eq_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_eq_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_lin_.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_lin_.con".
-inline cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero_.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero_.con".
-inline cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin_.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin_.con".
-inline cic:/CoRN/algebra/CPolynomials/_cpoly_zero_ap_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_ap_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin_.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin_.con".
-inline cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_linear_strext.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_linear_strext.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_linear_wd.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_linear_wd.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun.con".
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_double_comp_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_comp_ind.con".
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_triple_comp_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_triple_comp_ind.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_double_comp_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_comp_ind.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_triple_comp_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_triple_comp_ind.con".
(*#*
*** The polynomials form a semi-group and a monoid
*)
(*#*
*** The polynomials form a semi-group and a monoid
*)
-inline cic:/CoRN/algebra/CPolynomials/cpoly_plus.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_plus.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_plus_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_plus_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_zero_plus.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_zero_plus.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_plus_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_plus_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin_plus_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin_plus_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_plus_commutative.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_plus_commutative.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_plus_q_ap_q.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_plus_q_ap_q.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_p_plus_ap_p.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_p_plus_ap_p.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero_plus.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero_plus.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_strext.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_strext.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_wd.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_wd.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_plus_op.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_plus_associative.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_plus_associative.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_csemi_grp.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_csemi_grp.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_cm_proof.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_cm_proof.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_cmonoid.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_cmonoid.con".
(*#* *** The polynomials form a group
*)
(*#* *** The polynomials form a group
*)
-inline cic:/CoRN/algebra/CPolynomials/cpoly_inv.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_inv.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_inv_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_inv_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_inv_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_inv_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_inv_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_inv_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_strext.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_strext.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_wd.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_wd.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_inv_op.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_cg_proof.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_cg_proof.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_cgroup.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_cgroup.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_cag_proof.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_cag_proof.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_cabgroup.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_cabgroup.con".
(*#* *** The polynomials form a ring
*)
(*#* *** The polynomials form a ring
*)
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult_cr.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult_cr.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult_cr.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult_cr.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_strext.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_strext.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_wd.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_wd.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cs.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cs.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_strext.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_strext.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_wd.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_wd.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_op.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_dist.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_dist.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_cr_dist.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_cr_dist.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult_cr.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult_cr.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_commutative.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_commutative.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_dist_rht.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_dist_rht.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_assoc.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_assoc.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_one.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_one.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_one_mult.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_one_mult.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_one.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_one.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_mult_monoid.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_mult_monoid.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_cr_non_triv.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_cr_non_triv.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_is_CRing.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_is_CRing.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_cring.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_cring.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_constant_strext.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_constant_strext.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_constant_wd.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_constant_wd.con".
-inline cic:/CoRN/algebra/CPolynomials/_C_.con.
+inline "cic:/CoRN/algebra/CPolynomials/_C_.con".
-inline cic:/CoRN/algebra/CPolynomials/_X_.con.
+inline "cic:/CoRN/algebra/CPolynomials/_X_.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_strext.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_strext.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_wd.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_wd.con".
(* UNEXPORTED
End CPoly_CRing.
(* UNEXPORTED
End CPoly_CRing.
Implicit Arguments _X_ [CR].
*)
Implicit Arguments _X_ [CR].
*)
-inline cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun'.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun'.con".
(* UNEXPORTED
Implicit Arguments cpoly_linear_fun' [CR].
(* UNEXPORTED
Implicit Arguments cpoly_linear_fun' [CR].
-inline cic:/CoRN/algebra/CPolynomials/CR.var.
+inline "cic:/CoRN/algebra/CPolynomials/CR.var".
(* UNEXPORTED
Section helpful_section.
*)
(* UNEXPORTED
Section helpful_section.
*)
-inline cic:/CoRN/algebra/CPolynomials/p.var.
+inline "cic:/CoRN/algebra/CPolynomials/p.var".
-inline cic:/CoRN/algebra/CPolynomials/q.var.
+inline "cic:/CoRN/algebra/CPolynomials/q.var".
-inline cic:/CoRN/algebra/CPolynomials/c.var.
+inline "cic:/CoRN/algebra/CPolynomials/c.var".
-inline cic:/CoRN/algebra/CPolynomials/d.var.
+inline "cic:/CoRN/algebra/CPolynomials/d.var".
-inline cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con.
+inline "cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con".
-inline cic:/CoRN/algebra/CPolynomials/_linear_eq_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/_linear_eq_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/zero_eq_linear_.con.
+inline "cic:/CoRN/algebra/CPolynomials/zero_eq_linear_.con".
-inline cic:/CoRN/algebra/CPolynomials/_zero_eq_linear.con.
+inline "cic:/CoRN/algebra/CPolynomials/_zero_eq_linear.con".
-inline cic:/CoRN/algebra/CPolynomials/linear_eq_linear_.con.
+inline "cic:/CoRN/algebra/CPolynomials/linear_eq_linear_.con".
-inline cic:/CoRN/algebra/CPolynomials/_linear_eq_linear.con.
+inline "cic:/CoRN/algebra/CPolynomials/_linear_eq_linear.con".
-inline cic:/CoRN/algebra/CPolynomials/linear_ap_zero_.con.
+inline "cic:/CoRN/algebra/CPolynomials/linear_ap_zero_.con".
-inline cic:/CoRN/algebra/CPolynomials/_linear_ap_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/_linear_ap_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/linear_ap_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/linear_ap_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/zero_ap_linear_.con.
+inline "cic:/CoRN/algebra/CPolynomials/zero_ap_linear_.con".
-inline cic:/CoRN/algebra/CPolynomials/_zero_ap_linear.con.
+inline "cic:/CoRN/algebra/CPolynomials/_zero_ap_linear.con".
-inline cic:/CoRN/algebra/CPolynomials/zero_ap_linear.con.
+inline "cic:/CoRN/algebra/CPolynomials/zero_ap_linear.con".
-inline cic:/CoRN/algebra/CPolynomials/linear_ap_linear_.con.
+inline "cic:/CoRN/algebra/CPolynomials/linear_ap_linear_.con".
-inline cic:/CoRN/algebra/CPolynomials/_linear_ap_linear.con.
+inline "cic:/CoRN/algebra/CPolynomials/_linear_ap_linear.con".
-inline cic:/CoRN/algebra/CPolynomials/linear_ap_linear.con.
+inline "cic:/CoRN/algebra/CPolynomials/linear_ap_linear.con".
(* UNEXPORTED
End helpful_section.
*)
(* UNEXPORTED
End helpful_section.
*)
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_induc.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_induc.con".
-inline cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind.con".
-inline cic:/CoRN/algebra/CPolynomials/Cpoly_double_comp_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/Cpoly_double_comp_ind.con".
-inline cic:/CoRN/algebra/CPolynomials/Cpoly_triple_comp_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/Cpoly_triple_comp_ind.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_induc.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_induc.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind.con".
-inline cic:/CoRN/algebra/CPolynomials/poly_double_comp_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/poly_double_comp_ind.con".
-inline cic:/CoRN/algebra/CPolynomials/poly_triple_comp_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/poly_triple_comp_ind.con".
(* UNEXPORTED
Transparent cpoly_cring.
(* UNEXPORTED
Transparent cpoly_cring.
Transparent cpoly_csetoid.
*)
Transparent cpoly_csetoid.
*)
-inline cic:/CoRN/algebra/CPolynomials/cpoly_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_apply.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_apply_strext.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_apply_strext.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_apply_wd.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_apply_wd.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_apply_fun.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_apply_fun.con".
(* UNEXPORTED
End CPoly_CRing_ctd.
(* UNEXPORTED
End CPoly_CRing_ctd.
Section Poly_properties.
*)
Section Poly_properties.
*)
-inline cic:/CoRN/algebra/CPolynomials/R.var.
+inline "cic:/CoRN/algebra/CPolynomials/R.var".
(*#*
*** Constant and identity
*)
(*#*
*** Constant and identity
*)
-inline cic:/CoRN/algebra/CPolynomials/cpoly_X_.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_X_.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_C_.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_C_.con".
(* UNEXPORTED
Hint Resolve cpoly_X_ cpoly_C_: algebra.
*)
(* UNEXPORTED
Hint Resolve cpoly_X_ cpoly_C_: algebra.
*)
-inline cic:/CoRN/algebra/CPolynomials/cpoly_const_eq.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_const_eq.con".
-inline cic:/CoRN/algebra/CPolynomials/_c_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/_c_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/_c_one.con.
+inline "cic:/CoRN/algebra/CPolynomials/_c_one.con".
-inline cic:/CoRN/algebra/CPolynomials/_c_mult.con.
+inline "cic:/CoRN/algebra/CPolynomials/_c_mult.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_lin.con".
(* UNEXPORTED
Hint Resolve cpoly_lin: algebra.
(* UNEXPORTED
Hint Resolve cpoly_lin: algebra.
-inline cic:/CoRN/algebra/CPolynomials/poly_linear.con.
+inline "cic:/CoRN/algebra/CPolynomials/poly_linear.con".
(* UNEXPORTED
Hint Resolve _c_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve _c_zero: algebra.
*)
-inline cic:/CoRN/algebra/CPolynomials/poly_c_apzero.con.
+inline "cic:/CoRN/algebra/CPolynomials/poly_c_apzero.con".
-inline cic:/CoRN/algebra/CPolynomials/_c_mult_lin.con.
+inline "cic:/CoRN/algebra/CPolynomials/_c_mult_lin.con".
-inline cic:/CoRN/algebra/CPolynomials/lin_mult.con.
+inline "cic:/CoRN/algebra/CPolynomials/lin_mult.con".
(* UNEXPORTED
Hint Resolve lin_mult: algebra.
(* UNEXPORTED
Hint Resolve lin_mult: algebra.
(*#* *** Application of polynomials
*)
(*#* *** Application of polynomials
*)
-inline cic:/CoRN/algebra/CPolynomials/poly_eq_zero.con.
+inline "cic:/CoRN/algebra/CPolynomials/poly_eq_zero.con".
-inline cic:/CoRN/algebra/CPolynomials/apply_wd.con.
+inline "cic:/CoRN/algebra/CPolynomials/apply_wd.con".
-inline cic:/CoRN/algebra/CPolynomials/cpolyap_pres_eq.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpolyap_pres_eq.con".
-inline cic:/CoRN/algebra/CPolynomials/cpolyap_strext.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpolyap_strext.con".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_csetoid_op.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid_op.con".
-inline cic:/CoRN/algebra/CPolynomials/_c_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/_c_apply.con".
-inline cic:/CoRN/algebra/CPolynomials/_x_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/_x_apply.con".
-inline cic:/CoRN/algebra/CPolynomials/plus_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/plus_apply.con".
-inline cic:/CoRN/algebra/CPolynomials/inv_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/inv_apply.con".
(* UNEXPORTED
Hint Resolve plus_apply inv_apply: algebra.
*)
(* UNEXPORTED
Hint Resolve plus_apply inv_apply: algebra.
*)
-inline cic:/CoRN/algebra/CPolynomials/minus_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/minus_apply.con".
-inline cic:/CoRN/algebra/CPolynomials/_c_mult_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/_c_mult_apply.con".
(* UNEXPORTED
Hint Resolve _c_mult_apply: algebra.
*)
(* UNEXPORTED
Hint Resolve _c_mult_apply: algebra.
*)
-inline cic:/CoRN/algebra/CPolynomials/mult_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/mult_apply.con".
(* UNEXPORTED
Hint Resolve mult_apply: algebra.
*)
(* UNEXPORTED
Hint Resolve mult_apply: algebra.
*)
-inline cic:/CoRN/algebra/CPolynomials/one_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/one_apply.con".
(* UNEXPORTED
Hint Resolve one_apply: algebra.
*)
(* UNEXPORTED
Hint Resolve one_apply: algebra.
*)
-inline cic:/CoRN/algebra/CPolynomials/nexp_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/nexp_apply.con".
-inline cic:/CoRN/algebra/CPolynomials/poly_inv_apply.con.
+inline "cic:/CoRN/algebra/CPolynomials/poly_inv_apply.con".
-inline cic:/CoRN/algebra/CPolynomials/Sum0_cpoly_ap.con.
+inline "cic:/CoRN/algebra/CPolynomials/Sum0_cpoly_ap.con".
-inline cic:/CoRN/algebra/CPolynomials/Sum_cpoly_ap.con.
+inline "cic:/CoRN/algebra/CPolynomials/Sum_cpoly_ap.con".
(* UNEXPORTED
End Poly_properties.
(* UNEXPORTED
End Poly_properties.
Section Poly_Prop_Induction.
*)
Section Poly_Prop_Induction.
*)
-inline cic:/CoRN/algebra/CPolynomials/CR.var.
+inline "cic:/CoRN/algebra/CPolynomials/CR.var".
-inline cic:/CoRN/algebra/CPolynomials/cpoly_double_ind.con.
+inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind.con".
(* UNEXPORTED
End Poly_Prop_Induction.
(* UNEXPORTED
End Poly_Prop_Induction.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CRings".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CRings".
(* $Id: CRings.v,v 1.8 2004/04/23 10:00:53 lcf Exp $ *)
(*#* printing [*] %\ensuremath\times% #×# *)
(* $Id: CRings.v,v 1.8 2004/04/23 10:00:53 lcf Exp $ *)
(*#* printing [*] %\ensuremath\times% #×# *)
(*#* printing FortyEight %\ensuremath{\mathbf{48}}% #48# *)
(*#* printing FortyEight %\ensuremath{\mathbf{48}}% #48# *)
+include "algebra/CSums.ma".
(* UNEXPORTED
Transparent sym_eq.
(* UNEXPORTED
Transparent sym_eq.
** Definition of the notion of Ring
*)
** Definition of the notion of Ring
*)
-inline cic:/CoRN/algebra/CRings/distributive.con.
+inline "cic:/CoRN/algebra/CRings/distributive.con".
(* UNEXPORTED
Implicit Arguments distributive [S].
*)
(* UNEXPORTED
Implicit Arguments distributive [S].
*)
-inline cic:/CoRN/algebra/CRings/is_CRing.ind.
+inline "cic:/CoRN/algebra/CRings/is_CRing.ind".
+
+inline "cic:/CoRN/algebra/CRings/CRing.ind".
-inline cic:/CoRN/algebra/CRings/CRing.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/CRings/cr_crr.con" 0 (* compounds *).
-inline cic:/CoRN/algebra/CRings/cr_plus.con.
+inline "cic:/CoRN/algebra/CRings/cr_plus.con".
-inline cic:/CoRN/algebra/CRings/cr_inv.con.
+inline "cic:/CoRN/algebra/CRings/cr_inv.con".
-inline cic:/CoRN/algebra/CRings/cr_minus.con.
+inline "cic:/CoRN/algebra/CRings/cr_minus.con".
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
-inline cic:/CoRN/algebra/CRings/CRing_is_CRing.con.
+inline "cic:/CoRN/algebra/CRings/CRing_is_CRing.con".
-inline cic:/CoRN/algebra/CRings/mult_assoc.con.
+inline "cic:/CoRN/algebra/CRings/mult_assoc.con".
-inline cic:/CoRN/algebra/CRings/mult_commutes.con.
+inline "cic:/CoRN/algebra/CRings/mult_commutes.con".
-inline cic:/CoRN/algebra/CRings/mult_mon.con.
+inline "cic:/CoRN/algebra/CRings/mult_mon.con".
-inline cic:/CoRN/algebra/CRings/dist.con.
+inline "cic:/CoRN/algebra/CRings/dist.con".
-inline cic:/CoRN/algebra/CRings/ring_non_triv.con.
+inline "cic:/CoRN/algebra/CRings/ring_non_triv.con".
-inline cic:/CoRN/algebra/CRings/mult_wd.con.
+inline "cic:/CoRN/algebra/CRings/mult_wd.con".
-inline cic:/CoRN/algebra/CRings/mult_wdl.con.
+inline "cic:/CoRN/algebra/CRings/mult_wdl.con".
-inline cic:/CoRN/algebra/CRings/mult_wdr.con.
+inline "cic:/CoRN/algebra/CRings/mult_wdr.con".
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
(*#*
The multiplicative monoid of a ring is defined as follows.
*)
(*#*
The multiplicative monoid of a ring is defined as follows.
*)
-inline cic:/CoRN/algebra/CRings/Build_multCMonoid.con.
+inline "cic:/CoRN/algebra/CRings/Build_multCMonoid.con".
(* UNEXPORTED
End Ring_constructions.
(* UNEXPORTED
End Ring_constructions.
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
-inline cic:/CoRN/algebra/CRings/mmR.con.
+inline "cic:/CoRN/algebra/CRings/mmR.con".
-inline cic:/CoRN/algebra/CRings/mult_assoc_unfolded.con.
+inline "cic:/CoRN/algebra/CRings/mult_assoc_unfolded.con".
-inline cic:/CoRN/algebra/CRings/mult_commut_unfolded.con.
+inline "cic:/CoRN/algebra/CRings/mult_commut_unfolded.con".
(* UNEXPORTED
Hint Resolve mult_commut_unfolded: algebra.
*)
(* UNEXPORTED
Hint Resolve mult_commut_unfolded: algebra.
*)
-inline cic:/CoRN/algebra/CRings/mult_one.con.
+inline "cic:/CoRN/algebra/CRings/mult_one.con".
-inline cic:/CoRN/algebra/CRings/one_mult.con.
+inline "cic:/CoRN/algebra/CRings/one_mult.con".
-inline cic:/CoRN/algebra/CRings/ring_dist_unfolded.con.
+inline "cic:/CoRN/algebra/CRings/ring_dist_unfolded.con".
(* UNEXPORTED
Hint Resolve ring_dist_unfolded: algebra.
*)
(* UNEXPORTED
Hint Resolve ring_dist_unfolded: algebra.
*)
-inline cic:/CoRN/algebra/CRings/ring_distl_unfolded.con.
+inline "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con".
(* UNEXPORTED
End Ring_unfolded.
(* UNEXPORTED
End Ring_unfolded.
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
-inline cic:/CoRN/algebra/CRings/one_ap_zero.con.
+inline "cic:/CoRN/algebra/CRings/one_ap_zero.con".
-inline cic:/CoRN/algebra/CRings/is_zero_rht.con.
+inline "cic:/CoRN/algebra/CRings/is_zero_rht.con".
-inline cic:/CoRN/algebra/CRings/is_zero_lft.con.
+inline "cic:/CoRN/algebra/CRings/is_zero_lft.con".
(* UNEXPORTED
Implicit Arguments is_zero_rht [S].
(* UNEXPORTED
Implicit Arguments is_zero_rht [S].
Implicit Arguments is_zero_lft [S].
*)
Implicit Arguments is_zero_lft [S].
*)
-inline cic:/CoRN/algebra/CRings/cring_mult_zero.con.
+inline "cic:/CoRN/algebra/CRings/cring_mult_zero.con".
(* UNEXPORTED
Hint Resolve cring_mult_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve cring_mult_zero: algebra.
*)
-inline cic:/CoRN/algebra/CRings/x_mult_zero.con.
+inline "cic:/CoRN/algebra/CRings/x_mult_zero.con".
-inline cic:/CoRN/algebra/CRings/cring_mult_zero_op.con.
+inline "cic:/CoRN/algebra/CRings/cring_mult_zero_op.con".
(* UNEXPORTED
Hint Resolve cring_mult_zero_op: algebra.
*)
(* UNEXPORTED
Hint Resolve cring_mult_zero_op: algebra.
*)
-inline cic:/CoRN/algebra/CRings/cring_inv_mult_lft.con.
+inline "cic:/CoRN/algebra/CRings/cring_inv_mult_lft.con".
(* UNEXPORTED
Hint Resolve cring_inv_mult_lft: algebra.
*)
(* UNEXPORTED
Hint Resolve cring_inv_mult_lft: algebra.
*)
-inline cic:/CoRN/algebra/CRings/cring_inv_mult_rht.con.
+inline "cic:/CoRN/algebra/CRings/cring_inv_mult_rht.con".
(* UNEXPORTED
Hint Resolve cring_inv_mult_rht: algebra.
*)
(* UNEXPORTED
Hint Resolve cring_inv_mult_rht: algebra.
*)
-inline cic:/CoRN/algebra/CRings/cring_mult_ap_zero.con.
+inline "cic:/CoRN/algebra/CRings/cring_mult_ap_zero.con".
-inline cic:/CoRN/algebra/CRings/cring_mult_ap_zero_op.con.
+inline "cic:/CoRN/algebra/CRings/cring_mult_ap_zero_op.con".
-inline cic:/CoRN/algebra/CRings/inv_mult_invol.con.
+inline "cic:/CoRN/algebra/CRings/inv_mult_invol.con".
-inline cic:/CoRN/algebra/CRings/ring_dist_minus.con.
+inline "cic:/CoRN/algebra/CRings/ring_dist_minus.con".
(* UNEXPORTED
Hint Resolve ring_dist_minus: algebra.
*)
(* UNEXPORTED
Hint Resolve ring_dist_minus: algebra.
*)
-inline cic:/CoRN/algebra/CRings/ring_distl_minus.con.
+inline "cic:/CoRN/algebra/CRings/ring_distl_minus.con".
(* UNEXPORTED
Hint Resolve ring_distl_minus: algebra.
(* UNEXPORTED
Hint Resolve ring_distl_minus: algebra.
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
-inline cic:/CoRN/algebra/CRings/nexp.con.
+inline "cic:/CoRN/algebra/CRings/nexp.con".
-inline cic:/CoRN/algebra/CRings/nexp_well_def.con.
+inline "cic:/CoRN/algebra/CRings/nexp_well_def.con".
-inline cic:/CoRN/algebra/CRings/nexp_strong_ext.con.
+inline "cic:/CoRN/algebra/CRings/nexp_strong_ext.con".
-inline cic:/CoRN/algebra/CRings/nexp_op.con.
+inline "cic:/CoRN/algebra/CRings/nexp_op.con".
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
(*#*
The injection of Coq natural numbers into a ring is called [nring].
(*#*
The injection of Coq natural numbers into a ring is called [nring].
to have characteristic [0].
*)
to have characteristic [0].
*)
-inline cic:/CoRN/algebra/CRings/nring.con.
+inline "cic:/CoRN/algebra/CRings/nring.con".
-inline cic:/CoRN/algebra/CRings/Char0.con.
+inline "cic:/CoRN/algebra/CRings/Char0.con".
-inline cic:/CoRN/algebra/CRings/nring_comm_plus.con.
+inline "cic:/CoRN/algebra/CRings/nring_comm_plus.con".
-inline cic:/CoRN/algebra/CRings/nring_comm_mult.con.
+inline "cic:/CoRN/algebra/CRings/nring_comm_mult.con".
-inline cic:/CoRN/algebra/CRings/one_plus_one.con.
+inline "cic:/CoRN/algebra/CRings/one_plus_one.con".
-inline cic:/CoRN/algebra/CRings/x_plus_x.con.
+inline "cic:/CoRN/algebra/CRings/x_plus_x.con".
(* UNEXPORTED
Hint Resolve one_plus_one x_plus_x: algebra.
(* UNEXPORTED
Hint Resolve one_plus_one x_plus_x: algebra.
In a ring of characteristic zero, [nring] is really an injection.
*)
In a ring of characteristic zero, [nring] is really an injection.
*)
-inline cic:/CoRN/algebra/CRings/nring_different.con.
+inline "cic:/CoRN/algebra/CRings/nring_different.con".
(* UNEXPORTED
Section int_injection.
(* UNEXPORTED
Section int_injection.
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
(*#*
The injection of Coq integers into a ring is called [zring]. Again,
(*#*
The injection of Coq integers into a ring is called [zring]. Again,
one. It is kept to avoid having to redo all the proofs.
*)
one. It is kept to avoid having to redo all the proofs.
*)
-inline cic:/CoRN/algebra/CRings/zring_old.con.
+inline "cic:/CoRN/algebra/CRings/zring_old.con".
-inline cic:/CoRN/algebra/CRings/zring_old_zero.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_zero.con".
(* UNEXPORTED
Hint Resolve zring_old_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve zring_old_zero: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_old_diff.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_diff.con".
(* UNEXPORTED
Hint Resolve zring_old_diff.
*)
(* UNEXPORTED
Hint Resolve zring_old_diff.
*)
-inline cic:/CoRN/algebra/CRings/zring_old_plus_nat.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_plus_nat.con".
(* UNEXPORTED
Hint Resolve zring_old_plus_nat: algebra.
*)
(* UNEXPORTED
Hint Resolve zring_old_plus_nat: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_old_inv_nat.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_inv_nat.con".
(* UNEXPORTED
Hint Resolve zring_old_inv_nat: algebra.
(* UNEXPORTED
Hint Resolve zring_old_inv_nat: algebra.
Hint Resolve zring_old_diff: algebra.
*)
Hint Resolve zring_old_diff: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_old_plus.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_plus.con".
(* UNEXPORTED
Hint Resolve zring_old_plus: algebra.
*)
(* UNEXPORTED
Hint Resolve zring_old_plus: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_old_inv.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_inv.con".
(* UNEXPORTED
Hint Resolve zring_old_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve zring_old_inv: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_old_minus.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_minus.con".
(* UNEXPORTED
Hint Resolve zring_old_minus: algebra.
*)
(* UNEXPORTED
Hint Resolve zring_old_minus: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_old_mult.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_mult.con".
(* UNEXPORTED
Hint Resolve zring_old_mult: algebra.
*)
(* UNEXPORTED
Hint Resolve zring_old_mult: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_old_one.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_one.con".
(* UNEXPORTED
Hint Resolve zring_old_one: algebra.
*)
(* UNEXPORTED
Hint Resolve zring_old_one: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_old_inv_one.con.
+inline "cic:/CoRN/algebra/CRings/zring_old_inv_one.con".
(*#************** new def of zring. ***********************)
(*#* The [zring] function can be defined directly. This is done here.
*)
(*#************** new def of zring. ***********************)
(*#* The [zring] function can be defined directly. This is done here.
*)
-inline cic:/CoRN/algebra/CRings/pring_aux.con.
+inline "cic:/CoRN/algebra/CRings/pring_aux.con".
-inline cic:/CoRN/algebra/CRings/pring.con.
+inline "cic:/CoRN/algebra/CRings/pring.con".
-inline cic:/CoRN/algebra/CRings/zring.con.
+inline "cic:/CoRN/algebra/CRings/zring.con".
-inline cic:/CoRN/algebra/CRings/pring_aux_lemma.con.
+inline "cic:/CoRN/algebra/CRings/pring_aux_lemma.con".
-inline cic:/CoRN/algebra/CRings/double_nring.con.
+inline "cic:/CoRN/algebra/CRings/double_nring.con".
(* UNEXPORTED
Hint Resolve pring_aux_lemma double_nring: algebra.
*)
(* UNEXPORTED
Hint Resolve pring_aux_lemma double_nring: algebra.
*)
-inline cic:/CoRN/algebra/CRings/pring_aux_nring.con.
+inline "cic:/CoRN/algebra/CRings/pring_aux_nring.con".
(* UNEXPORTED
Hint Resolve pring_aux_nring: algebra.
*)
(* UNEXPORTED
Hint Resolve pring_aux_nring: algebra.
*)
-inline cic:/CoRN/algebra/CRings/pring_convert.con.
+inline "cic:/CoRN/algebra/CRings/pring_convert.con".
(* UNEXPORTED
Hint Resolve pring_convert: algebra.
*)
(* UNEXPORTED
Hint Resolve pring_convert: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_zring_old.con.
+inline "cic:/CoRN/algebra/CRings/zring_zring_old.con".
(* UNEXPORTED
Hint Resolve zring_zring_old: algebra.
*)
(* UNEXPORTED
Hint Resolve zring_zring_old: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zring_zero.con.
+inline "cic:/CoRN/algebra/CRings/zring_zero.con".
-inline cic:/CoRN/algebra/CRings/zring_diff.con.
+inline "cic:/CoRN/algebra/CRings/zring_diff.con".
-inline cic:/CoRN/algebra/CRings/zring_plus_nat.con.
+inline "cic:/CoRN/algebra/CRings/zring_plus_nat.con".
-inline cic:/CoRN/algebra/CRings/zring_inv_nat.con.
+inline "cic:/CoRN/algebra/CRings/zring_inv_nat.con".
-inline cic:/CoRN/algebra/CRings/zring_plus.con.
+inline "cic:/CoRN/algebra/CRings/zring_plus.con".
-inline cic:/CoRN/algebra/CRings/zring_inv.con.
+inline "cic:/CoRN/algebra/CRings/zring_inv.con".
-inline cic:/CoRN/algebra/CRings/zring_minus.con.
+inline "cic:/CoRN/algebra/CRings/zring_minus.con".
-inline cic:/CoRN/algebra/CRings/zring_mult.con.
+inline "cic:/CoRN/algebra/CRings/zring_mult.con".
-inline cic:/CoRN/algebra/CRings/zring_one.con.
+inline "cic:/CoRN/algebra/CRings/zring_one.con".
-inline cic:/CoRN/algebra/CRings/zring_inv_one.con.
+inline "cic:/CoRN/algebra/CRings/zring_inv_one.con".
(* UNEXPORTED
End int_injection.
(* UNEXPORTED
End int_injection.
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
(*#*
*** Infinite Ring sums
(*#*
*** Infinite Ring sums
Section infinite_ring_sums.
*)
Section infinite_ring_sums.
*)
-inline cic:/CoRN/algebra/CRings/Sum_upto.con.
+inline "cic:/CoRN/algebra/CRings/Sum_upto.con".
-inline cic:/CoRN/algebra/CRings/sum_upto_O.con.
+inline "cic:/CoRN/algebra/CRings/sum_upto_O.con".
-inline cic:/CoRN/algebra/CRings/Sum_from_upto.con.
+inline "cic:/CoRN/algebra/CRings/Sum_from_upto.con".
(*#*
Here's an alternative def of [Sum_from_upto], with a lemma that
it's equivalent to the original.
*)
(*#*
Here's an alternative def of [Sum_from_upto], with a lemma that
it's equivalent to the original.
*)
-inline cic:/CoRN/algebra/CRings/seq_from.con.
+inline "cic:/CoRN/algebra/CRings/seq_from.con".
-inline cic:/CoRN/algebra/CRings/Sum_from_upto_alt.con.
+inline "cic:/CoRN/algebra/CRings/Sum_from_upto_alt.con".
(* UNEXPORTED
End infinite_ring_sums.
(* UNEXPORTED
End infinite_ring_sums.
(*#* *** Ring Sums over Lists
*)
(*#* *** Ring Sums over Lists
*)
-inline cic:/CoRN/algebra/CRings/RList_Mem.con.
+inline "cic:/CoRN/algebra/CRings/RList_Mem.con".
-inline cic:/CoRN/algebra/CRings/List_Sum_upto.con.
+inline "cic:/CoRN/algebra/CRings/List_Sum_upto.con".
-inline cic:/CoRN/algebra/CRings/list_sum_upto_O.con.
+inline "cic:/CoRN/algebra/CRings/list_sum_upto_O.con".
-inline cic:/CoRN/algebra/CRings/List_Sum_from_upto.con.
+inline "cic:/CoRN/algebra/CRings/List_Sum_from_upto.con".
(* UNEXPORTED
End ring_sums_over_lists.
(* UNEXPORTED
End ring_sums_over_lists.
Section Dist_properties.
*)
Section Dist_properties.
*)
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
-inline cic:/CoRN/algebra/CRings/dist_1b.con.
+inline "cic:/CoRN/algebra/CRings/dist_1b.con".
(* UNEXPORTED
Hint Resolve dist_1b: algebra.
*)
(* UNEXPORTED
Hint Resolve dist_1b: algebra.
*)
-inline cic:/CoRN/algebra/CRings/dist_2a.con.
+inline "cic:/CoRN/algebra/CRings/dist_2a.con".
(* UNEXPORTED
Hint Resolve dist_2a: algebra.
*)
(* UNEXPORTED
Hint Resolve dist_2a: algebra.
*)
-inline cic:/CoRN/algebra/CRings/dist_2b.con.
+inline "cic:/CoRN/algebra/CRings/dist_2b.con".
(* UNEXPORTED
Hint Resolve dist_2b: algebra.
*)
(* UNEXPORTED
Hint Resolve dist_2b: algebra.
*)
-inline cic:/CoRN/algebra/CRings/mult_distr_sum0_lft.con.
+inline "cic:/CoRN/algebra/CRings/mult_distr_sum0_lft.con".
(* UNEXPORTED
Hint Resolve mult_distr_sum0_lft.
*)
(* UNEXPORTED
Hint Resolve mult_distr_sum0_lft.
*)
-inline cic:/CoRN/algebra/CRings/mult_distr_sum_lft.con.
+inline "cic:/CoRN/algebra/CRings/mult_distr_sum_lft.con".
(* UNEXPORTED
Hint Resolve mult_distr_sum_lft: algebra.
*)
(* UNEXPORTED
Hint Resolve mult_distr_sum_lft: algebra.
*)
-inline cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con.
+inline "cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con".
-inline cic:/CoRN/algebra/CRings/sumx_const.con.
+inline "cic:/CoRN/algebra/CRings/sumx_const.con".
(* UNEXPORTED
End Dist_properties.
(* UNEXPORTED
End Dist_properties.
Section NExp_properties.
*)
Section NExp_properties.
*)
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
-inline cic:/CoRN/algebra/CRings/nexp_wd.con.
+inline "cic:/CoRN/algebra/CRings/nexp_wd.con".
-inline cic:/CoRN/algebra/CRings/nexp_strext.con.
+inline "cic:/CoRN/algebra/CRings/nexp_strext.con".
-inline cic:/CoRN/algebra/CRings/nexp_Sn.con.
+inline "cic:/CoRN/algebra/CRings/nexp_Sn.con".
(* UNEXPORTED
Hint Resolve nexp_wd nexp_Sn: algebra.
*)
(* UNEXPORTED
Hint Resolve nexp_wd nexp_Sn: algebra.
*)
-inline cic:/CoRN/algebra/CRings/nexp_plus.con.
+inline "cic:/CoRN/algebra/CRings/nexp_plus.con".
(* UNEXPORTED
Hint Resolve nexp_plus: algebra.
*)
(* UNEXPORTED
Hint Resolve nexp_plus: algebra.
*)
-inline cic:/CoRN/algebra/CRings/one_nexp.con.
+inline "cic:/CoRN/algebra/CRings/one_nexp.con".
(* UNEXPORTED
Hint Resolve one_nexp: algebra.
*)
(* UNEXPORTED
Hint Resolve one_nexp: algebra.
*)
-inline cic:/CoRN/algebra/CRings/mult_nexp.con.
+inline "cic:/CoRN/algebra/CRings/mult_nexp.con".
(* UNEXPORTED
Hint Resolve mult_nexp: algebra.
*)
(* UNEXPORTED
Hint Resolve mult_nexp: algebra.
*)
-inline cic:/CoRN/algebra/CRings/nexp_mult.con.
+inline "cic:/CoRN/algebra/CRings/nexp_mult.con".
(* UNEXPORTED
Hint Resolve nexp_mult: algebra.
*)
(* UNEXPORTED
Hint Resolve nexp_mult: algebra.
*)
-inline cic:/CoRN/algebra/CRings/zero_nexp.con.
+inline "cic:/CoRN/algebra/CRings/zero_nexp.con".
(* UNEXPORTED
Hint Resolve zero_nexp: algebra.
*)
(* UNEXPORTED
Hint Resolve zero_nexp: algebra.
*)
-inline cic:/CoRN/algebra/CRings/inv_nexp_even.con.
+inline "cic:/CoRN/algebra/CRings/inv_nexp_even.con".
(* UNEXPORTED
Hint Resolve inv_nexp_even: algebra.
*)
(* UNEXPORTED
Hint Resolve inv_nexp_even: algebra.
*)
-inline cic:/CoRN/algebra/CRings/inv_nexp_two.con.
+inline "cic:/CoRN/algebra/CRings/inv_nexp_two.con".
(* UNEXPORTED
Hint Resolve inv_nexp_two: algebra.
*)
(* UNEXPORTED
Hint Resolve inv_nexp_two: algebra.
*)
-inline cic:/CoRN/algebra/CRings/inv_nexp_odd.con.
+inline "cic:/CoRN/algebra/CRings/inv_nexp_odd.con".
(* UNEXPORTED
Hint Resolve inv_nexp_odd: algebra.
*)
(* UNEXPORTED
Hint Resolve inv_nexp_odd: algebra.
*)
-inline cic:/CoRN/algebra/CRings/nexp_one.con.
+inline "cic:/CoRN/algebra/CRings/nexp_one.con".
(* UNEXPORTED
Hint Resolve nexp_one: algebra.
*)
(* UNEXPORTED
Hint Resolve nexp_one: algebra.
*)
-inline cic:/CoRN/algebra/CRings/nexp_two.con.
+inline "cic:/CoRN/algebra/CRings/nexp_two.con".
(* UNEXPORTED
Hint Resolve nexp_two: algebra.
*)
(* UNEXPORTED
Hint Resolve nexp_two: algebra.
*)
-inline cic:/CoRN/algebra/CRings/inv_one_even_nexp.con.
+inline "cic:/CoRN/algebra/CRings/inv_one_even_nexp.con".
(* UNEXPORTED
Hint Resolve inv_one_even_nexp: algebra.
*)
(* UNEXPORTED
Hint Resolve inv_one_even_nexp: algebra.
*)
-inline cic:/CoRN/algebra/CRings/inv_one_odd_nexp.con.
+inline "cic:/CoRN/algebra/CRings/inv_one_odd_nexp.con".
(* UNEXPORTED
Hint Resolve inv_one_odd_nexp: algebra.
*)
(* UNEXPORTED
Hint Resolve inv_one_odd_nexp: algebra.
*)
-inline cic:/CoRN/algebra/CRings/square_plus.con.
+inline "cic:/CoRN/algebra/CRings/square_plus.con".
-inline cic:/CoRN/algebra/CRings/square_minus.con.
+inline "cic:/CoRN/algebra/CRings/square_minus.con".
-inline cic:/CoRN/algebra/CRings/nexp_funny.con.
+inline "cic:/CoRN/algebra/CRings/nexp_funny.con".
(* UNEXPORTED
Hint Resolve nexp_funny: algebra.
*)
(* UNEXPORTED
Hint Resolve nexp_funny: algebra.
*)
-inline cic:/CoRN/algebra/CRings/nexp_funny'.con.
+inline "cic:/CoRN/algebra/CRings/nexp_funny'.con".
(* UNEXPORTED
Hint Resolve nexp_funny': algebra.
(* UNEXPORTED
Hint Resolve nexp_funny': algebra.
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
-inline cic:/CoRN/algebra/CRings/F.var.
+inline "cic:/CoRN/algebra/CRings/F.var".
-inline cic:/CoRN/algebra/CRings/G.var.
+inline "cic:/CoRN/algebra/CRings/G.var".
-inline cic:/CoRN/algebra/CRings/P.con.
+inline "cic:/CoRN/algebra/CRings/P.con".
-inline cic:/CoRN/algebra/CRings/Q.con.
+inline "cic:/CoRN/algebra/CRings/Q.con".
Section Part_Function_Mult.
*)
Section Part_Function_Mult.
*)
-inline cic:/CoRN/algebra/CRings/part_function_mult_strext.con.
+inline "cic:/CoRN/algebra/CRings/part_function_mult_strext.con".
-inline cic:/CoRN/algebra/CRings/Fmult.con.
+inline "cic:/CoRN/algebra/CRings/Fmult.con".
(* UNEXPORTED
End Part_Function_Mult.
(* UNEXPORTED
End Part_Function_Mult.
Section Part_Function_Nth_Power.
*)
Section Part_Function_Nth_Power.
*)
-inline cic:/CoRN/algebra/CRings/n.var.
+inline "cic:/CoRN/algebra/CRings/n.var".
-inline cic:/CoRN/algebra/CRings/part_function_nth_strext.con.
+inline "cic:/CoRN/algebra/CRings/part_function_nth_strext.con".
-inline cic:/CoRN/algebra/CRings/Fnth.con.
+inline "cic:/CoRN/algebra/CRings/Fnth.con".
(* UNEXPORTED
End Part_Function_Nth_Power.
(* UNEXPORTED
End Part_Function_Nth_Power.
-inline cic:/CoRN/algebra/CRings/R'.var.
+inline "cic:/CoRN/algebra/CRings/R'.var".
-inline cic:/CoRN/algebra/CRings/included_FMult.con.
+inline "cic:/CoRN/algebra/CRings/included_FMult.con".
-inline cic:/CoRN/algebra/CRings/included_FMult'.con.
+inline "cic:/CoRN/algebra/CRings/included_FMult'.con".
-inline cic:/CoRN/algebra/CRings/included_FMult''.con.
+inline "cic:/CoRN/algebra/CRings/included_FMult''.con".
-inline cic:/CoRN/algebra/CRings/n.var.
+inline "cic:/CoRN/algebra/CRings/n.var".
-inline cic:/CoRN/algebra/CRings/included_FNth.con.
+inline "cic:/CoRN/algebra/CRings/included_FNth.con".
-inline cic:/CoRN/algebra/CRings/included_FNth'.con.
+inline "cic:/CoRN/algebra/CRings/included_FNth'.con".
(* UNEXPORTED
End CRing_Ops.
*)
(* UNEXPORTED
End CRing_Ops.
*)
-inline cic:/CoRN/algebra/CRings/Fscalmult.con.
+inline "cic:/CoRN/algebra/CRings/Fscalmult.con".
(* UNEXPORTED
Implicit Arguments Fmult [R].
(* UNEXPORTED
Implicit Arguments Fmult [R].
Section ScalarMultiplication.
*)
Section ScalarMultiplication.
*)
-inline cic:/CoRN/algebra/CRings/R.var.
+inline "cic:/CoRN/algebra/CRings/R.var".
-inline cic:/CoRN/algebra/CRings/F.var.
+inline "cic:/CoRN/algebra/CRings/F.var".
-inline cic:/CoRN/algebra/CRings/P.con.
+inline "cic:/CoRN/algebra/CRings/P.con".
-inline cic:/CoRN/algebra/CRings/R'.var.
+inline "cic:/CoRN/algebra/CRings/R'.var".
-inline cic:/CoRN/algebra/CRings/included_FScalMult.con.
+inline "cic:/CoRN/algebra/CRings/included_FScalMult.con".
-inline cic:/CoRN/algebra/CRings/included_FScalMult'.con.
+inline "cic:/CoRN/algebra/CRings/included_FScalMult'.con".
(* UNEXPORTED
End ScalarMultiplication.
(* UNEXPORTED
End ScalarMultiplication.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSemiGroups".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSemiGroups".
(* $Id: CSemiGroups.v,v 1.8 2004/04/22 14:49:43 lcf Exp $ *)
(*#* printing [+] %\ensuremath+% #+# *)
(*#* printing {+} %\ensuremath+% #+# *)
(* $Id: CSemiGroups.v,v 1.8 2004/04/22 14:49:43 lcf Exp $ *)
(*#* printing [+] %\ensuremath+% #+# *)
(*#* printing {+} %\ensuremath+% #+# *)
-(* INCLUDE
-CSetoidInc
-*)
+include "algebra/CSetoidInc.ma".
**Definition of the notion of semigroup
*)
**Definition of the notion of semigroup
*)
-inline cic:/CoRN/algebra/CSemiGroups/is_CSemiGroup.con.
+inline "cic:/CoRN/algebra/CSemiGroups/is_CSemiGroup.con".
+
+inline "cic:/CoRN/algebra/CSemiGroups/CSemiGroup.ind".
-inline cic:/CoRN/algebra/CSemiGroups/CSemiGroup.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/CSemiGroups/csg_crr.con" 0 (* compounds *).
(*#*
%\begin{nameconvention}%
(*#*
%\begin{nameconvention}%
Section CSemiGroup_axioms.
*)
Section CSemiGroup_axioms.
*)
-inline cic:/CoRN/algebra/CSemiGroups/G.var.
+inline "cic:/CoRN/algebra/CSemiGroups/G.var".
-inline cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con.
+inline "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con".
-inline cic:/CoRN/algebra/CSemiGroups/plus_assoc.con.
+inline "cic:/CoRN/algebra/CSemiGroups/plus_assoc.con".
(* UNEXPORTED
End CSemiGroup_axioms.
(* UNEXPORTED
End CSemiGroup_axioms.
Section CSemiGroup_basics.
*)
Section CSemiGroup_basics.
*)
-inline cic:/CoRN/algebra/CSemiGroups/G.var.
+inline "cic:/CoRN/algebra/CSemiGroups/G.var".
-inline cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con.
+inline "cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con".
(* UNEXPORTED
End CSemiGroup_basics.
(* UNEXPORTED
End CSemiGroup_basics.
Section Part_Function_Plus.
*)
Section Part_Function_Plus.
*)
-inline cic:/CoRN/algebra/CSemiGroups/G.var.
+inline "cic:/CoRN/algebra/CSemiGroups/G.var".
-inline cic:/CoRN/algebra/CSemiGroups/F.var.
+inline "cic:/CoRN/algebra/CSemiGroups/F.var".
-inline cic:/CoRN/algebra/CSemiGroups/F'.var.
+inline "cic:/CoRN/algebra/CSemiGroups/F'.var".
-inline cic:/CoRN/algebra/CSemiGroups/P.con.
+inline "cic:/CoRN/algebra/CSemiGroups/P.con".
-inline cic:/CoRN/algebra/CSemiGroups/Q.con.
+inline "cic:/CoRN/algebra/CSemiGroups/Q.con".
-inline cic:/CoRN/algebra/CSemiGroups/part_function_plus_strext.con.
+inline "cic:/CoRN/algebra/CSemiGroups/part_function_plus_strext.con".
-inline cic:/CoRN/algebra/CSemiGroups/Fplus.con.
+inline "cic:/CoRN/algebra/CSemiGroups/Fplus.con".
(*#*
%\begin{convention}% Let [R:G->CProp].
%\end{convention}%
*)
(*#*
%\begin{convention}% Let [R:G->CProp].
%\end{convention}%
*)
-inline cic:/CoRN/algebra/CSemiGroups/R.var.
+inline "cic:/CoRN/algebra/CSemiGroups/R.var".
-inline cic:/CoRN/algebra/CSemiGroups/included_FPlus.con.
+inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con".
-inline cic:/CoRN/algebra/CSemiGroups/included_FPlus'.con.
+inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus'.con".
-inline cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con.
+inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con".
(* UNEXPORTED
End Part_Function_Plus.
(* UNEXPORTED
End Part_Function_Plus.
Section SubCSemiGroups.
*)
Section SubCSemiGroups.
*)
-inline cic:/CoRN/algebra/CSemiGroups/csg.var.
+inline "cic:/CoRN/algebra/CSemiGroups/csg.var".
-inline cic:/CoRN/algebra/CSemiGroups/P.var.
+inline "cic:/CoRN/algebra/CSemiGroups/P.var".
-inline cic:/CoRN/algebra/CSemiGroups/op_pres_P.var.
+inline "cic:/CoRN/algebra/CSemiGroups/op_pres_P.var".
-inline cic:/CoRN/algebra/CSemiGroups/subcrr.con.
+inline "cic:/CoRN/algebra/CSemiGroups/subcrr.con".
-inline cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con.
+inline "cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con".
(* UNEXPORTED
End SubCSemiGroups.
(* UNEXPORTED
End SubCSemiGroups.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSetoidFun".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSetoidFun".
(* $Id: CSetoidFun.v,v 1.10 2004/04/23 10:00:53 lcf Exp $ *)
(* $Id: CSetoidFun.v,v 1.10 2004/04/23 10:00:53 lcf Exp $ *)
-(* INCLUDE
-CSetoids
-*)
+include "algebra/CSetoids.ma".
(* UNEXPORTED
Section unary_function_composition.
(* UNEXPORTED
Section unary_function_composition.
setoid function from [S1] to [S2], and [g] from [S2]
to [S3] in the following definition of composition. *)
setoid function from [S1] to [S2], and [g] from [S2]
to [S3] in the following definition of composition. *)
-inline cic:/CoRN/algebra/CSetoidFun/S1.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S1.var".
-inline cic:/CoRN/algebra/CSetoidFun/S2.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S2.var".
-inline cic:/CoRN/algebra/CSetoidFun/S3.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S3.var".
-inline cic:/CoRN/algebra/CSetoidFun/f.var.
+inline "cic:/CoRN/algebra/CSetoidFun/f.var".
-inline cic:/CoRN/algebra/CSetoidFun/g.var.
+inline "cic:/CoRN/algebra/CSetoidFun/g.var".
-inline cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con.
+inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con".
(* UNEXPORTED
End unary_function_composition.
(* UNEXPORTED
End unary_function_composition.
Section unary_and_binary_function_composition.
*)
Section unary_and_binary_function_composition.
*)
-inline cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_un_fun.con.
+inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_un_fun.con".
-inline cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_fun.con.
+inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_fun.con".
-inline cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_un_bin_fun.con.
+inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_un_bin_fun.con".
(* UNEXPORTED
End unary_and_binary_function_composition.
(* UNEXPORTED
End unary_and_binary_function_composition.
Section function_projection.
*)
Section function_projection.
*)
-inline cic:/CoRN/algebra/CSetoidFun/proj_bin_fun.con.
+inline "cic:/CoRN/algebra/CSetoidFun/proj_bin_fun.con".
-inline cic:/CoRN/algebra/CSetoidFun/projected_bin_fun.con.
+inline "cic:/CoRN/algebra/CSetoidFun/projected_bin_fun.con".
(* UNEXPORTED
End function_projection.
(* UNEXPORTED
End function_projection.
-inline cic:/CoRN/algebra/CSetoidFun/S.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S.var".
-inline cic:/CoRN/algebra/CSetoidFun/binproj1.con.
+inline "cic:/CoRN/algebra/CSetoidFun/binproj1.con".
-inline cic:/CoRN/algebra/CSetoidFun/binproj1_strext.con.
+inline "cic:/CoRN/algebra/CSetoidFun/binproj1_strext.con".
-inline cic:/CoRN/algebra/CSetoidFun/cs_binproj1.con.
+inline "cic:/CoRN/algebra/CSetoidFun/cs_binproj1.con".
(* UNEXPORTED
End BinProj.
(* UNEXPORTED
End BinProj.
Section CombiningOperations.
*)
Section CombiningOperations.
*)
-inline cic:/CoRN/algebra/CSetoidFun/S1.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S1.var".
-inline cic:/CoRN/algebra/CSetoidFun/S2.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S2.var".
-inline cic:/CoRN/algebra/CSetoidFun/S3.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S3.var".
(*#*
In the following definition, we assume [f] is a setoid function from
(*#*
In the following definition, we assume [f] is a setoid function from
Section CombiningUnaryOperations.
*)
Section CombiningUnaryOperations.
*)
-inline cic:/CoRN/algebra/CSetoidFun/f.var.
+inline "cic:/CoRN/algebra/CSetoidFun/f.var".
-inline cic:/CoRN/algebra/CSetoidFun/op.var.
+inline "cic:/CoRN/algebra/CSetoidFun/op.var".
-inline cic:/CoRN/algebra/CSetoidFun/opOnFun.con.
+inline "cic:/CoRN/algebra/CSetoidFun/opOnFun.con".
(* UNEXPORTED
End CombiningUnaryOperations.
(* UNEXPORTED
End CombiningUnaryOperations.
-inline cic:/CoRN/algebra/CSetoidFun/S.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S.var".
(* UNEXPORTED
Section Conjunction.
*)
(* UNEXPORTED
Section Conjunction.
*)
-inline cic:/CoRN/algebra/CSetoidFun/P.var.
+inline "cic:/CoRN/algebra/CSetoidFun/P.var".
-inline cic:/CoRN/algebra/CSetoidFun/Q.var.
+inline "cic:/CoRN/algebra/CSetoidFun/Q.var".
-inline cic:/CoRN/algebra/CSetoidFun/conjP.con.
+inline "cic:/CoRN/algebra/CSetoidFun/conjP.con".
-inline cic:/CoRN/algebra/CSetoidFun/prj1.con.
+inline "cic:/CoRN/algebra/CSetoidFun/prj1.con".
-inline cic:/CoRN/algebra/CSetoidFun/prj2.con.
+inline "cic:/CoRN/algebra/CSetoidFun/prj2.con".
-inline cic:/CoRN/algebra/CSetoidFun/conj_wd.con.
+inline "cic:/CoRN/algebra/CSetoidFun/conj_wd.con".
(* UNEXPORTED
End Conjunction.
(* UNEXPORTED
End Conjunction.
-inline cic:/CoRN/algebra/CSetoidFun/P.var.
+inline "cic:/CoRN/algebra/CSetoidFun/P.var".
-inline cic:/CoRN/algebra/CSetoidFun/Q.var.
+inline "cic:/CoRN/algebra/CSetoidFun/Q.var".
(*#*
Although at this stage we never use it, for completeness's sake we also treat disjunction (corresponding to union of subsets).
*)
(*#*
Although at this stage we never use it, for completeness's sake we also treat disjunction (corresponding to union of subsets).
*)
-inline cic:/CoRN/algebra/CSetoidFun/disj.con.
+inline "cic:/CoRN/algebra/CSetoidFun/disj.con".
-inline cic:/CoRN/algebra/CSetoidFun/inj1.con.
+inline "cic:/CoRN/algebra/CSetoidFun/inj1.con".
-inline cic:/CoRN/algebra/CSetoidFun/inj2.con.
+inline "cic:/CoRN/algebra/CSetoidFun/inj2.con".
-inline cic:/CoRN/algebra/CSetoidFun/disj_wd.con.
+inline "cic:/CoRN/algebra/CSetoidFun/disj_wd.con".
(* UNEXPORTED
End Disjunction.
(* UNEXPORTED
End Disjunction.
The next definition is a bit tricky, and is useful for choosing among the elements that satisfy a predicate [P] those that also satisfy [R] in the case where [R] is only defined for elements satisfying [P]---consider [R] to be a condition on the image of an object via a function with domain [P]. We chose to call this operation [extension].
*)
The next definition is a bit tricky, and is useful for choosing among the elements that satisfy a predicate [P] those that also satisfy [R] in the case where [R] is only defined for elements satisfying [P]---consider [R] to be a condition on the image of an object via a function with domain [P]. We chose to call this operation [extension].
*)
-inline cic:/CoRN/algebra/CSetoidFun/P.var.
+inline "cic:/CoRN/algebra/CSetoidFun/P.var".
-inline cic:/CoRN/algebra/CSetoidFun/R.var.
+inline "cic:/CoRN/algebra/CSetoidFun/R.var".
-inline cic:/CoRN/algebra/CSetoidFun/extend.con.
+inline "cic:/CoRN/algebra/CSetoidFun/extend.con".
-inline cic:/CoRN/algebra/CSetoidFun/ext1.con.
+inline "cic:/CoRN/algebra/CSetoidFun/ext1.con".
-inline cic:/CoRN/algebra/CSetoidFun/ext2_a.con.
+inline "cic:/CoRN/algebra/CSetoidFun/ext2_a.con".
-inline cic:/CoRN/algebra/CSetoidFun/ext2.con.
+inline "cic:/CoRN/algebra/CSetoidFun/ext2.con".
-inline cic:/CoRN/algebra/CSetoidFun/extension_wd.con.
+inline "cic:/CoRN/algebra/CSetoidFun/extension_wd.con".
(* UNEXPORTED
End Extension.
(* UNEXPORTED
End Extension.
We are now ready to define the concept of partial function between arbitrary setoids.
*)
We are now ready to define the concept of partial function between arbitrary setoids.
*)
-inline cic:/CoRN/algebra/CSetoidFun/BinPartFunct.ind.
+inline "cic:/CoRN/algebra/CSetoidFun/BinPartFunct.ind".
+
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoidFun/bpfpfun.con" 0 (* compounds *).
(* UNEXPORTED
Implicit Arguments bpfpfun [S1 S2].
(* UNEXPORTED
Implicit Arguments bpfpfun [S1 S2].
The next lemma states that every partial function is well defined.
*)
The next lemma states that every partial function is well defined.
*)
-inline cic:/CoRN/algebra/CSetoidFun/bpfwdef.con.
+inline "cic:/CoRN/algebra/CSetoidFun/bpfwdef.con".
(*#* Similar for automorphisms. *)
(*#* Similar for automorphisms. *)
-inline cic:/CoRN/algebra/CSetoidFun/PartFunct.ind.
+inline "cic:/CoRN/algebra/CSetoidFun/PartFunct.ind".
+
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoidFun/pfpfun.con" 0 (* compounds *).
(* UNEXPORTED
Implicit Arguments pfpfun [S].
(* UNEXPORTED
Implicit Arguments pfpfun [S].
The next lemma states that every partial function is well defined.
*)
The next lemma states that every partial function is well defined.
*)
-inline cic:/CoRN/algebra/CSetoidFun/pfwdef.con.
+inline "cic:/CoRN/algebra/CSetoidFun/pfwdef.con".
(*#*
A few characteristics of this definition should be explained:
(*#*
A few characteristics of this definition should be explained:
-inline cic:/CoRN/algebra/CSetoidFun/S.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S.var".
(*#*
To begin with, we want to be able to ``see'' each total function as a partial function.
*)
(*#*
To begin with, we want to be able to ``see'' each total function as a partial function.
*)
-inline cic:/CoRN/algebra/CSetoidFun/total_eq_part.con.
+inline "cic:/CoRN/algebra/CSetoidFun/total_eq_part.con".
(* UNEXPORTED
Section Part_Function_Const.
(* UNEXPORTED
Section Part_Function_Const.
-inline cic:/CoRN/algebra/CSetoidFun/c.var.
+inline "cic:/CoRN/algebra/CSetoidFun/c.var".
-inline cic:/CoRN/algebra/CSetoidFun/Fconst.con.
+inline "cic:/CoRN/algebra/CSetoidFun/Fconst.con".
(* UNEXPORTED
End Part_Function_Const.
(* UNEXPORTED
End Part_Function_Const.
Section Part_Function_Id.
*)
Section Part_Function_Id.
*)
-inline cic:/CoRN/algebra/CSetoidFun/Fid.con.
+inline "cic:/CoRN/algebra/CSetoidFun/Fid.con".
(* UNEXPORTED
End Part_Function_Id.
(* UNEXPORTED
End Part_Function_Id.
Section Part_Function_Composition.
*)
Section Part_Function_Composition.
*)
-inline cic:/CoRN/algebra/CSetoidFun/G.var.
+inline "cic:/CoRN/algebra/CSetoidFun/G.var".
-inline cic:/CoRN/algebra/CSetoidFun/F.var.
+inline "cic:/CoRN/algebra/CSetoidFun/F.var".
-inline cic:/CoRN/algebra/CSetoidFun/P.con.
+inline "cic:/CoRN/algebra/CSetoidFun/P.con".
-inline cic:/CoRN/algebra/CSetoidFun/Q.con.
+inline "cic:/CoRN/algebra/CSetoidFun/Q.con".
-inline cic:/CoRN/algebra/CSetoidFun/R.con.
+inline "cic:/CoRN/algebra/CSetoidFun/R.con".
-inline cic:/CoRN/algebra/CSetoidFun/part_function_comp_strext.con.
+inline "cic:/CoRN/algebra/CSetoidFun/part_function_comp_strext.con".
-inline cic:/CoRN/algebra/CSetoidFun/part_function_comp_dom_wd.con.
+inline "cic:/CoRN/algebra/CSetoidFun/part_function_comp_dom_wd.con".
-inline cic:/CoRN/algebra/CSetoidFun/Fcomp.con.
+inline "cic:/CoRN/algebra/CSetoidFun/Fcomp.con".
(* UNEXPORTED
End Part_Function_Composition.
(* UNEXPORTED
End Part_Function_Composition.
Section BinPart_Function_Composition.
*)
Section BinPart_Function_Composition.
*)
-inline cic:/CoRN/algebra/CSetoidFun/S1.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S1.var".
-inline cic:/CoRN/algebra/CSetoidFun/S2.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S2.var".
-inline cic:/CoRN/algebra/CSetoidFun/S3.var.
+inline "cic:/CoRN/algebra/CSetoidFun/S3.var".
-inline cic:/CoRN/algebra/CSetoidFun/G.var.
+inline "cic:/CoRN/algebra/CSetoidFun/G.var".
-inline cic:/CoRN/algebra/CSetoidFun/F.var.
+inline "cic:/CoRN/algebra/CSetoidFun/F.var".
-inline cic:/CoRN/algebra/CSetoidFun/P.con.
+inline "cic:/CoRN/algebra/CSetoidFun/P.con".
-inline cic:/CoRN/algebra/CSetoidFun/Q.con.
+inline "cic:/CoRN/algebra/CSetoidFun/Q.con".
-inline cic:/CoRN/algebra/CSetoidFun/R.con.
+inline "cic:/CoRN/algebra/CSetoidFun/R.con".
-inline cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_strext.con.
+inline "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_strext.con".
-inline cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_dom_wd.con.
+inline "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_dom_wd.con".
-inline cic:/CoRN/algebra/CSetoidFun/BinFcomp.con.
+inline "cic:/CoRN/algebra/CSetoidFun/BinFcomp.con".
(* UNEXPORTED
End BinPart_Function_Composition.
(* UNEXPORTED
End BinPart_Function_Composition.
-inline cic:/CoRN/algebra/CSetoidFun/injective.con.
+inline "cic:/CoRN/algebra/CSetoidFun/injective.con".
-inline cic:/CoRN/algebra/CSetoidFun/injective_weak.con.
+inline "cic:/CoRN/algebra/CSetoidFun/injective_weak.con".
-inline cic:/CoRN/algebra/CSetoidFun/surjective.con.
+inline "cic:/CoRN/algebra/CSetoidFun/surjective.con".
(* UNEXPORTED
Implicit Arguments injective [A B].
(* UNEXPORTED
Implicit Arguments injective [A B].
Implicit Arguments surjective [A B].
*)
Implicit Arguments surjective [A B].
*)
-inline cic:/CoRN/algebra/CSetoidFun/injective_imp_injective_weak.con.
+inline "cic:/CoRN/algebra/CSetoidFun/injective_imp_injective_weak.con".
-inline cic:/CoRN/algebra/CSetoidFun/bijective.con.
+inline "cic:/CoRN/algebra/CSetoidFun/bijective.con".
(* UNEXPORTED
Implicit Arguments bijective [A B].
*)
(* UNEXPORTED
Implicit Arguments bijective [A B].
*)
-inline cic:/CoRN/algebra/CSetoidFun/id_is_bij.con.
+inline "cic:/CoRN/algebra/CSetoidFun/id_is_bij.con".
-inline cic:/CoRN/algebra/CSetoidFun/comp_resp_bij.con.
+inline "cic:/CoRN/algebra/CSetoidFun/comp_resp_bij.con".
-inline cic:/CoRN/algebra/CSetoidFun/inv.con.
+inline "cic:/CoRN/algebra/CSetoidFun/inv.con".
(* UNEXPORTED
Implicit Arguments inv [A B].
*)
(* UNEXPORTED
Implicit Arguments inv [A B].
*)
-inline cic:/CoRN/algebra/CSetoidFun/invfun.con.
+inline "cic:/CoRN/algebra/CSetoidFun/invfun.con".
(* UNEXPORTED
Implicit Arguments invfun [A B].
*)
(* UNEXPORTED
Implicit Arguments invfun [A B].
*)
-inline cic:/CoRN/algebra/CSetoidFun/inv1.con.
+inline "cic:/CoRN/algebra/CSetoidFun/inv1.con".
-inline cic:/CoRN/algebra/CSetoidFun/inv2.con.
+inline "cic:/CoRN/algebra/CSetoidFun/inv2.con".
-inline cic:/CoRN/algebra/CSetoidFun/inv_strext.con.
+inline "cic:/CoRN/algebra/CSetoidFun/inv_strext.con".
-inline cic:/CoRN/algebra/CSetoidFun/Inv.con.
+inline "cic:/CoRN/algebra/CSetoidFun/Inv.con".
(* UNEXPORTED
Implicit Arguments Inv [A B].
*)
(* UNEXPORTED
Implicit Arguments Inv [A B].
*)
-inline cic:/CoRN/algebra/CSetoidFun/Inv_bij.con.
+inline "cic:/CoRN/algebra/CSetoidFun/Inv_bij.con".
(* UNEXPORTED
End bijections.
(* UNEXPORTED
End bijections.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSetoidInc".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSetoidInc".
(* $Id: CSetoidInc.v,v 1.3 2004/04/22 14:49:43 lcf Exp $ *)
(*#* printing included %\ensuremath{\subseteq}% #⊆# *)
(* $Id: CSetoidInc.v,v 1.3 2004/04/22 14:49:43 lcf Exp $ *)
(*#* printing included %\ensuremath{\subseteq}% #⊆# *)
-(* INCLUDE
-CSetoidFun
-*)
+include "algebra/CSetoidFun.ma".
(* UNEXPORTED
Section inclusion.
(* UNEXPORTED
Section inclusion.
Let [S] be a setoid, and [P], [Q], [R] be predicates on [S]. *)
Let [S] be a setoid, and [P], [Q], [R] be predicates on [S]. *)
-inline cic:/CoRN/algebra/CSetoidInc/S.var.
+inline "cic:/CoRN/algebra/CSetoidInc/S.var".
-inline cic:/CoRN/algebra/CSetoidInc/included.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included.con".
(* UNEXPORTED
Section Basics.
*)
(* UNEXPORTED
Section Basics.
*)
-inline cic:/CoRN/algebra/CSetoidInc/P.var.
+inline "cic:/CoRN/algebra/CSetoidInc/P.var".
-inline cic:/CoRN/algebra/CSetoidInc/Q.var.
+inline "cic:/CoRN/algebra/CSetoidInc/Q.var".
-inline cic:/CoRN/algebra/CSetoidInc/R.var.
+inline "cic:/CoRN/algebra/CSetoidInc/R.var".
-inline cic:/CoRN/algebra/CSetoidInc/included_refl.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_refl.con".
-inline cic:/CoRN/algebra/CSetoidInc/included_trans.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_trans.con".
-inline cic:/CoRN/algebra/CSetoidInc/included_conj.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_conj.con".
-inline cic:/CoRN/algebra/CSetoidInc/included_conj'.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_conj'.con".
-inline cic:/CoRN/algebra/CSetoidInc/included_conj''.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_conj''.con".
-inline cic:/CoRN/algebra/CSetoidInc/included_conj_lft.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_conj_lft.con".
-inline cic:/CoRN/algebra/CSetoidInc/included_conj_rht.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_conj_rht.con".
-inline cic:/CoRN/algebra/CSetoidInc/included_extend.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_extend.con".
(* UNEXPORTED
End Basics.
(* UNEXPORTED
End Basics.
-inline cic:/CoRN/algebra/CSetoidInc/F.var.
+inline "cic:/CoRN/algebra/CSetoidInc/F.var".
-inline cic:/CoRN/algebra/CSetoidInc/G.var.
+inline "cic:/CoRN/algebra/CSetoidInc/G.var".
-inline cic:/CoRN/algebra/CSetoidInc/P.con.
+inline "cic:/CoRN/algebra/CSetoidInc/P.con".
-inline cic:/CoRN/algebra/CSetoidInc/Q.con.
+inline "cic:/CoRN/algebra/CSetoidInc/Q.con".
-inline cic:/CoRN/algebra/CSetoidInc/R.var.
+inline "cic:/CoRN/algebra/CSetoidInc/R.var".
-inline cic:/CoRN/algebra/CSetoidInc/included_FComp.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_FComp.con".
-inline cic:/CoRN/algebra/CSetoidInc/included_FComp'.con.
+inline "cic:/CoRN/algebra/CSetoidInc/included_FComp'.con".
(* UNEXPORTED
End inclusion.
(* UNEXPORTED
End inclusion.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSetoids".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSetoids".
(* $Id.v,v 1.18 2002/11/25 14:43:42 lcf Exp $ *)
(*#* printing [=] %\ensuremath{\equiv}% #≡# *)
(* $Id.v,v 1.18 2002/11/25 14:43:42 lcf Exp $ *)
(*#* printing [=] %\ensuremath{\equiv}% #≡# *)
i.e.%\% a set with an equivalence relation and an apartness relation compatible with it.
*)
i.e.%\% a set with an equivalence relation and an apartness relation compatible with it.
*)
+include "algebra/CLogic.ma".
+include "tactics/Step.ma".
-inline cic:/CoRN/algebra/CSetoids/Relation.con.
+inline "cic:/CoRN/algebra/CSetoids/Relation.con".
Section Properties_of_relations.
*)
Section Properties_of_relations.
*)
-inline cic:/CoRN/algebra/CSetoids/A.var.
+inline "cic:/CoRN/algebra/CSetoids/A.var".
-inline cic:/CoRN/algebra/CSetoids/irreflexive.con.
+inline "cic:/CoRN/algebra/CSetoids/irreflexive.con".
-inline cic:/CoRN/algebra/CSetoids/cotransitive.con.
+inline "cic:/CoRN/algebra/CSetoids/cotransitive.con".
-inline cic:/CoRN/algebra/CSetoids/tight_apart.con.
+inline "cic:/CoRN/algebra/CSetoids/tight_apart.con".
-inline cic:/CoRN/algebra/CSetoids/antisymmetric.con.
+inline "cic:/CoRN/algebra/CSetoids/antisymmetric.con".
(* UNEXPORTED
End Properties_of_relations.
(* UNEXPORTED
End Properties_of_relations.
Apartness, being the main relation, needs to be [CProp]-valued. Equality,
as it is characterized by a negative statement, lives in [Prop]. *)
Apartness, being the main relation, needs to be [CProp]-valued. Equality,
as it is characterized by a negative statement, lives in [Prop]. *)
-inline cic:/CoRN/algebra/CSetoids/is_CSetoid.ind.
+inline "cic:/CoRN/algebra/CSetoids/is_CSetoid.ind".
+
+inline "cic:/CoRN/algebra/CSetoids/CSetoid.ind".
-inline cic:/CoRN/algebra/CSetoids/CSetoid.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/cs_crr.con" 0 (* compounds *).
(* UNEXPORTED
Implicit Arguments cs_eq [c].
(* UNEXPORTED
Implicit Arguments cs_eq [c].
-inline cic:/CoRN/algebra/CSetoids/cs_neq.con.
+inline "cic:/CoRN/algebra/CSetoids/cs_neq.con".
(* UNEXPORTED
Implicit Arguments cs_neq [S].
(* UNEXPORTED
Implicit Arguments cs_neq [S].
Section CSetoid_axioms.
*)
Section CSetoid_axioms.
*)
-inline cic:/CoRN/algebra/CSetoids/S.var.
+inline "cic:/CoRN/algebra/CSetoids/S.var".
-inline cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con.
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con".
-inline cic:/CoRN/algebra/CSetoids/ap_irreflexive.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_irreflexive.con".
-inline cic:/CoRN/algebra/CSetoids/ap_symmetric.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_symmetric.con".
-inline cic:/CoRN/algebra/CSetoids/ap_cotransitive.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_cotransitive.con".
-inline cic:/CoRN/algebra/CSetoids/ap_tight.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_tight.con".
(* UNEXPORTED
End CSetoid_axioms.
(* UNEXPORTED
End CSetoid_axioms.
Section CSetoid_basics.
*)
Section CSetoid_basics.
*)
-inline cic:/CoRN/algebra/CSetoids/S.var.
+inline "cic:/CoRN/algebra/CSetoids/S.var".
In `there exists a unique [a:S] such that %\ldots%#...#', we now mean unique with respect to the setoid equality. We use [ex_unq] to denote unique existence.
*)
In `there exists a unique [a:S] such that %\ldots%#...#', we now mean unique with respect to the setoid equality. We use [ex_unq] to denote unique existence.
*)
-inline cic:/CoRN/algebra/CSetoids/ex_unq.con.
+inline "cic:/CoRN/algebra/CSetoids/ex_unq.con".
-inline cic:/CoRN/algebra/CSetoids/eq_reflexive.con.
+inline "cic:/CoRN/algebra/CSetoids/eq_reflexive.con".
-inline cic:/CoRN/algebra/CSetoids/eq_symmetric.con.
+inline "cic:/CoRN/algebra/CSetoids/eq_symmetric.con".
-inline cic:/CoRN/algebra/CSetoids/eq_transitive.con.
+inline "cic:/CoRN/algebra/CSetoids/eq_transitive.con".
(*#*
%\begin{shortcoming}%
(*#*
%\begin{shortcoming}%
%\end{nameconvention}%
*)
%\end{nameconvention}%
*)
-inline cic:/CoRN/algebra/CSetoids/eq_reflexive_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/eq_reflexive_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/eq_symmetric_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/eq_symmetric_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/eq_transitive_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/eq_transitive_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/eq_wdl.con.
+inline "cic:/CoRN/algebra/CSetoids/eq_wdl.con".
-inline cic:/CoRN/algebra/CSetoids/ap_irreflexive_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_irreflexive_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/ap_cotransitive_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_cotransitive_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/ap_symmetric_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_symmetric_unfolded.con".
(*#*
%\begin{shortcoming}%
(*#*
%\begin{shortcoming}%
-inline cic:/CoRN/algebra/CSetoids/eq_imp_not_ap.con.
+inline "cic:/CoRN/algebra/CSetoids/eq_imp_not_ap.con".
-inline cic:/CoRN/algebra/CSetoids/not_ap_imp_eq.con.
+inline "cic:/CoRN/algebra/CSetoids/not_ap_imp_eq.con".
-inline cic:/CoRN/algebra/CSetoids/neq_imp_notnot_ap.con.
+inline "cic:/CoRN/algebra/CSetoids/neq_imp_notnot_ap.con".
-inline cic:/CoRN/algebra/CSetoids/notnot_ap_imp_neq.con.
+inline "cic:/CoRN/algebra/CSetoids/notnot_ap_imp_neq.con".
-inline cic:/CoRN/algebra/CSetoids/ap_imp_neq.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_imp_neq.con".
-inline cic:/CoRN/algebra/CSetoids/not_neq_imp_eq.con.
+inline "cic:/CoRN/algebra/CSetoids/not_neq_imp_eq.con".
-inline cic:/CoRN/algebra/CSetoids/eq_imp_not_neq.con.
+inline "cic:/CoRN/algebra/CSetoids/eq_imp_not_neq.con".
(*#* **The product of setoids *)
(*#* **The product of setoids *)
-inline cic:/CoRN/algebra/CSetoids/prod_ap.con.
+inline "cic:/CoRN/algebra/CSetoids/prod_ap.con".
-inline cic:/CoRN/algebra/CSetoids/prod_eq.con.
+inline "cic:/CoRN/algebra/CSetoids/prod_eq.con".
-inline cic:/CoRN/algebra/CSetoids/prodcsetoid_is_CSetoid.con.
+inline "cic:/CoRN/algebra/CSetoids/prodcsetoid_is_CSetoid.con".
-inline cic:/CoRN/algebra/CSetoids/ProdCSetoid.con.
+inline "cic:/CoRN/algebra/CSetoids/ProdCSetoid.con".
(* UNEXPORTED
End product_csetoid.
(* UNEXPORTED
End product_csetoid.
Section CSetoid_relations_and_predicates.
*)
Section CSetoid_relations_and_predicates.
*)
-inline cic:/CoRN/algebra/CSetoids/S.var.
+inline "cic:/CoRN/algebra/CSetoids/S.var".
Section CSetoidPredicates.
*)
Section CSetoidPredicates.
*)
-inline cic:/CoRN/algebra/CSetoids/P.var.
+inline "cic:/CoRN/algebra/CSetoids/P.var".
-inline cic:/CoRN/algebra/CSetoids/pred_strong_ext.con.
+inline "cic:/CoRN/algebra/CSetoids/pred_strong_ext.con".
-inline cic:/CoRN/algebra/CSetoids/pred_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/pred_wd.con".
(* UNEXPORTED
End CSetoidPredicates.
*)
(* UNEXPORTED
End CSetoidPredicates.
*)
-inline cic:/CoRN/algebra/CSetoids/CSetoid_predicate.ind.
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_predicate.ind".
-inline cic:/CoRN/algebra/CSetoids/csp_wd.con.
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/csp_pred.con" 0 (* compounds *).
+
+inline "cic:/CoRN/algebra/CSetoids/csp_wd.con".
(*#* Similar, with [Prop] instead of [CProp]. *)
(*#* Similar, with [Prop] instead of [CProp]. *)
Section CSetoidPPredicates.
*)
Section CSetoidPPredicates.
*)
-inline cic:/CoRN/algebra/CSetoids/P.var.
+inline "cic:/CoRN/algebra/CSetoids/P.var".
-inline cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con.
+inline "cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con".
-inline cic:/CoRN/algebra/CSetoids/pred_wd'.con.
+inline "cic:/CoRN/algebra/CSetoids/pred_wd'.con".
(* UNEXPORTED
End CSetoidPPredicates.
(* UNEXPORTED
End CSetoidPPredicates.
(*#* ***Definition of a setoid predicate *)
(*#* ***Definition of a setoid predicate *)
-inline cic:/CoRN/algebra/CSetoids/CSetoid_predicate'.ind.
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_predicate'.ind".
+
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/csp'_pred.con" 0 (* compounds *).
-inline cic:/CoRN/algebra/CSetoids/csp'_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/csp'_wd.con".
Section CsetoidRelations.
*)
Section CsetoidRelations.
*)
-inline cic:/CoRN/algebra/CSetoids/R.var.
+inline "cic:/CoRN/algebra/CSetoids/R.var".
-inline cic:/CoRN/algebra/CSetoids/rel_wdr.con.
+inline "cic:/CoRN/algebra/CSetoids/rel_wdr.con".
-inline cic:/CoRN/algebra/CSetoids/rel_wdl.con.
+inline "cic:/CoRN/algebra/CSetoids/rel_wdl.con".
-inline cic:/CoRN/algebra/CSetoids/rel_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/rel_strext.con".
-inline cic:/CoRN/algebra/CSetoids/rel_strext_lft.con.
+inline "cic:/CoRN/algebra/CSetoids/rel_strext_lft.con".
-inline cic:/CoRN/algebra/CSetoids/rel_strext_rht.con.
+inline "cic:/CoRN/algebra/CSetoids/rel_strext_rht.con".
-inline cic:/CoRN/algebra/CSetoids/rel_strext_imp_lftarg.con.
+inline "cic:/CoRN/algebra/CSetoids/rel_strext_imp_lftarg.con".
-inline cic:/CoRN/algebra/CSetoids/rel_strext_imp_rhtarg.con.
+inline "cic:/CoRN/algebra/CSetoids/rel_strext_imp_rhtarg.con".
-inline cic:/CoRN/algebra/CSetoids/rel_strextarg_imp_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/rel_strextarg_imp_strext.con".
(*#* ***Definition of a setoid relation
The type of relations over a setoid. *)
(*#* ***Definition of a setoid relation
The type of relations over a setoid. *)
-inline cic:/CoRN/algebra/CSetoids/CSetoid_relation.ind.
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_relation.ind".
+
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/csr_rel.con" 0 (* compounds *).
(*#* ***[CProp] Relations
%\begin{convention}%
(*#* ***[CProp] Relations
%\begin{convention}%
Section CCsetoidRelations.
*)
Section CCsetoidRelations.
*)
-inline cic:/CoRN/algebra/CSetoids/R.var.
+inline "cic:/CoRN/algebra/CSetoids/R.var".
-inline cic:/CoRN/algebra/CSetoids/Crel_wdr.con.
+inline "cic:/CoRN/algebra/CSetoids/Crel_wdr.con".
-inline cic:/CoRN/algebra/CSetoids/Crel_wdl.con.
+inline "cic:/CoRN/algebra/CSetoids/Crel_wdl.con".
-inline cic:/CoRN/algebra/CSetoids/Crel_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/Crel_strext.con".
-inline cic:/CoRN/algebra/CSetoids/Crel_strext_lft.con.
+inline "cic:/CoRN/algebra/CSetoids/Crel_strext_lft.con".
-inline cic:/CoRN/algebra/CSetoids/Crel_strext_rht.con.
+inline "cic:/CoRN/algebra/CSetoids/Crel_strext_rht.con".
-inline cic:/CoRN/algebra/CSetoids/Crel_strext_imp_lftarg.con.
+inline "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_lftarg.con".
-inline cic:/CoRN/algebra/CSetoids/Crel_strext_imp_rhtarg.con.
+inline "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_rhtarg.con".
-inline cic:/CoRN/algebra/CSetoids/Crel_strextarg_imp_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/Crel_strextarg_imp_strext.con".
The type of relations over a setoid. *)
The type of relations over a setoid. *)
-inline cic:/CoRN/algebra/CSetoids/CCSetoid_relation.ind.
+inline "cic:/CoRN/algebra/CSetoids/CCSetoid_relation.ind".
-inline cic:/CoRN/algebra/CSetoids/Ccsr_wdr.con.
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/Ccsr_rel.con" 0 (* compounds *).
-inline cic:/CoRN/algebra/CSetoids/Ccsr_wdl.con.
+inline "cic:/CoRN/algebra/CSetoids/Ccsr_wdr.con".
+
+inline "cic:/CoRN/algebra/CSetoids/Ccsr_wdl.con".
-inline cic:/CoRN/algebra/CSetoids/ap_wdr.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_wdr.con".
-inline cic:/CoRN/algebra/CSetoids/ap_wdl.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_wdl.con".
-inline cic:/CoRN/algebra/CSetoids/ap_wdr_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_wdr_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/ap_wdl_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_wdl_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/ap_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/ap_strext.con".
-inline cic:/CoRN/algebra/CSetoids/predS_well_def.con.
+inline "cic:/CoRN/algebra/CSetoids/predS_well_def.con".
Section CSetoid_functions.
*)
Section CSetoid_functions.
*)
-inline cic:/CoRN/algebra/CSetoids/S1.var.
+inline "cic:/CoRN/algebra/CSetoids/S1.var".
-inline cic:/CoRN/algebra/CSetoids/S2.var.
+inline "cic:/CoRN/algebra/CSetoids/S2.var".
-inline cic:/CoRN/algebra/CSetoids/S3.var.
+inline "cic:/CoRN/algebra/CSetoids/S3.var".
(* UNEXPORTED
Section unary_functions.
(* UNEXPORTED
Section unary_functions.
[f] is a function from (the carrier of) [S1] to
(the carrier of) [S2]. *)
[f] is a function from (the carrier of) [S1] to
(the carrier of) [S2]. *)
-inline cic:/CoRN/algebra/CSetoids/f.var.
+inline "cic:/CoRN/algebra/CSetoids/f.var".
-inline cic:/CoRN/algebra/CSetoids/fun_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/fun_wd.con".
-inline cic:/CoRN/algebra/CSetoids/fun_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/fun_strext.con".
-inline cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con".
-inline cic:/CoRN/algebra/CSetoids/CSetoid_fun.ind.
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_fun.ind".
+
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/csf_fun.con" 0 (* compounds *).
-inline cic:/CoRN/algebra/CSetoids/csf_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/csf_wd.con".
-inline cic:/CoRN/algebra/CSetoids/Const_CSetoid_fun.con.
+inline "cic:/CoRN/algebra/CSetoids/Const_CSetoid_fun.con".
[f] is a function from [S1] and [S2] to [S3].
*)
[f] is a function from [S1] and [S2] to [S3].
*)
-inline cic:/CoRN/algebra/CSetoids/f.var.
+inline "cic:/CoRN/algebra/CSetoids/f.var".
-inline cic:/CoRN/algebra/CSetoids/bin_fun_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_fun_wd.con".
-inline cic:/CoRN/algebra/CSetoids/bin_fun_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_fun_strext.con".
-inline cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con".
-inline cic:/CoRN/algebra/CSetoids/CSetoid_bin_fun.ind.
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_bin_fun.ind".
-inline cic:/CoRN/algebra/CSetoids/csbf_wd.con.
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/csbf_fun.con" 0 (* compounds *).
-inline cic:/CoRN/algebra/CSetoids/csf_wd_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/csbf_wd.con".
-inline cic:/CoRN/algebra/CSetoids/csf_strext_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/csf_wd_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/csbf_wd_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/csf_strext_unfolded.con".
+
+inline "cic:/CoRN/algebra/CSetoids/csbf_wd_unfolded.con".
(* UNEXPORTED
End CSetoid_functions.
(* UNEXPORTED
End CSetoid_functions.
Section csetoid_inner_ops.
*)
Section csetoid_inner_ops.
*)
-inline cic:/CoRN/algebra/CSetoids/S.var.
+inline "cic:/CoRN/algebra/CSetoids/S.var".
(*#* Properties of binary operations *)
(*#* Properties of binary operations *)
-inline cic:/CoRN/algebra/CSetoids/commutes.con.
+inline "cic:/CoRN/algebra/CSetoids/commutes.con".
-inline cic:/CoRN/algebra/CSetoids/associative.con.
+inline "cic:/CoRN/algebra/CSetoids/associative.con".
(*#* Well-defined unary operations on a setoid. *)
(*#* Well-defined unary operations on a setoid. *)
-inline cic:/CoRN/algebra/CSetoids/un_op_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/un_op_wd.con".
-inline cic:/CoRN/algebra/CSetoids/un_op_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/un_op_strext.con".
-inline cic:/CoRN/algebra/CSetoids/CSetoid_un_op.con.
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_un_op.con".
-inline cic:/CoRN/algebra/CSetoids/Build_CSetoid_un_op.con.
+inline "cic:/CoRN/algebra/CSetoids/Build_CSetoid_un_op.con".
-inline cic:/CoRN/algebra/CSetoids/id_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/id_strext.con".
-inline cic:/CoRN/algebra/CSetoids/id_pres_eq.con.
+inline "cic:/CoRN/algebra/CSetoids/id_pres_eq.con".
-inline cic:/CoRN/algebra/CSetoids/id_un_op.con.
+inline "cic:/CoRN/algebra/CSetoids/id_un_op.con".
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/un_op_fun.con" 0 (* compounds *).
+
(* end hide *)
(* Begin_SpecReals *)
(* end hide *)
(* Begin_SpecReals *)
-inline cic:/CoRN/algebra/CSetoids/cs_un_op_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/cs_un_op_strext.con".
-inline cic:/CoRN/algebra/CSetoids/un_op_wd_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/un_op_wd_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/un_op_strext_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/un_op_strext_unfolded.con".
(*#* Well-defined binary operations on a setoid. *)
(*#* Well-defined binary operations on a setoid. *)
-inline cic:/CoRN/algebra/CSetoids/bin_op_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op_wd.con".
-inline cic:/CoRN/algebra/CSetoids/bin_op_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op_strext.con".
-inline cic:/CoRN/algebra/CSetoids/CSetoid_bin_op.con.
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_bin_op.con".
-inline cic:/CoRN/algebra/CSetoids/Build_CSetoid_bin_op.con.
+inline "cic:/CoRN/algebra/CSetoids/Build_CSetoid_bin_op.con".
-inline cic:/CoRN/algebra/CSetoids/cs_bin_op_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/cs_bin_op_wd.con".
-inline cic:/CoRN/algebra/CSetoids/cs_bin_op_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/cs_bin_op_strext.con".
(* Begin_SpecReals *)
(* begin hide *)
(* Begin_SpecReals *)
(* begin hide *)
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/bin_op_bin_fun.con" 0 (* compounds *).
+
(* end hide *)
(* End_SpecReals *)
(* end hide *)
(* End_SpecReals *)
-inline cic:/CoRN/algebra/CSetoids/bin_op_wd_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op_wd_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/bin_op_strext_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op_strext_unfolded.con".
-inline cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_lft.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_lft.con".
-inline cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_rht.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_rht.con".
-inline cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_lft.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_lft.con".
-inline cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_rht.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_rht.con".
-inline cic:/CoRN/algebra/CSetoids/bin_op2un_op_rht.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op2un_op_rht.con".
-inline cic:/CoRN/algebra/CSetoids/bin_op2un_op_lft.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op2un_op_lft.con".
Section csetoid_outer_ops.
*)
Section csetoid_outer_ops.
*)
-inline cic:/CoRN/algebra/CSetoids/S1.var.
+inline "cic:/CoRN/algebra/CSetoids/S1.var".
-inline cic:/CoRN/algebra/CSetoids/S2.var.
+inline "cic:/CoRN/algebra/CSetoids/S2.var".
(*#*
Well-defined outer operations on a setoid.
*)
(*#*
Well-defined outer operations on a setoid.
*)
-inline cic:/CoRN/algebra/CSetoids/outer_op_well_def.con.
+inline "cic:/CoRN/algebra/CSetoids/outer_op_well_def.con".
-inline cic:/CoRN/algebra/CSetoids/outer_op_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/outer_op_strext.con".
-inline cic:/CoRN/algebra/CSetoids/CSetoid_outer_op.con.
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_outer_op.con".
-inline cic:/CoRN/algebra/CSetoids/Build_CSetoid_outer_op.con.
+inline "cic:/CoRN/algebra/CSetoids/Build_CSetoid_outer_op.con".
-inline cic:/CoRN/algebra/CSetoids/csoo_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/csoo_wd.con".
-inline cic:/CoRN/algebra/CSetoids/csoo_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/csoo_strext.con".
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/outer_op_bin_fun.con" 0 (* compounds *).
+
-inline cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con.
+inline "cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con".
(* UNEXPORTED
End csetoid_outer_ops.
(* UNEXPORTED
End csetoid_outer_ops.
-inline cic:/CoRN/algebra/CSetoids/S.var.
+inline "cic:/CoRN/algebra/CSetoids/S.var".
+
+inline "cic:/CoRN/algebra/CSetoids/P.var".
-inline cic:/CoRN/algebra/CSetoids/P.var.
+inline "cic:/CoRN/algebra/CSetoids/subcsetoid_crr.ind".
-inline cic:/CoRN/algebra/CSetoids/subcsetoid_crr.ind.
+coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/scs_elem.con" 0 (* compounds *).
(*#* Though [scs_elem] is declared as a coercion, it does not satisfy the
uniform inheritance condition and will not be inserted. However it will
also not be printed, which is handy.
*)
(*#* Though [scs_elem] is declared as a coercion, it does not satisfy the
uniform inheritance condition and will not be inserted. However it will
also not be printed, which is handy.
*)
-inline cic:/CoRN/algebra/CSetoids/restrict_relation.con.
+inline "cic:/CoRN/algebra/CSetoids/restrict_relation.con".
-inline cic:/CoRN/algebra/CSetoids/Crestrict_relation.con.
+inline "cic:/CoRN/algebra/CSetoids/Crestrict_relation.con".
-inline cic:/CoRN/algebra/CSetoids/subcsetoid_eq.con.
+inline "cic:/CoRN/algebra/CSetoids/subcsetoid_eq.con".
-inline cic:/CoRN/algebra/CSetoids/subcsetoid_ap.con.
+inline "cic:/CoRN/algebra/CSetoids/subcsetoid_ap.con".
-inline cic:/CoRN/algebra/CSetoids/subcsetoid_equiv.con.
+inline "cic:/CoRN/algebra/CSetoids/subcsetoid_equiv.con".
-inline cic:/CoRN/algebra/CSetoids/subcsetoid_is_CSetoid.con.
+inline "cic:/CoRN/algebra/CSetoids/subcsetoid_is_CSetoid.con".
-inline cic:/CoRN/algebra/CSetoids/Build_SubCSetoid.con.
+inline "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid.con".
Section SubCSetoid_unary_operations.
*)
Section SubCSetoid_unary_operations.
*)
-inline cic:/CoRN/algebra/CSetoids/f.var.
+inline "cic:/CoRN/algebra/CSetoids/f.var".
-inline cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con.
+inline "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con".
(*#*
%\begin{convention}%
Assume [pr:un_op_pres_pred].
%\end{convention}% *)
(*#*
%\begin{convention}%
Assume [pr:un_op_pres_pred].
%\end{convention}% *)
-inline cic:/CoRN/algebra/CSetoids/pr.var.
+inline "cic:/CoRN/algebra/CSetoids/pr.var".
-inline cic:/CoRN/algebra/CSetoids/restr_un_op.con.
+inline "cic:/CoRN/algebra/CSetoids/restr_un_op.con".
-inline cic:/CoRN/algebra/CSetoids/restr_un_op_wd.con.
+inline "cic:/CoRN/algebra/CSetoids/restr_un_op_wd.con".
-inline cic:/CoRN/algebra/CSetoids/restr_un_op_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/restr_un_op_strext.con".
-inline cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_un_op.con.
+inline "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_un_op.con".
(* UNEXPORTED
End SubCSetoid_unary_operations.
(* UNEXPORTED
End SubCSetoid_unary_operations.
Section SubCSetoid_binary_operations.
*)
Section SubCSetoid_binary_operations.
*)
-inline cic:/CoRN/algebra/CSetoids/f.var.
+inline "cic:/CoRN/algebra/CSetoids/f.var".
-inline cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con.
+inline "cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con".
(*#*
%\begin{convention}%
(*#*
%\begin{convention}%
-inline cic:/CoRN/algebra/CSetoids/pr.var.
+inline "cic:/CoRN/algebra/CSetoids/pr.var".
-inline cic:/CoRN/algebra/CSetoids/restr_bin_op.con.
+inline "cic:/CoRN/algebra/CSetoids/restr_bin_op.con".
-inline cic:/CoRN/algebra/CSetoids/restr_bin_op_well_def.con.
+inline "cic:/CoRN/algebra/CSetoids/restr_bin_op_well_def.con".
-inline cic:/CoRN/algebra/CSetoids/restr_bin_op_strext.con.
+inline "cic:/CoRN/algebra/CSetoids/restr_bin_op_strext.con".
-inline cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_bin_op.con.
+inline "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_bin_op.con".
-inline cic:/CoRN/algebra/CSetoids/restr_f_assoc.con.
+inline "cic:/CoRN/algebra/CSetoids/restr_f_assoc.con".
(* UNEXPORTED
End SubCSetoid_binary_operations.
(* UNEXPORTED
End SubCSetoid_binary_operations.
-inline cic:/CoRN/algebra/CSetoids/proper_caseZ_diff_CS.con.
+inline "cic:/CoRN/algebra/CSetoids/proper_caseZ_diff_CS.con".
(*#*
Finally, we characterize functions defined on the natural numbers also as setoid functions, similarly to what we already did for predicates.
*)
(*#*
Finally, we characterize functions defined on the natural numbers also as setoid functions, similarly to what we already did for predicates.
*)
-inline cic:/CoRN/algebra/CSetoids/nat_less_n_fun.con.
+inline "cic:/CoRN/algebra/CSetoids/nat_less_n_fun.con".
-inline cic:/CoRN/algebra/CSetoids/nat_less_n_fun'.con.
+inline "cic:/CoRN/algebra/CSetoids/nat_less_n_fun'.con".
(* UNEXPORTED
Implicit Arguments nat_less_n_fun [S n].
(* UNEXPORTED
Implicit Arguments nat_less_n_fun [S n].
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSums".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSums".
(* $Id: CSums.v,v 1.8 2004/04/23 10:00:54 lcf Exp $ *)
(*#* printing Sum0 %\ensuremath{\sum_0}% #∑<sub>0</sub># *)
(* $Id: CSums.v,v 1.8 2004/04/23 10:00:54 lcf Exp $ *)
(*#* printing Sum0 %\ensuremath{\sum_0}% #∑<sub>0</sub># *)
(*#* printing Sumx %\ensuremath{\sum'}% #∑'&*)
(*#* printing Sumx %\ensuremath{\sum'}% #∑'&*)
-(* INCLUDE
-CAbGroups
-*)
-
-(* INCLUDE
-Peano_dec
-*)
+include "algebra/CAbGroups.ma".
-inline cic:/CoRN/algebra/CSums/G.var.
+inline "cic:/CoRN/algebra/CSums/G.var".
(* Sum1 and Sum use subtraction *)
(* Sum1 and Sum use subtraction *)
-inline cic:/CoRN/algebra/CSums/Sumlist.con.
+inline "cic:/CoRN/algebra/CSums/Sumlist.con".
-inline cic:/CoRN/algebra/CSums/Sumx.con.
+inline "cic:/CoRN/algebra/CSums/Sumx.con".
(*#*
It is sometimes useful to view a function defined on $\{0,\ldots,i-1\}$
(*#*
It is sometimes useful to view a function defined on $\{0,\ldots,i-1\}$
[Zero] when the input is greater than or equal to [i].
*)
[Zero] when the input is greater than or equal to [i].
*)
-inline cic:/CoRN/algebra/CSums/part_tot_nat_fun.con.
+inline "cic:/CoRN/algebra/CSums/part_tot_nat_fun.con".
-inline cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch1.con.
+inline "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch1.con".
-inline cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch2.con.
+inline "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch2.con".
(*#* [Sum0] defines the sum for [i=0..(n-1)] *)
(*#* [Sum0] defines the sum for [i=0..(n-1)] *)
-inline cic:/CoRN/algebra/CSums/Sum0.con.
+inline "cic:/CoRN/algebra/CSums/Sum0.con".
(*#* [Sum1] defines the sum for [i=m..(n-1)] *)
(*#* [Sum1] defines the sum for [i=m..(n-1)] *)
-inline cic:/CoRN/algebra/CSums/Sum1.con.
+inline "cic:/CoRN/algebra/CSums/Sum1.con".
-inline cic:/CoRN/algebra/CSums/Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sum.con".
(* Sum i=m..n *)
(*#* [Sum2] is similar to [Sum1], but does not require the summand to be
defined outside where it is being added. *)
(* Sum i=m..n *)
(*#* [Sum2] is similar to [Sum1], but does not require the summand to be
defined outside where it is being added. *)
-inline cic:/CoRN/algebra/CSums/Sum2.con.
+inline "cic:/CoRN/algebra/CSums/Sum2.con".
-inline cic:/CoRN/algebra/CSums/Sum_one.con.
+inline "cic:/CoRN/algebra/CSums/Sum_one.con".
(* UNEXPORTED
Hint Resolve Sum_one: algebra.
*)
(* UNEXPORTED
Hint Resolve Sum_one: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_empty.con.
+inline "cic:/CoRN/algebra/CSums/Sum_empty.con".
(* UNEXPORTED
Hint Resolve Sum_empty: algebra.
*)
(* UNEXPORTED
Hint Resolve Sum_empty: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sum_Sum.con".
(* UNEXPORTED
Hint Resolve Sum_Sum: algebra.
*)
(* UNEXPORTED
Hint Resolve Sum_Sum: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_first.con.
+inline "cic:/CoRN/algebra/CSums/Sum_first.con".
-inline cic:/CoRN/algebra/CSums/Sum_last.con.
+inline "cic:/CoRN/algebra/CSums/Sum_last.con".
(* UNEXPORTED
Hint Resolve Sum_last: algebra.
*)
(* UNEXPORTED
Hint Resolve Sum_last: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_last'.con.
+inline "cic:/CoRN/algebra/CSums/Sum_last'.con".
(*#*
We add some extensionality results which will be quite useful
when working with integration.
*)
(*#*
We add some extensionality results which will be quite useful
when working with integration.
*)
-inline cic:/CoRN/algebra/CSums/Sum0_strext.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_strext.con".
-inline cic:/CoRN/algebra/CSums/Sum_strext.con.
+inline "cic:/CoRN/algebra/CSums/Sum_strext.con".
-inline cic:/CoRN/algebra/CSums/Sumx_strext.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_strext.con".
-inline cic:/CoRN/algebra/CSums/Sum0_strext'.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_strext'.con".
-inline cic:/CoRN/algebra/CSums/Sum_strext'.con.
+inline "cic:/CoRN/algebra/CSums/Sum_strext'.con".
-inline cic:/CoRN/algebra/CSums/Sum0_wd.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_wd.con".
-inline cic:/CoRN/algebra/CSums/Sum_wd.con.
+inline "cic:/CoRN/algebra/CSums/Sum_wd.con".
-inline cic:/CoRN/algebra/CSums/Sumx_wd.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_wd.con".
-inline cic:/CoRN/algebra/CSums/Sum_wd'.con.
+inline "cic:/CoRN/algebra/CSums/Sum_wd'.con".
-inline cic:/CoRN/algebra/CSums/Sum2_wd.con.
+inline "cic:/CoRN/algebra/CSums/Sum2_wd.con".
-inline cic:/CoRN/algebra/CSums/Sum0_plus_Sum0.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_plus_Sum0.con".
(* UNEXPORTED
Hint Resolve Sum0_plus_Sum0: algebra.
*)
(* UNEXPORTED
Hint Resolve Sum0_plus_Sum0: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_plus_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sum_plus_Sum.con".
-inline cic:/CoRN/algebra/CSums/Sumx_plus_Sumx.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_plus_Sumx.con".
-inline cic:/CoRN/algebra/CSums/Sum2_plus_Sum2.con.
+inline "cic:/CoRN/algebra/CSums/Sum2_plus_Sum2.con".
-inline cic:/CoRN/algebra/CSums/inv_Sum0.con.
+inline "cic:/CoRN/algebra/CSums/inv_Sum0.con".
(* UNEXPORTED
Hint Resolve inv_Sum0: algebra.
*)
(* UNEXPORTED
Hint Resolve inv_Sum0: algebra.
*)
-inline cic:/CoRN/algebra/CSums/inv_Sum.con.
+inline "cic:/CoRN/algebra/CSums/inv_Sum.con".
(* UNEXPORTED
Hint Resolve inv_Sum: algebra.
*)
(* UNEXPORTED
Hint Resolve inv_Sum: algebra.
*)
-inline cic:/CoRN/algebra/CSums/inv_Sumx.con.
+inline "cic:/CoRN/algebra/CSums/inv_Sumx.con".
-inline cic:/CoRN/algebra/CSums/inv_Sum2.con.
+inline "cic:/CoRN/algebra/CSums/inv_Sum2.con".
-inline cic:/CoRN/algebra/CSums/Sum_minus_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sum_minus_Sum.con".
(* UNEXPORTED
Hint Resolve Sum_minus_Sum: algebra.
*)
(* UNEXPORTED
Hint Resolve Sum_minus_Sum: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sumx_minus_Sumx.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_minus_Sumx.con".
-inline cic:/CoRN/algebra/CSums/Sum2_minus_Sum2.con.
+inline "cic:/CoRN/algebra/CSums/Sum2_minus_Sum2.con".
-inline cic:/CoRN/algebra/CSums/Sum_apzero.con.
+inline "cic:/CoRN/algebra/CSums/Sum_apzero.con".
-inline cic:/CoRN/algebra/CSums/Sum_zero.con.
+inline "cic:/CoRN/algebra/CSums/Sum_zero.con".
-inline cic:/CoRN/algebra/CSums/Sum_term.con.
+inline "cic:/CoRN/algebra/CSums/Sum_term.con".
-inline cic:/CoRN/algebra/CSums/Sum0_shift.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_shift.con".
(* UNEXPORTED
Hint Resolve Sum0_shift: algebra.
*)
(* UNEXPORTED
Hint Resolve Sum0_shift: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_shift.con.
+inline "cic:/CoRN/algebra/CSums/Sum_shift.con".
-inline cic:/CoRN/algebra/CSums/Sum_big_shift.con.
+inline "cic:/CoRN/algebra/CSums/Sum_big_shift.con".
-inline cic:/CoRN/algebra/CSums/Sumx_Sum0.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_Sum0.con".
-inline cic:/CoRN/algebra/CSums/G.var.
+inline "cic:/CoRN/algebra/CSums/G.var".
-inline cic:/CoRN/algebra/CSums/Mengolli_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Mengolli_Sum.con".
-inline cic:/CoRN/algebra/CSums/Mengolli_Sum_gen.con.
+inline "cic:/CoRN/algebra/CSums/Mengolli_Sum_gen.con".
-inline cic:/CoRN/algebra/CSums/str_Mengolli_Sum_gen.con.
+inline "cic:/CoRN/algebra/CSums/str_Mengolli_Sum_gen.con".
-inline cic:/CoRN/algebra/CSums/Sumx_to_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_to_Sum.con".
(* UNEXPORTED
End More_Sums.
(* UNEXPORTED
End More_Sums.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CVectorSpace".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/CVectorSpace".
(* $Id: CVectorSpace.v,v 1.4 2004/04/23 10:00:54 lcf Exp $ *)
(*#* printing ['] %{'}% #'# *)
(* $Id: CVectorSpace.v,v 1.4 2004/04/23 10:00:54 lcf Exp $ *)
(*#* printing ['] %{'}% #'# *)
+include "algebra/CFields.ma".
-inline cic:/CoRN/algebra/CVectorSpace/VSpace.ind.
+inline "cic:/CoRN/algebra/CVectorSpace/VSpace.ind".
+
+coercion "cic:/matita/CoRN-Decl/algebra/CVectorSpace/vs_vs.con" 0 (* compounds *).
-inline cic:/CoRN/algebra/CVectorSpace/F.var.
+inline "cic:/CoRN/algebra/CVectorSpace/F.var".
-inline cic:/CoRN/algebra/CVectorSpace/V.var.
+inline "cic:/CoRN/algebra/CVectorSpace/V.var".
-inline cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con.
+inline "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con".
-inline cic:/CoRN/algebra/CVectorSpace/zero_vs_op.con.
+inline "cic:/CoRN/algebra/CVectorSpace/zero_vs_op.con".
(* UNEXPORTED
Hint Resolve vs_op_zero zero_vs_op: algebra.
*)
(* UNEXPORTED
Hint Resolve vs_op_zero zero_vs_op: algebra.
*)
-inline cic:/CoRN/algebra/CVectorSpace/vs_op_inv_V.con.
+inline "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_V.con".
-inline cic:/CoRN/algebra/CVectorSpace/vs_op_inv_S.con.
+inline "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_S.con".
(* UNEXPORTED
Hint Resolve vs_op_inv_V vs_op_inv_S: algebra.
*)
(* UNEXPORTED
Hint Resolve vs_op_inv_V vs_op_inv_S: algebra.
*)
-inline cic:/CoRN/algebra/CVectorSpace/vs_inv_assoc.con.
+inline "cic:/CoRN/algebra/CVectorSpace/vs_inv_assoc.con".
(* UNEXPORTED
Hint Resolve vs_inv_assoc: algebra.
*)
(* UNEXPORTED
Hint Resolve vs_inv_assoc: algebra.
*)
-inline cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_l.con.
+inline "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_l.con".
-inline cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_r.con.
+inline "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_r.con".
(* note this is the same proof as mult_resp_ap_zero *)
(* note this is the same proof as mult_resp_ap_zero *)
-inline cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_rht.con.
+inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_rht.con".
-inline cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con.
+inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con".
-inline cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con.
+inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con".
(* UNEXPORTED
End VS_basics.
(* UNEXPORTED
End VS_basics.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/Cauchy_COF".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/Cauchy_COF".
(* $Id: Cauchy_COF.v,v 1.8 2004/04/23 10:00:54 lcf Exp $ *)
(* $Id: Cauchy_COF.v,v 1.8 2004/04/23 10:00:54 lcf Exp $ *)
-(* INCLUDE
-COrdCauchy
-*)
+include "algebra/COrdCauchy.ma".
-(* INCLUDE
-RingReflection
-*)
+include "tactics/RingReflection.ma".
(*#*
* The Field of Cauchy Sequences
(*#*
* The Field of Cauchy Sequences
-inline cic:/CoRN/algebra/Cauchy_COF/F.var.
+inline "cic:/CoRN/algebra/Cauchy_COF/F.var".
than the other, equality is the negation of the apartness.
*)
than the other, equality is the negation of the apartness.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_Set.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_Set.con".
(* UNEXPORTED
Section CSetoid_Structure.
*)
(* UNEXPORTED
Section CSetoid_Structure.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_lt.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_lt.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_eq.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_eq.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_lt_cotrans.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_lt_cotrans.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_cotrans.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_cotrans.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_symmetric.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_symmetric.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_lt_irreflexive.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_lt_irreflexive.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_irreflexive.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_irreflexive.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_eq_tight.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_eq_tight.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con".
(* UNEXPORTED
End CSetoid_Structure.
(* UNEXPORTED
End CSetoid_Structure.
are specifically proved are just the necessary ones to get the group axioms.
*)
are specifically proved are just the necessary ones to get the group axioms.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_zero.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_zero.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus_lft_ext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus_lft_ext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus_assoc.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus_assoc.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_zero_lft_unit.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_zero_lft_unit.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus_comm.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus_comm.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_inv.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_inv.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_inv_is_inv.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_inv_is_inv.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_inv_ext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_inv_ext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rinv.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rinv.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_CAbGroup.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_CAbGroup.con".
(* UNEXPORTED
End Group_Structure.
(* UNEXPORTED
End Group_Structure.
Same comments as previously.
*)
Same comments as previously.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_one.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_one.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_one_ap_zero.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_one_ap_zero.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_plus.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_plus.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_minus.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_minus.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_one_rht_unit.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_one_rht_unit.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_comm.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_comm.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_ap_zero'.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_ap_zero'.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_lft_ext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_lft_ext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_rht_ext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_rht_ext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_strext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_strext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rmult.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rmult.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_assoc.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_assoc.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_one_lft_unit.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_one_lft_unit.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_CRing.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_CRing.con".
(* UNEXPORTED
End Ring_Structure.
(* UNEXPORTED
End Ring_Structure.
quite straightforwardly.
*)
quite straightforwardly.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_integral_domain.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_integral_domain.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_recip.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_recip.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_recip_strext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_recip_strext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse'.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse'.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_CField.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_CField.con".
(* UNEXPORTED
End Field_Structure.
(* UNEXPORTED
End Field_Structure.
defined at the beginning.
*)
defined at the beginning.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_lt_strext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_lt_strext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rlt.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rlt.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rlt_transitive.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rlt_transitive.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rlt_strict.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rlt_strict.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus_resp_lt.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus_resp_lt.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_resp_lt.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_resp_lt.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_COrdField.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_COrdField.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_1.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_1.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_2.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_2.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_1.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_1.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Eq_alt_1.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_1.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_2.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_2.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_1.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_1.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con".
(* UNEXPORTED
End Auxiliary.
(* UNEXPORTED
End Auxiliary.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/Expon".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/Expon".
(* $Id: Expon.v,v 1.5 2004/04/23 10:00:54 lcf Exp $ *)
(*#* printing [^^] %\ensuremath{\hat{\ }}% #^# *)
(* $Id: Expon.v,v 1.5 2004/04/23 10:00:54 lcf Exp $ *)
(*#* printing [^^] %\ensuremath{\hat{\ }}% #^# *)
+include "algebra/COrdCauchy.ma".
-(* INCLUDE
-COrdCauchy
-*)
-
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
(*#* *Exponentiation
**More properties about [nexp]
(*#* *Exponentiation
**More properties about [nexp]
-inline cic:/CoRN/algebra/Expon/R.var.
+inline "cic:/CoRN/algebra/Expon/R.var".
-inline cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con.
+inline "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con".
(* UNEXPORTED
Hint Resolve nexp_resp_ap_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve nexp_resp_ap_zero: algebra.
*)
-inline cic:/CoRN/algebra/Expon/nexp_distr_div.con.
+inline "cic:/CoRN/algebra/Expon/nexp_distr_div.con".
-inline cic:/CoRN/algebra/Expon/nexp_distr_div'.con.
+inline "cic:/CoRN/algebra/Expon/nexp_distr_div'.con".
-inline cic:/CoRN/algebra/Expon/small_nexp_resp_lt.con.
+inline "cic:/CoRN/algebra/Expon/small_nexp_resp_lt.con".
-inline cic:/CoRN/algebra/Expon/great_nexp_resp_lt.con.
+inline "cic:/CoRN/algebra/Expon/great_nexp_resp_lt.con".
-inline cic:/CoRN/algebra/Expon/small_nexp_resp_le.con.
+inline "cic:/CoRN/algebra/Expon/small_nexp_resp_le.con".
-inline cic:/CoRN/algebra/Expon/great_nexp_resp_le.con.
+inline "cic:/CoRN/algebra/Expon/great_nexp_resp_le.con".
-inline cic:/CoRN/algebra/Expon/nexp_resp_leEq.con.
+inline "cic:/CoRN/algebra/Expon/nexp_resp_leEq.con".
-inline cic:/CoRN/algebra/Expon/nexp_resp_leEq_one.con.
+inline "cic:/CoRN/algebra/Expon/nexp_resp_leEq_one.con".
-inline cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_even.con.
+inline "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_even.con".
-inline cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_odd.con.
+inline "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_odd.con".
-inline cic:/CoRN/algebra/Expon/nexp_distr_recip.con.
+inline "cic:/CoRN/algebra/Expon/nexp_distr_recip.con".
(* UNEXPORTED
Hint Resolve nexp_distr_recip: algebra.
*)
(* UNEXPORTED
Hint Resolve nexp_distr_recip: algebra.
*)
-inline cic:/CoRN/algebra/Expon/nexp_even_nonneg.con.
+inline "cic:/CoRN/algebra/Expon/nexp_even_nonneg.con".
-inline cic:/CoRN/algebra/Expon/nexp_resp_le'.con.
+inline "cic:/CoRN/algebra/Expon/nexp_resp_le'.con".
-inline cic:/CoRN/algebra/Expon/nexp_resp_le.con.
+inline "cic:/CoRN/algebra/Expon/nexp_resp_le.con".
-inline cic:/CoRN/algebra/Expon/bin_less_un.con.
+inline "cic:/CoRN/algebra/Expon/bin_less_un.con".
(* UNEXPORTED
End More_Nexp.
(* UNEXPORTED
End More_Nexp.
-inline cic:/CoRN/algebra/Expon/R.var.
+inline "cic:/CoRN/algebra/Expon/R.var".
(*#*
It would be nicer to define [zexp] using [caseZdiff], but we already
have most properties now.
*)
(*#*
It would be nicer to define [zexp] using [caseZdiff], but we already
have most properties now.
*)
-inline cic:/CoRN/algebra/Expon/zexp.con.
+inline "cic:/CoRN/algebra/Expon/zexp.con".
(* UNEXPORTED
End Zexp_def.
(* UNEXPORTED
End Zexp_def.
Section Zexp_properties.
*)
Section Zexp_properties.
*)
-inline cic:/CoRN/algebra/Expon/R.var.
+inline "cic:/CoRN/algebra/Expon/R.var".
-inline cic:/CoRN/algebra/Expon/zexp_zero.con.
+inline "cic:/CoRN/algebra/Expon/zexp_zero.con".
(* UNEXPORTED
Hint Resolve zexp_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_zero: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_nexp.con.
+inline "cic:/CoRN/algebra/Expon/zexp_nexp.con".
(* UNEXPORTED
Hint Resolve zexp_nexp: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_nexp: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_inv_nexp.con.
+inline "cic:/CoRN/algebra/Expon/zexp_inv_nexp.con".
(* UNEXPORTED
Hint Resolve zexp_inv_nexp: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_inv_nexp: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_inv_nexp'.con.
+inline "cic:/CoRN/algebra/Expon/zexp_inv_nexp'.con".
(* UNEXPORTED
Hint Resolve zexp_inv_nexp': algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_inv_nexp': algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_strext.con.
+inline "cic:/CoRN/algebra/Expon/zexp_strext.con".
-inline cic:/CoRN/algebra/Expon/zexp_wd.con.
+inline "cic:/CoRN/algebra/Expon/zexp_wd.con".
(* UNEXPORTED
Hint Resolve zexp_wd: algebra_c.
*)
(* UNEXPORTED
Hint Resolve zexp_wd: algebra_c.
*)
-inline cic:/CoRN/algebra/Expon/zexp_plus1.con.
+inline "cic:/CoRN/algebra/Expon/zexp_plus1.con".
(* UNEXPORTED
Hint Resolve zexp_plus1: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_plus1: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_resp_ap_zero.con.
+inline "cic:/CoRN/algebra/Expon/zexp_resp_ap_zero.con".
(* UNEXPORTED
Hint Resolve zexp_resp_ap_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_resp_ap_zero: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_inv.con.
+inline "cic:/CoRN/algebra/Expon/zexp_inv.con".
(* UNEXPORTED
Hint Resolve zexp_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_inv: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_inv1.con.
+inline "cic:/CoRN/algebra/Expon/zexp_inv1.con".
(* UNEXPORTED
Hint Resolve zexp_inv1: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_inv1: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_plus.con.
+inline "cic:/CoRN/algebra/Expon/zexp_plus.con".
(* UNEXPORTED
Hint Resolve zexp_plus: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_plus: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_minus.con.
+inline "cic:/CoRN/algebra/Expon/zexp_minus.con".
(* UNEXPORTED
Hint Resolve zexp_minus: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_minus: algebra.
*)
-inline cic:/CoRN/algebra/Expon/one_zexp.con.
+inline "cic:/CoRN/algebra/Expon/one_zexp.con".
(* UNEXPORTED
Hint Resolve one_zexp: algebra.
*)
(* UNEXPORTED
Hint Resolve one_zexp: algebra.
*)
-inline cic:/CoRN/algebra/Expon/mult_zexp.con.
+inline "cic:/CoRN/algebra/Expon/mult_zexp.con".
(* UNEXPORTED
Hint Resolve mult_zexp: algebra.
*)
(* UNEXPORTED
Hint Resolve mult_zexp: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_mult.con.
+inline "cic:/CoRN/algebra/Expon/zexp_mult.con".
(* UNEXPORTED
Hint Resolve zexp_mult: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_mult: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_two.con.
+inline "cic:/CoRN/algebra/Expon/zexp_two.con".
(* UNEXPORTED
Hint Resolve zexp_two: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_two: algebra.
*)
-inline cic:/CoRN/algebra/Expon/inv_zexp_even.con.
+inline "cic:/CoRN/algebra/Expon/inv_zexp_even.con".
(* UNEXPORTED
Hint Resolve inv_zexp_even: algebra.
*)
(* UNEXPORTED
Hint Resolve inv_zexp_even: algebra.
*)
-inline cic:/CoRN/algebra/Expon/inv_zexp_two.con.
+inline "cic:/CoRN/algebra/Expon/inv_zexp_two.con".
(* UNEXPORTED
Hint Resolve inv_zexp_two: algebra.
*)
(* UNEXPORTED
Hint Resolve inv_zexp_two: algebra.
*)
-inline cic:/CoRN/algebra/Expon/inv_zexp_odd.con.
+inline "cic:/CoRN/algebra/Expon/inv_zexp_odd.con".
-inline cic:/CoRN/algebra/Expon/zexp_one.con.
+inline "cic:/CoRN/algebra/Expon/zexp_one.con".
(* UNEXPORTED
Hint Resolve zexp_one: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_one: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_funny.con.
+inline "cic:/CoRN/algebra/Expon/zexp_funny.con".
(* UNEXPORTED
Hint Resolve zexp_funny: algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_funny: algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_funny'.con.
+inline "cic:/CoRN/algebra/Expon/zexp_funny'.con".
(* UNEXPORTED
Hint Resolve zexp_funny': algebra.
*)
(* UNEXPORTED
Hint Resolve zexp_funny': algebra.
*)
-inline cic:/CoRN/algebra/Expon/zexp_pos.con.
+inline "cic:/CoRN/algebra/Expon/zexp_pos.con".
(* UNEXPORTED
End Zexp_properties.
(* UNEXPORTED
End Zexp_properties.
-inline cic:/CoRN/algebra/Expon/R.var.
+inline "cic:/CoRN/algebra/Expon/R.var".
-inline cic:/CoRN/algebra/Expon/root_unique.con.
+inline "cic:/CoRN/algebra/Expon/root_unique.con".
-inline cic:/CoRN/algebra/Expon/root_one.con.
+inline "cic:/CoRN/algebra/Expon/root_one.con".
(* UNEXPORTED
End Root_Unique.
(* UNEXPORTED
End Root_Unique.
set "baseuri" "cic:/matita/CoRN-Decl/algebra/ListType".
set "baseuri" "cic:/matita/CoRN-Decl/algebra/ListType".
(* begin hide *)
(*#**********************************************************************)
(* begin hide *)
(*#**********************************************************************)
library of Coq but moved to the Type level.
*)
library of Coq but moved to the Type level.
*)
(* UNEXPORTED
Section List.
*)
(* UNEXPORTED
Section List.
*)
-inline cic:/CoRN/algebra/ListType/A.var.
+inline "cic:/CoRN/algebra/ListType/A.var".
-inline cic:/CoRN/algebra/ListType/list.ind.
+inline "cic:/CoRN/algebra/ListType/list.ind".
-inline cic:/CoRN/algebra/ListType/app.con.
+inline "cic:/CoRN/algebra/ListType/app.con".
-inline cic:/CoRN/algebra/ListType/app_nil_end.con.
+inline "cic:/CoRN/algebra/ListType/app_nil_end.con".
(* UNEXPORTED
Hint Resolve app_nil_end: list v62.
*)
(* UNEXPORTED
Hint Resolve app_nil_end: list v62.
*)
-inline cic:/CoRN/algebra/ListType/app_ass.con.
+inline "cic:/CoRN/algebra/ListType/app_ass.con".
(* UNEXPORTED
Hint Resolve app_ass: list v62.
*)
(* UNEXPORTED
Hint Resolve app_ass: list v62.
*)
-inline cic:/CoRN/algebra/ListType/ass_app.con.
+inline "cic:/CoRN/algebra/ListType/ass_app.con".
(* UNEXPORTED
Hint Resolve ass_app: list v62.
*)
(* UNEXPORTED
Hint Resolve ass_app: list v62.
*)
-inline cic:/CoRN/algebra/ListType/tail.con.
+inline "cic:/CoRN/algebra/ListType/tail.con".
-inline cic:/CoRN/algebra/ListType/nil_cons.con.
+inline "cic:/CoRN/algebra/ListType/nil_cons.con".
(*#***************************************)
(*#***************************************)
(*#***************************************)
(*#***************************************)
-inline cic:/CoRN/algebra/ListType/length.con.
+inline "cic:/CoRN/algebra/ListType/length.con".
(*#*****************************)
(*#*****************************)
-inline cic:/CoRN/algebra/ListType/lel.con.
+inline "cic:/CoRN/algebra/ListType/lel.con".
(* UNEXPORTED
Hint Unfold lel: list.
*)
(* UNEXPORTED
Hint Unfold lel: list.
*)
-inline cic:/CoRN/algebra/ListType/a.var.
+inline "cic:/CoRN/algebra/ListType/a.var".
-inline cic:/CoRN/algebra/ListType/b.var.
+inline "cic:/CoRN/algebra/ListType/b.var".
-inline cic:/CoRN/algebra/ListType/l.var.
+inline "cic:/CoRN/algebra/ListType/l.var".
-inline cic:/CoRN/algebra/ListType/m.var.
+inline "cic:/CoRN/algebra/ListType/m.var".
-inline cic:/CoRN/algebra/ListType/n.var.
+inline "cic:/CoRN/algebra/ListType/n.var".
-inline cic:/CoRN/algebra/ListType/lel_refl.con.
+inline "cic:/CoRN/algebra/ListType/lel_refl.con".
-inline cic:/CoRN/algebra/ListType/lel_trans.con.
+inline "cic:/CoRN/algebra/ListType/lel_trans.con".
-inline cic:/CoRN/algebra/ListType/lel_cons_cons.con.
+inline "cic:/CoRN/algebra/ListType/lel_cons_cons.con".
-inline cic:/CoRN/algebra/ListType/lel_cons.con.
+inline "cic:/CoRN/algebra/ListType/lel_cons.con".
-inline cic:/CoRN/algebra/ListType/lel_tail.con.
+inline "cic:/CoRN/algebra/ListType/lel_tail.con".
-inline cic:/CoRN/algebra/ListType/lel_nil.con.
+inline "cic:/CoRN/algebra/ListType/lel_nil.con".
(* UNEXPORTED
End length_order.
(* UNEXPORTED
End length_order.
-inline cic:/CoRN/algebra/ListType/In.con.
+inline "cic:/CoRN/algebra/ListType/In.con".
-inline cic:/CoRN/algebra/ListType/in_eq.con.
+inline "cic:/CoRN/algebra/ListType/in_eq.con".
(* UNEXPORTED
Hint Resolve in_eq: list v62.
*)
(* UNEXPORTED
Hint Resolve in_eq: list v62.
*)
-inline cic:/CoRN/algebra/ListType/in_cons.con.
+inline "cic:/CoRN/algebra/ListType/in_cons.con".
(* UNEXPORTED
Hint Resolve in_cons: list v62.
*)
(* UNEXPORTED
Hint Resolve in_cons: list v62.
*)
-inline cic:/CoRN/algebra/ListType/in_app_or.con.
+inline "cic:/CoRN/algebra/ListType/in_app_or.con".
(* UNEXPORTED
Hint Immediate in_app_or: list v62.
*)
(* UNEXPORTED
Hint Immediate in_app_or: list v62.
*)
-inline cic:/CoRN/algebra/ListType/in_or_app.con.
+inline "cic:/CoRN/algebra/ListType/in_or_app.con".
(* UNEXPORTED
Hint Resolve in_or_app: list v62.
*)
(* UNEXPORTED
Hint Resolve in_or_app: list v62.
*)
-inline cic:/CoRN/algebra/ListType/incl.con.
+inline "cic:/CoRN/algebra/ListType/incl.con".
(* UNEXPORTED
Hint Unfold incl: list v62.
*)
(* UNEXPORTED
Hint Unfold incl: list v62.
*)
-inline cic:/CoRN/algebra/ListType/incl_refl.con.
+inline "cic:/CoRN/algebra/ListType/incl_refl.con".
(* UNEXPORTED
Hint Resolve incl_refl: list v62.
*)
(* UNEXPORTED
Hint Resolve incl_refl: list v62.
*)
-inline cic:/CoRN/algebra/ListType/incl_tl.con.
+inline "cic:/CoRN/algebra/ListType/incl_tl.con".
(* UNEXPORTED
Hint Immediate incl_tl: list v62.
*)
(* UNEXPORTED
Hint Immediate incl_tl: list v62.
*)
-inline cic:/CoRN/algebra/ListType/incl_tran.con.
+inline "cic:/CoRN/algebra/ListType/incl_tran.con".
-inline cic:/CoRN/algebra/ListType/incl_appl.con.
+inline "cic:/CoRN/algebra/ListType/incl_appl.con".
(* UNEXPORTED
Hint Immediate incl_appl: list v62.
*)
(* UNEXPORTED
Hint Immediate incl_appl: list v62.
*)
-inline cic:/CoRN/algebra/ListType/incl_appr.con.
+inline "cic:/CoRN/algebra/ListType/incl_appr.con".
(* UNEXPORTED
Hint Immediate incl_appr: list v62.
*)
(* UNEXPORTED
Hint Immediate incl_appr: list v62.
*)
-inline cic:/CoRN/algebra/ListType/incl_cons.con.
+inline "cic:/CoRN/algebra/ListType/incl_cons.con".
(* UNEXPORTED
Hint Resolve incl_cons: list v62.
*)
(* UNEXPORTED
Hint Resolve incl_cons: list v62.
*)
-inline cic:/CoRN/algebra/ListType/incl_app.con.
+inline "cic:/CoRN/algebra/ListType/incl_app.con".
-inline cic:/CoRN/algebra/ListType/A.var.
+inline "cic:/CoRN/algebra/ListType/A.var".
-inline cic:/CoRN/algebra/ListType/B.var.
+inline "cic:/CoRN/algebra/ListType/B.var".
-inline cic:/CoRN/algebra/ListType/f.var.
+inline "cic:/CoRN/algebra/ListType/f.var".
-inline cic:/CoRN/algebra/ListType/map.con.
+inline "cic:/CoRN/algebra/ListType/map.con".
set "baseuri" "cic:/matita/CoRN-Decl/complex/AbsCC".
set "baseuri" "cic:/matita/CoRN-Decl/complex/AbsCC".
(* $Id: AbsCC.v,v 1.2 2004/04/23 10:00:54 lcf Exp $ *)
(* $Id: AbsCC.v,v 1.2 2004/04/23 10:00:54 lcf Exp $ *)
-(* INCLUDE
-CComplex
-*)
+include "complex/CComplex.ma".
(*#* * Absolute value on [CC]
** Properties of [AbsCC] *)
(*#* * Absolute value on [CC]
** Properties of [AbsCC] *)
Section AbsCC_properties.
*)
Section AbsCC_properties.
*)
-inline cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con".
-inline cic:/CoRN/complex/AbsCC/AbsCC_ap_zero_imp_pos.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero_imp_pos.con".
-inline cic:/CoRN/complex/AbsCC/AbsCC_wd.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_wd.con".
(* UNEXPORTED
Hint Resolve AbsCC_wd: algebra_c.
*)
(* UNEXPORTED
Hint Resolve AbsCC_wd: algebra_c.
*)
-inline cic:/CoRN/complex/AbsCC/cc_inv_abs.con.
+inline "cic:/CoRN/complex/AbsCC/cc_inv_abs.con".
(* UNEXPORTED
Hint Resolve cc_inv_abs: algebra.
*)
(* UNEXPORTED
Hint Resolve cc_inv_abs: algebra.
*)
-inline cic:/CoRN/complex/AbsCC/cc_minus_abs.con.
+inline "cic:/CoRN/complex/AbsCC/cc_minus_abs.con".
-inline cic:/CoRN/complex/AbsCC/cc_mult_abs.con.
+inline "cic:/CoRN/complex/AbsCC/cc_mult_abs.con".
(* UNEXPORTED
Hint Resolve cc_mult_abs: algebra.
*)
(* UNEXPORTED
Hint Resolve cc_mult_abs: algebra.
*)
-inline cic:/CoRN/complex/AbsCC/AbsCC_minzero.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_minzero.con".
-inline cic:/CoRN/complex/AbsCC/AbsCC_IR.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_IR.con".
(* UNEXPORTED
Hint Resolve AbsCC_IR: algebra.
*)
(* UNEXPORTED
Hint Resolve AbsCC_IR: algebra.
*)
-inline cic:/CoRN/complex/AbsCC/cc_div_abs.con.
+inline "cic:/CoRN/complex/AbsCC/cc_div_abs.con".
-inline cic:/CoRN/complex/AbsCC/cc_div_abs'.con.
+inline "cic:/CoRN/complex/AbsCC/cc_div_abs'.con".
-inline cic:/CoRN/complex/AbsCC/AbsCC_zero.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_zero.con".
(* UNEXPORTED
Hint Resolve AbsCC_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve AbsCC_zero: algebra.
*)
-inline cic:/CoRN/complex/AbsCC/AbsCC_one.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_one.con".
-inline cic:/CoRN/complex/AbsCC/cc_pow_abs.con.
+inline "cic:/CoRN/complex/AbsCC/cc_pow_abs.con".
-inline cic:/CoRN/complex/AbsCC/AbsCC_pos.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_pos.con".
-inline cic:/CoRN/complex/AbsCC/AbsCC_ap_zero.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero.con".
-inline cic:/CoRN/complex/AbsCC/AbsCC_small_imp_eq.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_small_imp_eq.con".
-inline cic:/CoRN/complex/AbsCC/l_1_1_2.con.
+inline "cic:/CoRN/complex/AbsCC/l_1_1_2.con".
Hint Resolve l_1_1_2: algebra.
*)
Hint Resolve l_1_1_2: algebra.
*)
-inline cic:/CoRN/complex/AbsCC/AbsCC_square_Re_Im.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_square_Re_Im.con".
(* UNEXPORTED
Hint Resolve AbsCC_square_Re_Im: algebra.
(* UNEXPORTED
Hint Resolve AbsCC_square_Re_Im: algebra.
-inline cic:/CoRN/complex/AbsCC/l_1_2_3_CC.con.
+inline "cic:/CoRN/complex/AbsCC/l_1_2_3_CC.con".
Hint Resolve l_1_2_3_CC: algebra.
*)
Hint Resolve l_1_2_3_CC: algebra.
*)
-inline cic:/CoRN/complex/AbsCC/AbsCC_mult_conj.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_mult_conj.con".
(* UNEXPORTED
Hint Resolve CC_conj_mult: algebra.
(* UNEXPORTED
Hint Resolve CC_conj_mult: algebra.
-inline cic:/CoRN/complex/AbsCC/l_2_1_2.con.
+inline "cic:/CoRN/complex/AbsCC/l_2_1_2.con".
(* UNEXPORTED
Hint Resolve l_2_1_2: algebra.
(* UNEXPORTED
Hint Resolve l_2_1_2: algebra.
-inline cic:/CoRN/complex/AbsCC/AbsCC_mult_square.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_mult_square.con".
-inline cic:/CoRN/complex/AbsCC/AbsCC_square_ap_zero.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_square_ap_zero.con".
-inline cic:/CoRN/complex/AbsCC/cc_recip_char.con.
+inline "cic:/CoRN/complex/AbsCC/cc_recip_char.con".
-inline cic:/CoRN/complex/AbsCC/AbsCC_strext.con.
+inline "cic:/CoRN/complex/AbsCC/AbsCC_strext.con".
-inline cic:/CoRN/complex/AbsCC/AbsSmallCC.con.
+inline "cic:/CoRN/complex/AbsCC/AbsSmallCC.con".
-inline cic:/CoRN/complex/AbsCC/Cexis_AFS_CC.con.
+inline "cic:/CoRN/complex/AbsCC/Cexis_AFS_CC.con".
(* The following lemmas are just auxiliary results *)
(* begin hide *)
(* The following lemmas are just auxiliary results *)
(* begin hide *)
-inline cic:/CoRN/complex/AbsCC/l_4_1_2.con.
+inline "cic:/CoRN/complex/AbsCC/l_4_1_2.con".
-inline cic:/CoRN/complex/AbsCC/l_4_2_3.con.
+inline "cic:/CoRN/complex/AbsCC/l_4_2_3.con".
-inline cic:/CoRN/complex/AbsCC/l_4_3_4.con.
+inline "cic:/CoRN/complex/AbsCC/l_4_3_4.con".
(*#* ** The triangle inequality *)
(*#* ** The triangle inequality *)
-inline cic:/CoRN/complex/AbsCC/triangle.con.
+inline "cic:/CoRN/complex/AbsCC/triangle.con".
-inline cic:/CoRN/complex/AbsCC/triangle_Sum.con.
+inline "cic:/CoRN/complex/AbsCC/triangle_Sum.con".
set "baseuri" "cic:/matita/CoRN-Decl/complex/CComplex".
set "baseuri" "cic:/matita/CoRN-Decl/complex/CComplex".
(* $Id: CComplex.v,v 1.8 2004/04/23 10:00:55 lcf Exp $ *)
(*#* printing Re %\ensuremath{\Re}% #ℜ# *)
(* $Id: CComplex.v,v 1.8 2004/04/23 10:00:55 lcf Exp $ *)
(*#* printing Re %\ensuremath{\Re}% #ℜ# *)
(*#* printing CCX %\ensuremath{\mathbb C[X]}% #<b>C</b>[X]# *)
(*#* printing CCX %\ensuremath{\mathbb C[X]}% #<b>C</b>[X]# *)
+include "reals/NRootIR.ma".
(*#* * Complex Numbers
** Algebraic structure
(*#* * Complex Numbers
** Algebraic structure
Section Complex_Numbers.
*)
Section Complex_Numbers.
*)
-inline cic:/CoRN/complex/CComplex/CC_set.ind.
+inline "cic:/CoRN/complex/CComplex/CC_set.ind".
-inline cic:/CoRN/complex/CComplex/cc_ap.con.
+inline "cic:/CoRN/complex/CComplex/cc_ap.con".
-inline cic:/CoRN/complex/CComplex/cc_eq.con.
+inline "cic:/CoRN/complex/CComplex/cc_eq.con".
-inline cic:/CoRN/complex/CComplex/cc_is_CSetoid.con.
+inline "cic:/CoRN/complex/CComplex/cc_is_CSetoid.con".
-inline cic:/CoRN/complex/CComplex/cc_csetoid.con.
+inline "cic:/CoRN/complex/CComplex/cc_csetoid.con".
-inline cic:/CoRN/complex/CComplex/cc_plus.con.
+inline "cic:/CoRN/complex/CComplex/cc_plus.con".
-inline cic:/CoRN/complex/CComplex/cc_mult.con.
+inline "cic:/CoRN/complex/CComplex/cc_mult.con".
-inline cic:/CoRN/complex/CComplex/cc_zero.con.
+inline "cic:/CoRN/complex/CComplex/cc_zero.con".
-inline cic:/CoRN/complex/CComplex/cc_one.con.
+inline "cic:/CoRN/complex/CComplex/cc_one.con".
-inline cic:/CoRN/complex/CComplex/cc_i.con.
+inline "cic:/CoRN/complex/CComplex/cc_i.con".
-inline cic:/CoRN/complex/CComplex/cc_inv.con.
+inline "cic:/CoRN/complex/CComplex/cc_inv.con".
(* not needed anymore
Lemma cc_plus_op_proof : (bin_op_wd cc_csetoid cc_plus).
(* not needed anymore
Lemma cc_plus_op_proof : (bin_op_wd cc_csetoid cc_plus).
-inline cic:/CoRN/complex/CComplex/cc_inv_strext.con.
+inline "cic:/CoRN/complex/CComplex/cc_inv_strext.con".
-inline cic:/CoRN/complex/CComplex/cc_plus_strext.con.
+inline "cic:/CoRN/complex/CComplex/cc_plus_strext.con".
-inline cic:/CoRN/complex/CComplex/cc_mult_strext.con.
+inline "cic:/CoRN/complex/CComplex/cc_mult_strext.con".
-inline cic:/CoRN/complex/CComplex/cc_inv_op.con.
+inline "cic:/CoRN/complex/CComplex/cc_inv_op.con".
-inline cic:/CoRN/complex/CComplex/cc_plus_op.con.
+inline "cic:/CoRN/complex/CComplex/cc_plus_op.con".
-inline cic:/CoRN/complex/CComplex/cc_mult_op.con.
+inline "cic:/CoRN/complex/CComplex/cc_mult_op.con".
-inline cic:/CoRN/complex/CComplex/cc_csg_associative.con.
+inline "cic:/CoRN/complex/CComplex/cc_csg_associative.con".
-inline cic:/CoRN/complex/CComplex/cc_cr_mult_associative.con.
+inline "cic:/CoRN/complex/CComplex/cc_cr_mult_associative.con".
-inline cic:/CoRN/complex/CComplex/cc_csemi_grp.con.
+inline "cic:/CoRN/complex/CComplex/cc_csemi_grp.con".
-inline cic:/CoRN/complex/CComplex/cc_cm_proof.con.
+inline "cic:/CoRN/complex/CComplex/cc_cm_proof.con".
-inline cic:/CoRN/complex/CComplex/cc_cmonoid.con.
+inline "cic:/CoRN/complex/CComplex/cc_cmonoid.con".
-inline cic:/CoRN/complex/CComplex/cc_cg_proof.con.
+inline "cic:/CoRN/complex/CComplex/cc_cg_proof.con".
-inline cic:/CoRN/complex/CComplex/cc_cr_dist.con.
+inline "cic:/CoRN/complex/CComplex/cc_cr_dist.con".
-inline cic:/CoRN/complex/CComplex/cc_cr_non_triv.con.
+inline "cic:/CoRN/complex/CComplex/cc_cr_non_triv.con".
-inline cic:/CoRN/complex/CComplex/cc_cgroup.con.
+inline "cic:/CoRN/complex/CComplex/cc_cgroup.con".
-inline cic:/CoRN/complex/CComplex/cc_cabgroup.con.
+inline "cic:/CoRN/complex/CComplex/cc_cabgroup.con".
-inline cic:/CoRN/complex/CComplex/cc_cr_mult_mon.con.
+inline "cic:/CoRN/complex/CComplex/cc_cr_mult_mon.con".
-inline cic:/CoRN/complex/CComplex/cc_mult_commutes.con.
+inline "cic:/CoRN/complex/CComplex/cc_mult_commutes.con".
-inline cic:/CoRN/complex/CComplex/cc_isCRing.con.
+inline "cic:/CoRN/complex/CComplex/cc_isCRing.con".
-inline cic:/CoRN/complex/CComplex/cc_cring.con.
+inline "cic:/CoRN/complex/CComplex/cc_cring.con".
-inline cic:/CoRN/complex/CComplex/cc_ap_zero.con.
+inline "cic:/CoRN/complex/CComplex/cc_ap_zero.con".
-inline cic:/CoRN/complex/CComplex/cc_inv_aid.con.
+inline "cic:/CoRN/complex/CComplex/cc_inv_aid.con".
(*#*
If [x [~=] Zero] or [y [~=] Zero], then [x [/] x[^]2 [+] y[^]2 [~=] Zero] or
[[--]y[/]x[^]2[+]y[^]2 [~=] Zero].
*)
(*#*
If [x [~=] Zero] or [y [~=] Zero], then [x [/] x[^]2 [+] y[^]2 [~=] Zero] or
[[--]y[/]x[^]2[+]y[^]2 [~=] Zero].
*)
-inline cic:/CoRN/complex/CComplex/cc_inv_aid2.con.
+inline "cic:/CoRN/complex/CComplex/cc_inv_aid2.con".
(*
REMARK KEPT FOR SENTIMENTAL REASONS...
(*
REMARK KEPT FOR SENTIMENTAL REASONS...
-inline cic:/CoRN/complex/CComplex/cc_recip.con.
+inline "cic:/CoRN/complex/CComplex/cc_recip.con".
-inline cic:/CoRN/complex/CComplex/cc_cfield_proof.con.
+inline "cic:/CoRN/complex/CComplex/cc_cfield_proof.con".
-inline cic:/CoRN/complex/CComplex/cc_Recip_proof.con.
+inline "cic:/CoRN/complex/CComplex/cc_Recip_proof.con".
(* UNEXPORTED
Opaque cc_recip.
(* UNEXPORTED
Opaque cc_recip.
-inline cic:/CoRN/complex/CComplex/cc_cfield.con.
+inline "cic:/CoRN/complex/CComplex/cc_cfield.con".
-inline cic:/CoRN/complex/CComplex/CC.con.
+inline "cic:/CoRN/complex/CComplex/CC.con".
(*#*
Maps from reals to complex and vice-versa are defined, as well as conjugate,
absolute value and the imaginary unit [I] *)
(*#*
Maps from reals to complex and vice-versa are defined, as well as conjugate,
absolute value and the imaginary unit [I] *)
-inline cic:/CoRN/complex/CComplex/cc_set_CC.con.
+inline "cic:/CoRN/complex/CComplex/cc_set_CC.con".
-inline cic:/CoRN/complex/CComplex/cc_IR.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR.con".
-inline cic:/CoRN/complex/CComplex/CC_conj.con.
+inline "cic:/CoRN/complex/CComplex/CC_conj.con".
(* old def
Definition CC_conj' : CC->CC := [z:CC_set] (CC_set_rec [_:CC_set]CC_set [Re0,Im0:IR] (Build_CC_set Re0 [--]Im0) z).
*)
(* old def
Definition CC_conj' : CC->CC := [z:CC_set] (CC_set_rec [_:CC_set]CC_set [Re0,Im0:IR] (Build_CC_set Re0 [--]Im0) z).
*)
-inline cic:/CoRN/complex/CComplex/AbsCC.con.
+inline "cic:/CoRN/complex/CComplex/AbsCC.con".
-inline cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con.
+inline "cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con".
(* UNEXPORTED
End Complex_Numbers.
(* UNEXPORTED
End Complex_Numbers.
-inline cic:/CoRN/complex/CComplex/II.con.
+inline "cic:/CoRN/complex/CComplex/II.con".
(*#* ** Properties of [II] *)
(*#* ** Properties of [II] *)
-inline cic:/CoRN/complex/CComplex/I_square.con.
+inline "cic:/CoRN/complex/CComplex/I_square.con".
(* UNEXPORTED
Hint Resolve I_square: algebra.
*)
(* UNEXPORTED
Hint Resolve I_square: algebra.
*)
-inline cic:/CoRN/complex/CComplex/I_square'.con.
+inline "cic:/CoRN/complex/CComplex/I_square'.con".
-inline cic:/CoRN/complex/CComplex/I_recip_lft.con.
+inline "cic:/CoRN/complex/CComplex/I_recip_lft.con".
-inline cic:/CoRN/complex/CComplex/I_recip_rht.con.
+inline "cic:/CoRN/complex/CComplex/I_recip_rht.con".
-inline cic:/CoRN/complex/CComplex/mult_I.con.
+inline "cic:/CoRN/complex/CComplex/mult_I.con".
-inline cic:/CoRN/complex/CComplex/I_wd.con.
+inline "cic:/CoRN/complex/CComplex/I_wd.con".
(*#* ** Properties of [Re] and [Im] *)
(*#* ** Properties of [Re] and [Im] *)
-inline cic:/CoRN/complex/CComplex/calculate_norm.con.
+inline "cic:/CoRN/complex/CComplex/calculate_norm.con".
-inline cic:/CoRN/complex/CComplex/calculate_Re.con.
+inline "cic:/CoRN/complex/CComplex/calculate_Re.con".
-inline cic:/CoRN/complex/CComplex/calculate_Im.con.
+inline "cic:/CoRN/complex/CComplex/calculate_Im.con".
-inline cic:/CoRN/complex/CComplex/Re_wd.con.
+inline "cic:/CoRN/complex/CComplex/Re_wd.con".
-inline cic:/CoRN/complex/CComplex/Im_wd.con.
+inline "cic:/CoRN/complex/CComplex/Im_wd.con".
-inline cic:/CoRN/complex/CComplex/Re_resp_plus.con.
+inline "cic:/CoRN/complex/CComplex/Re_resp_plus.con".
-inline cic:/CoRN/complex/CComplex/Re_resp_inv.con.
+inline "cic:/CoRN/complex/CComplex/Re_resp_inv.con".
-inline cic:/CoRN/complex/CComplex/Im_resp_plus.con.
+inline "cic:/CoRN/complex/CComplex/Im_resp_plus.con".
-inline cic:/CoRN/complex/CComplex/Im_resp_inv.con.
+inline "cic:/CoRN/complex/CComplex/Im_resp_inv.con".
-inline cic:/CoRN/complex/CComplex/cc_calculate_square.con.
+inline "cic:/CoRN/complex/CComplex/cc_calculate_square.con".
(* UNEXPORTED
End I_properties.
(* UNEXPORTED
End I_properties.
Section Conj_properties.
*)
Section Conj_properties.
*)
-inline cic:/CoRN/complex/CComplex/CC_conj_plus.con.
+inline "cic:/CoRN/complex/CComplex/CC_conj_plus.con".
-inline cic:/CoRN/complex/CComplex/CC_conj_mult.con.
+inline "cic:/CoRN/complex/CComplex/CC_conj_mult.con".
(* UNEXPORTED
Hint Resolve CC_conj_mult: algebra.
*)
(* UNEXPORTED
Hint Resolve CC_conj_mult: algebra.
*)
-inline cic:/CoRN/complex/CComplex/CC_conj_strext.con.
+inline "cic:/CoRN/complex/CComplex/CC_conj_strext.con".
-inline cic:/CoRN/complex/CComplex/CC_conj_conj.con.
+inline "cic:/CoRN/complex/CComplex/CC_conj_conj.con".
-inline cic:/CoRN/complex/CComplex/CC_conj_zero.con.
+inline "cic:/CoRN/complex/CComplex/CC_conj_zero.con".
-inline cic:/CoRN/complex/CComplex/CC_conj_one.con.
+inline "cic:/CoRN/complex/CComplex/CC_conj_one.con".
(* UNEXPORTED
Hint Resolve CC_conj_one: algebra.
*)
(* UNEXPORTED
Hint Resolve CC_conj_one: algebra.
*)
-inline cic:/CoRN/complex/CComplex/CC_conj_nexp.con.
+inline "cic:/CoRN/complex/CComplex/CC_conj_nexp.con".
(* UNEXPORTED
End Conj_properties.
(* UNEXPORTED
End Conj_properties.
Section cc_IR_properties.
*)
Section cc_IR_properties.
*)
-inline cic:/CoRN/complex/CComplex/Re_cc_IR.con.
+inline "cic:/CoRN/complex/CComplex/Re_cc_IR.con".
-inline cic:/CoRN/complex/CComplex/Im_cc_IR.con.
+inline "cic:/CoRN/complex/CComplex/Im_cc_IR.con".
-inline cic:/CoRN/complex/CComplex/cc_IR_wd.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_wd.con".
(* UNEXPORTED
Hint Resolve cc_IR_wd: algebra_c.
*)
(* UNEXPORTED
Hint Resolve cc_IR_wd: algebra_c.
*)
-inline cic:/CoRN/complex/CComplex/cc_IR_resp_ap.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_resp_ap.con".
-inline cic:/CoRN/complex/CComplex/cc_IR_mult.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_mult.con".
(* UNEXPORTED
Hint Resolve cc_IR_mult: algebra.
*)
(* UNEXPORTED
Hint Resolve cc_IR_mult: algebra.
*)
-inline cic:/CoRN/complex/CComplex/cc_IR_mult_lft.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_mult_lft.con".
-inline cic:/CoRN/complex/CComplex/cc_IR_mult_rht.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_mult_rht.con".
-inline cic:/CoRN/complex/CComplex/cc_IR_plus.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_plus.con".
(* UNEXPORTED
Hint Resolve cc_IR_plus: algebra.
*)
(* UNEXPORTED
Hint Resolve cc_IR_plus: algebra.
*)
-inline cic:/CoRN/complex/CComplex/cc_IR_minus.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_minus.con".
-inline cic:/CoRN/complex/CComplex/cc_IR_zero.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_zero.con".
(* UNEXPORTED
Hint Resolve cc_IR_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve cc_IR_zero: algebra.
*)
-inline cic:/CoRN/complex/CComplex/cc_IR_one.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_one.con".
(* UNEXPORTED
Hint Resolve cc_IR_one: algebra.
*)
(* UNEXPORTED
Hint Resolve cc_IR_one: algebra.
*)
-inline cic:/CoRN/complex/CComplex/cc_IR_nring.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_nring.con".
-inline cic:/CoRN/complex/CComplex/cc_IR_nexp.con.
+inline "cic:/CoRN/complex/CComplex/cc_IR_nexp.con".
(* UNEXPORTED
End cc_IR_properties.
(* UNEXPORTED
End cc_IR_properties.
(*#* ** [CC] has characteristic zero *)
(*#* ** [CC] has characteristic zero *)
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
-inline cic:/CoRN/complex/CComplex/char0_CC.con.
+inline "cic:/CoRN/complex/CComplex/char0_CC.con".
-(* INCLUDE
-Opaque_algebra
-*)
+include "tactics/Opaque_algebra.ma".
-inline cic:/CoRN/complex/CComplex/poly_apzero_CC.con.
+inline "cic:/CoRN/complex/CComplex/poly_apzero_CC.con".
-inline cic:/CoRN/complex/CComplex/poly_CC_extensional.con.
+inline "cic:/CoRN/complex/CComplex/poly_CC_extensional.con".
set "baseuri" "cic:/matita/CoRN-Decl/complex/Complex_Exponential".
set "baseuri" "cic:/matita/CoRN-Decl/complex/Complex_Exponential".
(* $Id: Complex_Exponential.v,v 1.4 2004/04/23 10:00:55 lcf Exp $ *)
(*#* printing ExpCC %\ensuremath{\exp_{\mathbb C}}% *)
(* $Id: Complex_Exponential.v,v 1.4 2004/04/23 10:00:55 lcf Exp $ *)
(*#* printing ExpCC %\ensuremath{\exp_{\mathbb C}}% *)
+include "complex/AbsCC.ma".
-(* INCLUDE
-Exponential
-*)
+include "transc/Exponential.ma".
(*#* ** The Complex Exponential *)
(*#* ** The Complex Exponential *)
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC.con".
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_wd.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_wd.con".
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_1.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_1.con".
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_2.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_2.con".
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_3.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_3.con".
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_4.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_4.con".
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_plus.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_plus.con".
(* UNEXPORTED
Hint Resolve ExpCC_plus: algebra.
*)
(* UNEXPORTED
Hint Resolve ExpCC_plus: algebra.
*)
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_Zero.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_Zero.con".
(* UNEXPORTED
Hint Resolve ExpCC_Zero: algebra.
*)
(* UNEXPORTED
Hint Resolve ExpCC_Zero: algebra.
*)
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_inv_aid.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv_aid.con".
(* UNEXPORTED
Hint Resolve ExpCC_inv_aid: algebra.
*)
(* UNEXPORTED
Hint Resolve ExpCC_inv_aid: algebra.
*)
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_ap_zero.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_ap_zero.con".
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_inv.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv.con".
(* UNEXPORTED
Hint Resolve ExpCC_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve ExpCC_inv: algebra.
*)
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_pow.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_pow.con".
(* UNEXPORTED
Hint Resolve ExpCC_pow: algebra.
*)
(* UNEXPORTED
Hint Resolve ExpCC_pow: algebra.
*)
-inline cic:/CoRN/complex/Complex_Exponential/AbsCC_ExpCC.con.
+inline "cic:/CoRN/complex/Complex_Exponential/AbsCC_ExpCC.con".
(* UNEXPORTED
Hint Resolve AbsCC_ExpCC: algebra.
*)
(* UNEXPORTED
Hint Resolve AbsCC_ExpCC: algebra.
*)
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_Periodic.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_Periodic.con".
(* UNEXPORTED
Hint Resolve ExpCC_Periodic: algebra.
*)
(* UNEXPORTED
Hint Resolve ExpCC_Periodic: algebra.
*)
-inline cic:/CoRN/complex/Complex_Exponential/ExpCC_Exp.con.
+inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_Exp.con".
(* UNEXPORTED
Hint Resolve ExpCC_Exp: algebra.
(* UNEXPORTED
Hint Resolve ExpCC_Exp: algebra.
-inline cic:/CoRN/complex/Complex_Exponential/Euler.con.
+inline "cic:/CoRN/complex/Complex_Exponential/Euler.con".
set "baseuri" "cic:/matita/CoRN-Decl/complex/NRootCC".
set "baseuri" "cic:/matita/CoRN-Decl/complex/NRootCC".
(* $Id: NRootCC.v,v 1.9 2004/04/23 10:00:55 lcf Exp $ *)
(*#* printing sqrt_Half %\ensuremath{\sqrt{\frac12}}% *)
(* $Id: NRootCC.v,v 1.9 2004/04/23 10:00:55 lcf Exp $ *)
(*#* printing sqrt_Half %\ensuremath{\sqrt{\frac12}}% *)
(*#* printing nroot_minus_I %\ensuremath{\sqrt[n]{-\imath}}% *)
(*#* printing nroot_minus_I %\ensuremath{\sqrt[n]{-\imath}}% *)
-(* INCLUDE
-CComplex
-*)
-
-(* INCLUDE
-Wf_nat
-*)
-
-(* INCLUDE
-ArithRing
-*)
+include "complex/CComplex.ma".
(*#* * Roots of Complex Numbers
(*#* * Roots of Complex Numbers
-inline cic:/CoRN/complex/NRootCC/cc_ap_zero.con.
+inline "cic:/CoRN/complex/NRootCC/cc_ap_zero.con".
-inline cic:/CoRN/complex/NRootCC/C_cc_ap_zero.con.
+inline "cic:/CoRN/complex/NRootCC/C_cc_ap_zero.con".
(* UNEXPORTED
End CC_ap_zero.
(* UNEXPORTED
End CC_ap_zero.
-inline cic:/CoRN/complex/NRootCC/imag_to_real.con.
+inline "cic:/CoRN/complex/NRootCC/imag_to_real.con".
(* UNEXPORTED
End Imag_to_Real.
(* UNEXPORTED
End Imag_to_Real.
-inline cic:/CoRN/complex/NRootCC/sqrt_Half.con.
+inline "cic:/CoRN/complex/NRootCC/sqrt_Half.con".
-inline cic:/CoRN/complex/NRootCC/sqrt_I.con.
+inline "cic:/CoRN/complex/NRootCC/sqrt_I.con".
-inline cic:/CoRN/complex/NRootCC/sqrt_I_nexp.con.
+inline "cic:/CoRN/complex/NRootCC/sqrt_I_nexp.con".
-inline cic:/CoRN/complex/NRootCC/nroot_I_nexp_aux.con.
+inline "cic:/CoRN/complex/NRootCC/nroot_I_nexp_aux.con".
-inline cic:/CoRN/complex/NRootCC/nroot_I.con.
+inline "cic:/CoRN/complex/NRootCC/nroot_I.con".
-inline cic:/CoRN/complex/NRootCC/nroot_I_nexp.con.
+inline "cic:/CoRN/complex/NRootCC/nroot_I_nexp.con".
(* UNEXPORTED
Hint Resolve nroot_I_nexp: algebra.
*)
(* UNEXPORTED
Hint Resolve nroot_I_nexp: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nroot_minus_I.con.
+inline "cic:/CoRN/complex/NRootCC/nroot_minus_I.con".
-inline cic:/CoRN/complex/NRootCC/nroot_minus_I_nexp.con.
+inline "cic:/CoRN/complex/NRootCC/nroot_minus_I_nexp.con".
(* UNEXPORTED
End NRootI.
(* UNEXPORTED
End NRootI.
-inline cic:/CoRN/complex/NRootCC/a.var.
+inline "cic:/CoRN/complex/NRootCC/a.var".
-inline cic:/CoRN/complex/NRootCC/b.var.
+inline "cic:/CoRN/complex/NRootCC/b.var".
-inline cic:/CoRN/complex/NRootCC/b_.var.
+inline "cic:/CoRN/complex/NRootCC/b_.var".
-inline cic:/CoRN/complex/NRootCC/c2.con.
+inline "cic:/CoRN/complex/NRootCC/c2.con".
-inline cic:/CoRN/complex/NRootCC/nrCC1_c2pos.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_c2pos.con".
-inline cic:/CoRN/complex/NRootCC/c.con.
+inline "cic:/CoRN/complex/NRootCC/c.con".
-inline cic:/CoRN/complex/NRootCC/a'2.con.
+inline "cic:/CoRN/complex/NRootCC/a'2.con".
-inline cic:/CoRN/complex/NRootCC/nrCC1_a'2pos.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_a'2pos.con".
-inline cic:/CoRN/complex/NRootCC/a'.con.
+inline "cic:/CoRN/complex/NRootCC/a'.con".
-inline cic:/CoRN/complex/NRootCC/b'2.con.
+inline "cic:/CoRN/complex/NRootCC/b'2.con".
-inline cic:/CoRN/complex/NRootCC/nrCC1_b'2pos.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_b'2pos.con".
-inline cic:/CoRN/complex/NRootCC/b'.con.
+inline "cic:/CoRN/complex/NRootCC/b'.con".
-inline cic:/CoRN/complex/NRootCC/nrCC1_a3.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_a3.con".
-inline cic:/CoRN/complex/NRootCC/nrCC1_a4.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_a4.con".
(* UNEXPORTED
Hint Resolve nrCC1_a4: algebra.
*)
(* UNEXPORTED
Hint Resolve nrCC1_a4: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrCC1_a5.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_a5.con".
-inline cic:/CoRN/complex/NRootCC/nrCC1_a6.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_a6.con".
-inline cic:/CoRN/complex/NRootCC/nrCC1_a6'.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_a6'.con".
(* UNEXPORTED
Hint Resolve nrCC1_a5: algebra.
*)
(* UNEXPORTED
Hint Resolve nrCC1_a5: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrCC1_a7_upper.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_a7_upper.con".
-inline cic:/CoRN/complex/NRootCC/nrCC1_a7_lower.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC1_a7_lower.con".
(* UNEXPORTED
Hint Resolve nrCC1_a3 nrCC1_a7_upper nrCC1_a7_lower: algebra.
*)
(* UNEXPORTED
Hint Resolve nrCC1_a3 nrCC1_a7_upper nrCC1_a7_lower: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrootCC_1_upper.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_1_upper.con".
-inline cic:/CoRN/complex/NRootCC/nrootCC_1_lower.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_1_lower.con".
-inline cic:/CoRN/complex/NRootCC/nrootCC_1_ap_real.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_real.con".
(* UNEXPORTED
End NRootCC_1_ap_real.
(* UNEXPORTED
End NRootCC_1_ap_real.
-inline cic:/CoRN/complex/NRootCC/a.var.
+inline "cic:/CoRN/complex/NRootCC/a.var".
-inline cic:/CoRN/complex/NRootCC/b.var.
+inline "cic:/CoRN/complex/NRootCC/b.var".
-inline cic:/CoRN/complex/NRootCC/a_.var.
+inline "cic:/CoRN/complex/NRootCC/a_.var".
-inline cic:/CoRN/complex/NRootCC/c'.con.
+inline "cic:/CoRN/complex/NRootCC/c'.con".
-inline cic:/CoRN/complex/NRootCC/a'.con.
+inline "cic:/CoRN/complex/NRootCC/a'.con".
-inline cic:/CoRN/complex/NRootCC/b'.con.
+inline "cic:/CoRN/complex/NRootCC/b'.con".
Hint Resolve sqrt_I_nexp: algebra.
*)
Hint Resolve sqrt_I_nexp: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrootCC_1_ap_imag.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_imag.con".
(* UNEXPORTED
End NRootCC_1_ap_imag.
(* UNEXPORTED
End NRootCC_1_ap_imag.
(*#* We now define the roots of arbitrary non zero complex numbers. *)
(*#* We now define the roots of arbitrary non zero complex numbers. *)
-inline cic:/CoRN/complex/NRootCC/nrootCC_1.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_1.con".
(* UNEXPORTED
End NRootCC_1.
(* UNEXPORTED
End NRootCC_1.
-inline cic:/CoRN/complex/NRootCC/n.var.
+inline "cic:/CoRN/complex/NRootCC/n.var".
-inline cic:/CoRN/complex/NRootCC/c.var.
+inline "cic:/CoRN/complex/NRootCC/c.var".
-inline cic:/CoRN/complex/NRootCC/z.var.
+inline "cic:/CoRN/complex/NRootCC/z.var".
-inline cic:/CoRN/complex/NRootCC/c_.var.
+inline "cic:/CoRN/complex/NRootCC/c_.var".
-inline cic:/CoRN/complex/NRootCC/nrootCC_2'.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_2'.con".
-inline cic:/CoRN/complex/NRootCC/nrootCC_2.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_2.con".
(* UNEXPORTED
End NRootCC_2.
(* UNEXPORTED
End NRootCC_2.
-inline cic:/CoRN/complex/NRootCC/Im_poly.con.
+inline "cic:/CoRN/complex/NRootCC/Im_poly.con".
-inline cic:/CoRN/complex/NRootCC/nrCC3_a1.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_a1.con".
-inline cic:/CoRN/complex/NRootCC/nrCC3_a2.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_a2.con".
(*#*
%\begin{convention}% Let [a,b : IR], [b_ : (b [#] Zero)] and [n : nat].
%\end{convention}%
*)
(*#*
%\begin{convention}% Let [a,b : IR], [b_ : (b [#] Zero)] and [n : nat].
%\end{convention}%
*)
-inline cic:/CoRN/complex/NRootCC/a.var.
+inline "cic:/CoRN/complex/NRootCC/a.var".
-inline cic:/CoRN/complex/NRootCC/b.var.
+inline "cic:/CoRN/complex/NRootCC/b.var".
-inline cic:/CoRN/complex/NRootCC/b_.var.
+inline "cic:/CoRN/complex/NRootCC/b_.var".
-inline cic:/CoRN/complex/NRootCC/n.var.
+inline "cic:/CoRN/complex/NRootCC/n.var".
-inline cic:/CoRN/complex/NRootCC/nrCC3_poly''.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_poly''.con".
-inline cic:/CoRN/complex/NRootCC/nrCC3_a3.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_a3.con".
-inline cic:/CoRN/complex/NRootCC/nrCC3_a4.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_a4.con".
-inline cic:/CoRN/complex/NRootCC/nrCC3_a5.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_a5.con".
-inline cic:/CoRN/complex/NRootCC/nrCC3_a6.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_a6.con".
-inline cic:/CoRN/complex/NRootCC/nrCC3_poly'.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_poly'.con".
(* UNEXPORTED
Hint Resolve nrCC3_a3: algebra.
*)
(* UNEXPORTED
Hint Resolve nrCC3_a3: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrCC3_a7.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_a7.con".
-inline cic:/CoRN/complex/NRootCC/nrCC3_a8.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_a8.con".
(* UNEXPORTED
Hint Resolve nth_coeff_p_mult_c_: algebra.
(* UNEXPORTED
Hint Resolve nth_coeff_p_mult_c_: algebra.
Hint Resolve nrCC3_a6: algebra.
*)
Hint Resolve nrCC3_a6: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrCC3_a9.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC3_a9.con".
-inline cic:/CoRN/complex/NRootCC/nrootCC_3_poly.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_3_poly.con".
(* UNEXPORTED
Hint Resolve nrCC3_a1 nrCC3_a7: algebra.
*)
(* UNEXPORTED
Hint Resolve nrCC3_a1 nrCC3_a7: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrootCC_3_.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_3_.con".
(* UNEXPORTED
Hint Resolve nrootCC_3_: algebra.
(* UNEXPORTED
Hint Resolve nrootCC_3_: algebra.
Hint Resolve calculate_Im: algebra.
*)
Hint Resolve calculate_Im: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrootCC_3.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_3.con".
(* UNEXPORTED
Hint Resolve nrCC3_a2: algebra.
(* UNEXPORTED
Hint Resolve nrCC3_a2: algebra.
Hint Resolve nrCC3_a9: algebra.
*)
Hint Resolve nrCC3_a9: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrootCC_3_degree.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_3_degree.con".
(* UNEXPORTED
End NRootCC_3.
(* UNEXPORTED
End NRootCC_3.
-inline cic:/CoRN/complex/NRootCC/c.var.
+inline "cic:/CoRN/complex/NRootCC/c.var".
-inline cic:/CoRN/complex/NRootCC/n.var.
+inline "cic:/CoRN/complex/NRootCC/n.var".
-inline cic:/CoRN/complex/NRootCC/n_.var.
+inline "cic:/CoRN/complex/NRootCC/n_.var".
-inline cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con".
-inline cic:/CoRN/complex/NRootCC/nrootCC_3'.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_3'.con".
-inline cic:/CoRN/complex/NRootCC/nrootCC_3'_degree.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_3'_degree.con".
(* UNEXPORTED
End NRootCC_3'.
(* UNEXPORTED
End NRootCC_3'.
-inline cic:/CoRN/complex/NRootCC/a.var.
+inline "cic:/CoRN/complex/NRootCC/a.var".
-inline cic:/CoRN/complex/NRootCC/b.var.
+inline "cic:/CoRN/complex/NRootCC/b.var".
-inline cic:/CoRN/complex/NRootCC/b_.var.
+inline "cic:/CoRN/complex/NRootCC/b_.var".
-inline cic:/CoRN/complex/NRootCC/n.var.
+inline "cic:/CoRN/complex/NRootCC/n.var".
-inline cic:/CoRN/complex/NRootCC/n_.var.
+inline "cic:/CoRN/complex/NRootCC/n_.var".
-inline cic:/CoRN/complex/NRootCC/c.con.
+inline "cic:/CoRN/complex/NRootCC/c.con".
Hint Resolve nrootCC_3: algebra.
*)
Hint Resolve nrootCC_3: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrCC4_a1.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a1.con".
(*#*
%\begin{convention}% Let [r2',c2 : IR] and [r2'_ : (r2' [#] Zero)].
%\end{convention}%
*)
(*#*
%\begin{convention}% Let [r2',c2 : IR] and [r2'_ : (r2' [#] Zero)].
%\end{convention}%
*)
-inline cic:/CoRN/complex/NRootCC/r2'.var.
+inline "cic:/CoRN/complex/NRootCC/r2'.var".
-inline cic:/CoRN/complex/NRootCC/c2.var.
+inline "cic:/CoRN/complex/NRootCC/c2.var".
-inline cic:/CoRN/complex/NRootCC/r2'_.var.
+inline "cic:/CoRN/complex/NRootCC/r2'_.var".
(* UNEXPORTED
Hint Resolve nrootCC_3': algebra.
*)
(* UNEXPORTED
Hint Resolve nrootCC_3': algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrCC4_a1'.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a1'.con".
(* UNEXPORTED
End NRootCC_4_solutions.
(* UNEXPORTED
End NRootCC_4_solutions.
-inline cic:/CoRN/complex/NRootCC/r.var.
+inline "cic:/CoRN/complex/NRootCC/r.var".
-inline cic:/CoRN/complex/NRootCC/r_property.var.
+inline "cic:/CoRN/complex/NRootCC/r_property.var".
-inline cic:/CoRN/complex/NRootCC/y2.var.
+inline "cic:/CoRN/complex/NRootCC/y2.var".
-inline cic:/CoRN/complex/NRootCC/y2_property.var.
+inline "cic:/CoRN/complex/NRootCC/y2_property.var".
-inline cic:/CoRN/complex/NRootCC/nrCC4_a2.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a2.con".
-inline cic:/CoRN/complex/NRootCC/nrCC4_a3.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a3.con".
-inline cic:/CoRN/complex/NRootCC/nrCC4_a4.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a4.con".
-inline cic:/CoRN/complex/NRootCC/nrCC4_y.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_y.con".
-inline cic:/CoRN/complex/NRootCC/y.con.
+inline "cic:/CoRN/complex/NRootCC/y.con".
-inline cic:/CoRN/complex/NRootCC/nrCC4_x.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_x.con".
-inline cic:/CoRN/complex/NRootCC/x.con.
+inline "cic:/CoRN/complex/NRootCC/x.con".
-inline cic:/CoRN/complex/NRootCC/nrCC4_a5.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a5.con".
-inline cic:/CoRN/complex/NRootCC/nrCC4_a6.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a6.con".
-inline cic:/CoRN/complex/NRootCC/nrCC4_z.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_z.con".
-inline cic:/CoRN/complex/NRootCC/z.con.
+inline "cic:/CoRN/complex/NRootCC/z.con".
-inline cic:/CoRN/complex/NRootCC/nrCC4_a7.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a7.con".
(* UNEXPORTED
Hint Resolve nrCC4_a6: algebra.
*)
(* UNEXPORTED
Hint Resolve nrCC4_a6: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrCC4_a8.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a8.con".
-inline cic:/CoRN/complex/NRootCC/nrCC4_a9.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a9.con".
(* UNEXPORTED
End NRootCC_4_equations.
*)
(* UNEXPORTED
End NRootCC_4_equations.
*)
-inline cic:/CoRN/complex/NRootCC/nrCC4_a10.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC4_a10.con".
-inline cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real.con".
(* UNEXPORTED
End NRootCC_4_ap_real.
(* UNEXPORTED
End NRootCC_4_ap_real.
-inline cic:/CoRN/complex/NRootCC/a.var.
+inline "cic:/CoRN/complex/NRootCC/a.var".
-inline cic:/CoRN/complex/NRootCC/b.var.
+inline "cic:/CoRN/complex/NRootCC/b.var".
-inline cic:/CoRN/complex/NRootCC/a_.var.
+inline "cic:/CoRN/complex/NRootCC/a_.var".
-inline cic:/CoRN/complex/NRootCC/n.var.
+inline "cic:/CoRN/complex/NRootCC/n.var".
-inline cic:/CoRN/complex/NRootCC/n_.var.
+inline "cic:/CoRN/complex/NRootCC/n_.var".
-inline cic:/CoRN/complex/NRootCC/c'.con.
+inline "cic:/CoRN/complex/NRootCC/c'.con".
-inline cic:/CoRN/complex/NRootCC/a'.con.
+inline "cic:/CoRN/complex/NRootCC/a'.con".
-inline cic:/CoRN/complex/NRootCC/b'.con.
+inline "cic:/CoRN/complex/NRootCC/b'.con".
-inline cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real'.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real'.con".
(* UNEXPORTED
Hint Resolve nroot_minus_I_nexp: algebra.
*)
(* UNEXPORTED
Hint Resolve nroot_minus_I_nexp: algebra.
*)
-inline cic:/CoRN/complex/NRootCC/nrootCC_4_ap_imag.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_imag.con".
(* UNEXPORTED
End NRootCC_4_ap_imag.
*)
(* UNEXPORTED
End NRootCC_4_ap_imag.
*)
-inline cic:/CoRN/complex/NRootCC/nrootCC_4.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_4.con".
(* UNEXPORTED
End NRootCC_4.
(* UNEXPORTED
End NRootCC_4.
-inline cic:/CoRN/complex/NRootCC/nrCC_5a2.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC_5a2.con".
-inline cic:/CoRN/complex/NRootCC/nrCC_5a3.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC_5a3.con".
(* UNEXPORTED
Hint Resolve nrCC_5a3: algebra.
(* UNEXPORTED
Hint Resolve nrCC_5a3: algebra.
-inline cic:/CoRN/complex/NRootCC/c.var.
+inline "cic:/CoRN/complex/NRootCC/c.var".
-inline cic:/CoRN/complex/NRootCC/c_.var.
+inline "cic:/CoRN/complex/NRootCC/c_.var".
-inline cic:/CoRN/complex/NRootCC/nrCC_5a4.con.
+inline "cic:/CoRN/complex/NRootCC/nrCC_5a4.con".
-inline cic:/CoRN/complex/NRootCC/nrootCC_5.con.
+inline "cic:/CoRN/complex/NRootCC/nrootCC_5.con".
(* UNEXPORTED
End NRootCC_5.
(* UNEXPORTED
End NRootCC_5.
-inline cic:/CoRN/complex/NRootCC/CnrootCC.con.
+inline "cic:/CoRN/complex/NRootCC/CnrootCC.con".
set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/IDA/Ch6".
set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/IDA/Ch6".
-(* INCLUDE
-CSemiGroups
-*)
+include "CoRN.ma".
+
+include "algebra/CSemiGroups.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation.con".
+include "model/setoids/Zsetoid.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation_Z_0.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation_Z_0.con".
+include "devel/loeb/per/csetfun.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/n_ary_operation.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/n_ary_operation.con".
+include "model/setoids/Nsetoid.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/plus1.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/plus1.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/to_plus1_strext.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus1_strext.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/plus2.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/plus2.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/to_plus2_strext.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus2_strext.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/plus3.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/plus3.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/on.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/on.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con".
(* Print Zmult_is_assoc.*)
(* Print Zmult_is_assoc.*)
+include "model/setoids/Qsetoid.ma".
(* Print Qplus_is_assoc.*)
(* Print Qplus_is_assoc.*)
-inline cic:/CoRN/devel/loeb/IDA/Ch6/X.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/X.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/f.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/g.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/g.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/h.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/h.var".
(* Check comp_as_bin_op.*)
(* Check comp_as_bin_op.*)
(* blz 66 Example 2eblok 1 *)
(* blz 66 Example 2eblok 1 *)
-(* INCLUDE
-Zsemigroup
-*)
+include "model/semigroups/Zsemigroup.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/Zplus_is_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Zplus_is_CSemiGroup.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/Zmult_is_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Zmult_is_CSemiGroup.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/A.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/empty_word.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/empty_word.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/app.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/app.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_irreflexive.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_irreflexive.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_symmetric.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_symmetric.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_cotransitive.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_cotransitive.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_tight.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_tight.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_is_CSetoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_is_CSetoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_as_csetoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_as_csetoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/app_strext.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/app_strext.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/app_as_csb_fun.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/app_as_csb_fun.con".
-(* INCLUDE
-CSemiGroups
-*)
+include "algebra/CSemiGroups.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm_reflexive.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm_reflexive.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/Astar_is_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_is_CSemiGroup.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/Astar_as_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_as_CSemiGroup.con".
(* UNEXPORTED
End p66E2b4.
(* UNEXPORTED
End p66E2b4.
-inline cic:/CoRN/devel/loeb/IDA/Ch6/is_unit.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit.con".
+include "model/monoids/Zmonoid.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/X.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/X.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Astar_empty_word.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Astar_empty_word.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/unique_unit.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/unique_unit.con".
+include "model/monoids/Nmonoid.ma".
(* Print nat_is_CMonoid.*)
(* Print nat_is_CMonoid.*)
+include "model/monoids/Zmonoid.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1.ind.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.ind".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_irreflexive.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_irreflexive.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_symmetric.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_symmetric.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_cotransitive.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_cotransitive.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq_dec.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq_dec.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/is_e1.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_e1.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/not_M1_eq_e1_u.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_M1_eq_e1_u.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_tight.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_tight.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSetoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSetoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSetoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSetoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult_strext.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult_strext.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult_as_bin_fun.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult_as_bin_fun.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSemiGroup.con".
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSemiGroup.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CMonoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CMonoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult_strext.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult_strext.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult_as_bin_fun.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult_as_bin_fun.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CSemiGroup.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CSemiGroup.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit_M2.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit_M2.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit_M2.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit_M2.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CMonoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CMonoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/two_element_CMonoids.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/two_element_CMonoids.con".
(* UNEXPORTED
End p68E1b1.
(* UNEXPORTED
End p68E1b1.
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
(* UNEXPORTED
Section D9S.
*)
(* UNEXPORTED
Section D9S.
*)
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/dprod_strext.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_strext.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/dprod_as_csb_fun.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_as_csb_fun.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CSemiGroup.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CSemiGroup.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_lft_unit.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_lft_unit.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CMonoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CMonoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/PM1M2.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/PM1M2.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/uu.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/uu.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/e1u.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1u.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/ex_69.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_69.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/I.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/I.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/C.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/C.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/Cunit.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Cunit.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_C.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_C.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/K.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/K.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_K.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_K.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/K_is_Monoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/K_is_Monoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/A.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_lft_unit.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_lft_unit.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_is_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_is_CMonoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_as_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_as_CMonoid.con".
+include "devel/loeb/per/lst2fun.ma".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/A.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/ZerolessOne.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ZerolessOne.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/to_word.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/to_word'.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/to_word'_strext.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'_strext.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/to_word_as_CSetoid_fun.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_as_CSetoid_fun.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/to_word_bijective.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_bijective.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/pres_plus_to_word.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/pres_plus_to_word.con".
(* UNEXPORTED
End p70text.
(* UNEXPORTED
End p70text.
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/isomorphism.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphism.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/c.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/c.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid_CSetoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid_CSetoid.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/is_generated_by.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_generated_by.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/f.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/f_strext.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/surjective_f.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/surjective_f.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/not_injective_f.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_injective_f.con".
(* UNEXPORTED
End p71E1'.
(* UNEXPORTED
End p71E1'.
-inline cic:/CoRN/devel/loeb/IDA/Ch6/A.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/L.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/L.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/L_strext.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_strext.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/L_as_CSetoid_fun.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_as_CSetoid_fun.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/L_is_morphism.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_is_morphism.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/S1.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/S1.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/S2.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/S2.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/f.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/isof.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/isof.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/iso_inv.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/iso_inv.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/not_isomorphic_M1_M2.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_isomorphic_M1_M2.con".
(* UNEXPORTED
End p71E2b1.
(* UNEXPORTED
End p71E2b1.
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M1.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M2.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/f.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/f_strext'.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext'.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun'.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun'.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic_PM1M2_PM2M1.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic_PM1M2_PM2M1.con".
(* UNEXPORTED
End p71E2b2.
(* UNEXPORTED
End p71E2b2.
-inline cic:/CoRN/devel/loeb/IDA/Ch6/M.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/D.var.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/D.var".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/member.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/member.con".
(* UNEXPORTED
Implicit Arguments member [A].
*)
(* UNEXPORTED
Implicit Arguments member [A].
*)
-inline cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_unit.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_unit.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/member_app.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/member_app.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum_app.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum_app.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_Dbrack.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_Dbrack.con".
-inline cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_as_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_as_CMonoid.con".
set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/per/csetfun".
set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/per/csetfun".
-(* INCLUDE
-CSetoids
-*)
-(* INCLUDE
-CSetoidFun
-*)
+include "algebra/CSetoids.ma".
+
+include "algebra/CSetoidFun.ma".
-inline cic:/CoRN/devel/loeb/per/csetfun/ap_fun.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/ap_fun.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/eq_fun.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/eq_fun.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/irrefl_apfun.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/irrefl_apfun.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/cotrans_apfun.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/cotrans_apfun.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/ta_apfun.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/ta_apfun.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/sym_apfun.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/sym_apfun.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/FS_is_CSetoid.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CSetoid.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSetoid.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSetoid.con".
(* UNEXPORTED
Print associative.
*)
(* UNEXPORTED
Print associative.
*)
-inline cic:/CoRN/devel/loeb/per/csetfun/comp.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/comp.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/comp_as_bin_op.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/comp_as_bin_op.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/assoc_comp.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/assoc_comp.con".
-(* INCLUDE
-CSemiGroups
-*)
+include "algebra/CSemiGroups.ma".
-inline cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSemiGroup.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSemiGroup.con".
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
-inline cic:/CoRN/devel/loeb/per/csetfun/FS_id.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/FS_id.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/id_is_rht_unit.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/id_is_rht_unit.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/id_is_lft_unit.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/id_is_lft_unit.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/FS_is_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CMonoid.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/FS_as_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CMonoid.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/PS_as_CMonoid.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CMonoid.con".
+include "algebra/CGroups.ma".
-inline cic:/CoRN/devel/loeb/per/csetfun/Inv_is_bij.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/Inv_is_bij.con".
(* Lemma Inv_is_bij :
forall (A B : CSetoid) (f : CSetoid_fun A B) (H : bijective f),
(* Lemma Inv_is_bij :
forall (A B : CSetoid) (f : CSetoid_fun A B) (H : bijective f),
-inline cic:/CoRN/devel/loeb/per/csetfun/PS_Inv.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/PS_Inv.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/Inv_as_un_op.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/Inv_as_un_op.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/PS_is_CGroup.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/PS_is_CGroup.con".
-inline cic:/CoRN/devel/loeb/per/csetfun/PS_as_CGroup.con.
+inline "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CGroup.con".
(* In het algemeen niet Abels! *)
(* In het algemeen niet Abels! *)
set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/per/lst2fun".
set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/per/lst2fun".
-inline cic:/CoRN/devel/loeb/per/lst2fun/F'.con.
-inline cic:/CoRN/devel/loeb/per/lst2fun/F.ind.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/F'.con".
-inline cic:/CoRN/devel/loeb/per/lst2fun/to_nat.con.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/F.ind".
+
+coercion "cic:/matita/CoRN-Decl/devel/loeb/per/lst2fun/F_crr.con" 0 (* compounds *).
+
+inline "cic:/CoRN/devel/loeb/per/lst2fun/to_nat.con".
(* UNEXPORTED
Implicit Arguments to_nat [n].
*)
(* UNEXPORTED
Implicit Arguments to_nat [n].
*)
-(* INCLUDE
-CSetoids
-*)
+coercion "cic:/matita/CoRN-Decl/devel/loeb/per/lst2fun/to_nat.con" 0 (* compounds *).
+
+include "algebra/CSetoids.ma".
-inline cic:/CoRN/devel/loeb/per/lst2fun/Feq.con.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/Feq.con".
-inline cic:/CoRN/devel/loeb/per/lst2fun/Fap.con.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/Fap.con".
-inline cic:/CoRN/devel/loeb/per/lst2fun/Fap_irreflexive.con.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/Fap_irreflexive.con".
-inline cic:/CoRN/devel/loeb/per/lst2fun/Fap_symmetric.con.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/Fap_symmetric.con".
-inline cic:/CoRN/devel/loeb/per/lst2fun/Fap_cotransitive.con.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/Fap_cotransitive.con".
-inline cic:/CoRN/devel/loeb/per/lst2fun/Fap_tight.con.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/Fap_tight.con".
-inline cic:/CoRN/devel/loeb/per/lst2fun/less.con.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/less.con".
-inline cic:/CoRN/devel/loeb/per/lst2fun/CSetoid_of_less.con.
+inline "cic:/CoRN/devel/loeb/per/lst2fun/CSetoid_of_less.con".
set "baseuri" "cic:/matita/CoRN-Decl/fta/CC_Props".
set "baseuri" "cic:/matita/CoRN-Decl/fta/CC_Props".
(* $Id: CC_Props.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
(* $Id: CC_Props.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
+include "complex/AbsCC.ma".
(*#* * More properties of complex numbers
** Sequences and limits *)
(*#* * More properties of complex numbers
** Sequences and limits *)
Hint Resolve AbsIR_sqrt_sqr: algebra.
*)
Hint Resolve AbsIR_sqrt_sqr: algebra.
*)
-inline cic:/CoRN/fta/CC_Props/absCC_absIR_re.con.
+inline "cic:/CoRN/fta/CC_Props/absCC_absIR_re.con".
+
+inline "cic:/CoRN/fta/CC_Props/absCC_absIR_im.con".
-inline cic:/CoRN/fta/CC_Props/absCC_absIR_im.con.
+inline "cic:/CoRN/fta/CC_Props/seq_re.con".
-inline cic:/CoRN/fta/CC_Props/seq_re.con.
+inline "cic:/CoRN/fta/CC_Props/seq_im.con".
-inline cic:/CoRN/fta/CC_Props/seq_im.con.
+inline "cic:/CoRN/fta/CC_Props/CC_Cauchy_prop.con".
-inline cic:/CoRN/fta/CC_Props/CC_Cauchy_prop.con.
+inline "cic:/CoRN/fta/CC_Props/CC_CauchySeq.ind".
-inline cic:/CoRN/fta/CC_Props/CC_CauchySeq.ind.
+coercion "cic:/matita/CoRN-Decl/fta/CC_Props/CC_seq.con" 0 (* compounds *).
-inline cic:/CoRN/fta/CC_Props/re_is_Cauchy.con.
+inline "cic:/CoRN/fta/CC_Props/re_is_Cauchy.con".
-inline cic:/CoRN/fta/CC_Props/im_is_Cauchy.con.
+inline "cic:/CoRN/fta/CC_Props/im_is_Cauchy.con".
-inline cic:/CoRN/fta/CC_Props/CC_Cauchy2re.con.
+inline "cic:/CoRN/fta/CC_Props/CC_Cauchy2re.con".
-inline cic:/CoRN/fta/CC_Props/CC_Cauchy2im.con.
+inline "cic:/CoRN/fta/CC_Props/CC_Cauchy2im.con".
-inline cic:/CoRN/fta/CC_Props/LimCC.con.
+inline "cic:/CoRN/fta/CC_Props/LimCC.con".
-inline cic:/CoRN/fta/CC_Props/CC_SeqLimit.con.
+inline "cic:/CoRN/fta/CC_Props/CC_SeqLimit.con".
-inline cic:/CoRN/fta/CC_Props/AbsSmall_sqr.con.
+inline "cic:/CoRN/fta/CC_Props/AbsSmall_sqr.con".
-inline cic:/CoRN/fta/CC_Props/AbsSmall_AbsCC.con.
+inline "cic:/CoRN/fta/CC_Props/AbsSmall_AbsCC.con".
-inline cic:/CoRN/fta/CC_Props/LimCC_is_lim.con.
+inline "cic:/CoRN/fta/CC_Props/LimCC_is_lim.con".
-inline cic:/CoRN/fta/CC_Props/CC_SeqLimit_uniq.con.
+inline "cic:/CoRN/fta/CC_Props/CC_SeqLimit_uniq.con".
-inline cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con.
+inline "cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con".
(*#* ** Continuity for [CC]
*)
(*#* ** Continuity for [CC]
*)
-inline cic:/CoRN/fta/CC_Props/f.var.
+inline "cic:/CoRN/fta/CC_Props/f.var".
(* (CSetoid_un_op CC). *)
(* (CSetoid_un_op CC). *)
-inline cic:/CoRN/fta/CC_Props/CCfunLim.con.
+inline "cic:/CoRN/fta/CC_Props/CCfunLim.con".
-inline cic:/CoRN/fta/CC_Props/CCcontinAt.con.
+inline "cic:/CoRN/fta/CC_Props/CCcontinAt.con".
-inline cic:/CoRN/fta/CC_Props/CCcontin.con.
+inline "cic:/CoRN/fta/CC_Props/CCcontin.con".
-inline cic:/CoRN/fta/CC_Props/CCfunLim_SeqLimit.con.
+inline "cic:/CoRN/fta/CC_Props/CCfunLim_SeqLimit.con".
-inline cic:/CoRN/fta/CC_Props/f_seq.con.
+inline "cic:/CoRN/fta/CC_Props/f_seq.con".
-inline cic:/CoRN/fta/CC_Props/poly_pres_lim.con.
+inline "cic:/CoRN/fta/CC_Props/poly_pres_lim.con".
(* UNEXPORTED
End Continuity_for_CC.
*)
(* UNEXPORTED
End Continuity_for_CC.
*)
-inline cic:/CoRN/fta/CC_Props/seq_yields_zero.con.
+inline "cic:/CoRN/fta/CC_Props/seq_yields_zero.con".
set "baseuri" "cic:/matita/CoRN-Decl/fta/CPoly_Contin1".
set "baseuri" "cic:/matita/CoRN-Decl/fta/CPoly_Contin1".
(* $Id: CPoly_Contin1.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
(* $Id: CPoly_Contin1.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
-(* INCLUDE
-CC_Props
-*)
+include "fta/CC_Props.ma".
(*#* * Continuity of complex polynomials
*)
(*#* * Continuity of complex polynomials
*)
Section Mult_CC_Continuous.
*)
Section Mult_CC_Continuous.
*)
-inline cic:/CoRN/fta/CPoly_Contin1/mult_absCC.con.
+inline "cic:/CoRN/fta/CPoly_Contin1/mult_absCC.con".
-inline cic:/CoRN/fta/CPoly_Contin1/estimate_absCC.con.
+inline "cic:/CoRN/fta/CPoly_Contin1/estimate_absCC.con".
-inline cic:/CoRN/fta/CPoly_Contin1/mult_CC_contin.con.
+inline "cic:/CoRN/fta/CPoly_Contin1/mult_CC_contin.con".
(* UNEXPORTED
End Mult_CC_Continuous.
(* UNEXPORTED
End Mult_CC_Continuous.
-inline cic:/CoRN/fta/CPoly_Contin1/g.var.
+inline "cic:/CoRN/fta/CPoly_Contin1/g.var".
-inline cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con.
+inline "cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con".
-inline cic:/CoRN/fta/CPoly_Contin1/contin_polyCC.con.
+inline "cic:/CoRN/fta/CPoly_Contin1/contin_polyCC.con".
(* UNEXPORTED
End CPoly_CC_Continuous.
(* UNEXPORTED
End CPoly_CC_Continuous.
set "baseuri" "cic:/matita/CoRN-Decl/fta/CPoly_Rev".
set "baseuri" "cic:/matita/CoRN-Decl/fta/CPoly_Rev".
(* $Id: CPoly_Rev.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
(* $Id: CPoly_Rev.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
-(* INCLUDE
-CPoly_Degree
-*)
+include "algebra/CPoly_Degree.ma".
(*#* * Reverse of polynomials
*)
(*#* * Reverse of polynomials
*)
-inline cic:/CoRN/fta/CPoly_Rev/R.var.
+inline "cic:/CoRN/fta/CPoly_Rev/R.var".
-inline cic:/CoRN/fta/CPoly_Rev/RX.con.
+inline "cic:/CoRN/fta/CPoly_Rev/RX.con".
-inline cic:/CoRN/fta/CPoly_Rev/monom.con.
+inline "cic:/CoRN/fta/CPoly_Rev/monom.con".
-inline cic:/CoRN/fta/CPoly_Rev/monom_coeff.con.
+inline "cic:/CoRN/fta/CPoly_Rev/monom_coeff.con".
-inline cic:/CoRN/fta/CPoly_Rev/monom_coeff'.con.
+inline "cic:/CoRN/fta/CPoly_Rev/monom_coeff'.con".
(* UNEXPORTED
Hint Resolve monom_coeff monom_coeff': algebra.
*)
(* UNEXPORTED
Hint Resolve monom_coeff monom_coeff': algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/monom_degree.con.
+inline "cic:/CoRN/fta/CPoly_Rev/monom_degree.con".
-inline cic:/CoRN/fta/CPoly_Rev/monom_S.con.
+inline "cic:/CoRN/fta/CPoly_Rev/monom_S.con".
(* UNEXPORTED
Hint Resolve monom_S: algebra.
*)
(* UNEXPORTED
Hint Resolve monom_S: algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/monom_wd_lft.con.
+inline "cic:/CoRN/fta/CPoly_Rev/monom_wd_lft.con".
(* UNEXPORTED
Hint Resolve monom_wd_lft: algebra_c.
*)
(* UNEXPORTED
Hint Resolve monom_wd_lft: algebra_c.
*)
-inline cic:/CoRN/fta/CPoly_Rev/monom_mult'.con.
+inline "cic:/CoRN/fta/CPoly_Rev/monom_mult'.con".
(* UNEXPORTED
Hint Resolve monom_mult': algebra.
*)
(* UNEXPORTED
Hint Resolve monom_mult': algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/monom_mult.con.
+inline "cic:/CoRN/fta/CPoly_Rev/monom_mult.con".
-inline cic:/CoRN/fta/CPoly_Rev/monom_sum.con.
+inline "cic:/CoRN/fta/CPoly_Rev/monom_sum.con".
(* UNEXPORTED
End Monomials.
(* UNEXPORTED
End Monomials.
-inline cic:/CoRN/fta/CPoly_Rev/R.var.
+inline "cic:/CoRN/fta/CPoly_Rev/R.var".
-inline cic:/CoRN/fta/CPoly_Rev/RX.con.
+inline "cic:/CoRN/fta/CPoly_Rev/RX.con".
-inline cic:/CoRN/fta/CPoly_Rev/Rev.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev.con".
-inline cic:/CoRN/fta/CPoly_Rev/Rev_coeff.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_coeff.con".
-inline cic:/CoRN/fta/CPoly_Rev/Rev_coeff'.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_coeff'.con".
(* UNEXPORTED
Hint Resolve Rev_coeff Rev_coeff': algebra.
*)
(* UNEXPORTED
Hint Resolve Rev_coeff Rev_coeff': algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/Rev_wd.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_wd.con".
(* UNEXPORTED
Hint Resolve Rev_wd: algebra_c.
*)
(* UNEXPORTED
Hint Resolve Rev_wd: algebra_c.
*)
-inline cic:/CoRN/fta/CPoly_Rev/Rev_rev.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_rev.con".
(* UNEXPORTED
Hint Resolve Rev_rev: algebra.
*)
(* UNEXPORTED
Hint Resolve Rev_rev: algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/Rev_degree_le.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_degree_le.con".
-inline cic:/CoRN/fta/CPoly_Rev/Rev_degree.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_degree.con".
-inline cic:/CoRN/fta/CPoly_Rev/Rev_monom.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_monom.con".
(* UNEXPORTED
Hint Resolve Rev_monom: algebra.
*)
(* UNEXPORTED
Hint Resolve Rev_monom: algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/Rev_zero.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_zero.con".
(* UNEXPORTED
Hint Resolve Rev_zero: algebra.
*)
(* UNEXPORTED
Hint Resolve Rev_zero: algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/Rev_plus.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_plus.con".
(* UNEXPORTED
Hint Resolve Rev_plus: algebra.
*)
(* UNEXPORTED
Hint Resolve Rev_plus: algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/Rev_minus.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_minus.con".
(* UNEXPORTED
Hint Resolve Rev_minus: algebra.
*)
(* UNEXPORTED
Hint Resolve Rev_minus: algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/Rev_sum0.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_sum0.con".
(* UNEXPORTED
Hint Resolve Rev_sum0: algebra.
*)
(* UNEXPORTED
Hint Resolve Rev_sum0: algebra.
*)
-inline cic:/CoRN/fta/CPoly_Rev/Rev_sum.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_sum.con".
-inline cic:/CoRN/fta/CPoly_Rev/Rev_mult.con.
+inline "cic:/CoRN/fta/CPoly_Rev/Rev_mult.con".
(* UNEXPORTED
End Poly_Reverse.
(* UNEXPORTED
End Poly_Reverse.
set "baseuri" "cic:/matita/CoRN-Decl/fta/CPoly_Shift".
set "baseuri" "cic:/matita/CoRN-Decl/fta/CPoly_Shift".
(* $Id: CPoly_Shift.v,v 1.4 2004/04/23 10:00:56 lcf Exp $ *)
(* $Id: CPoly_Shift.v,v 1.4 2004/04/23 10:00:56 lcf Exp $ *)
-(* INCLUDE
-CComplex
-*)
+include "complex/CComplex.ma".
(*#* * Shifting polynomials
This can be done for [CRings] in general, but we do it here
(*#* * Shifting polynomials
This can be done for [CRings] in general, but we do it here
-inline cic:/CoRN/fta/CPoly_Shift/Shift.con.
+inline "cic:/CoRN/fta/CPoly_Shift/Shift.con".
-inline cic:/CoRN/fta/CPoly_Shift/Shift_apply.con.
+inline "cic:/CoRN/fta/CPoly_Shift/Shift_apply.con".
(* UNEXPORTED
Hint Resolve Shift_apply: algebra.
*)
(* UNEXPORTED
Hint Resolve Shift_apply: algebra.
*)
-inline cic:/CoRN/fta/CPoly_Shift/Shift_wdr.con.
+inline "cic:/CoRN/fta/CPoly_Shift/Shift_wdr.con".
-inline cic:/CoRN/fta/CPoly_Shift/Shift_shift.con.
+inline "cic:/CoRN/fta/CPoly_Shift/Shift_shift.con".
-inline cic:/CoRN/fta/CPoly_Shift/Shift_mult.con.
+inline "cic:/CoRN/fta/CPoly_Shift/Shift_mult.con".
-inline cic:/CoRN/fta/CPoly_Shift/Shift_degree_le.con.
+inline "cic:/CoRN/fta/CPoly_Shift/Shift_degree_le.con".
-inline cic:/CoRN/fta/CPoly_Shift/Shift_monic.con.
+inline "cic:/CoRN/fta/CPoly_Shift/Shift_monic.con".
(* UNEXPORTED
End Poly_Shifted.
(* UNEXPORTED
End Poly_Shifted.
set "baseuri" "cic:/matita/CoRN-Decl/fta/FTA".
set "baseuri" "cic:/matita/CoRN-Decl/fta/FTA".
(* $Id: FTA.v,v 1.6 2004/04/23 10:00:57 lcf Exp $ *)
(* $Id: FTA.v,v 1.6 2004/04/23 10:00:57 lcf Exp $ *)
-(* INCLUDE
-CPoly_Rev
-*)
+include "fta/CPoly_Rev.ma".
+include "fta/FTAreg.ma".
(*#* * Fundamental Theorem of Algebra
%\begin{convention}% Let [n:nat] and [f] be a complex polynomial of
(*#* * Fundamental Theorem of Algebra
%\begin{convention}% Let [n:nat] and [f] be a complex polynomial of
-inline cic:/CoRN/fta/FTA/f.var.
+inline "cic:/CoRN/fta/FTA/f.var".
-inline cic:/CoRN/fta/FTA/n.var.
+inline "cic:/CoRN/fta/FTA/n.var".
-inline cic:/CoRN/fta/FTA/f_degree.var.
+inline "cic:/CoRN/fta/FTA/f_degree.var".
-inline cic:/CoRN/fta/FTA/FTA_reg'.con.
+inline "cic:/CoRN/fta/FTA/FTA_reg'.con".
(* UNEXPORTED
End FTA_reg'.
(* UNEXPORTED
End FTA_reg'.
-inline cic:/CoRN/fta/FTA/f.var.
+inline "cic:/CoRN/fta/FTA/f.var".
-inline cic:/CoRN/fta/FTA/n.var.
+inline "cic:/CoRN/fta/FTA/n.var".
-inline cic:/CoRN/fta/FTA/f_degree.var.
+inline "cic:/CoRN/fta/FTA/f_degree.var".
-inline cic:/CoRN/fta/FTA/c.var.
+inline "cic:/CoRN/fta/FTA/c.var".
-inline cic:/CoRN/fta/FTA/f_c.var.
+inline "cic:/CoRN/fta/FTA/f_c.var".
-inline cic:/CoRN/fta/FTA/FTA_1a.con.
+inline "cic:/CoRN/fta/FTA/FTA_1a.con".
-inline cic:/CoRN/fta/FTA/g.con.
+inline "cic:/CoRN/fta/FTA/g.con".
-inline cic:/CoRN/fta/FTA/FTA_1b.con.
+inline "cic:/CoRN/fta/FTA/FTA_1b.con".
-inline cic:/CoRN/fta/FTA/FTA_1.con.
+inline "cic:/CoRN/fta/FTA/FTA_1.con".
-inline cic:/CoRN/fta/FTA/FTA_1'.con.
+inline "cic:/CoRN/fta/FTA/FTA_1'.con".
-inline cic:/CoRN/fta/FTA/FTA'.con.
+inline "cic:/CoRN/fta/FTA/FTA'.con".
-inline cic:/CoRN/fta/FTA/FTA.con.
+inline "cic:/CoRN/fta/FTA/FTA.con".
-inline cic:/CoRN/fta/FTA/FTA_a_la_Henk.con.
+inline "cic:/CoRN/fta/FTA/FTA_a_la_Henk.con".
(* UNEXPORTED
End Fund_Thm_Alg.
(* UNEXPORTED
End Fund_Thm_Alg.
set "baseuri" "cic:/matita/CoRN-Decl/fta/FTAreg".
set "baseuri" "cic:/matita/CoRN-Decl/fta/FTAreg".
(* $Id: FTAreg.v,v 1.4 2004/04/23 10:00:57 lcf Exp $ *)
(* $Id: FTAreg.v,v 1.4 2004/04/23 10:00:57 lcf Exp $ *)
-(* INCLUDE
-KneserLemma
-*)
+include "fta/KneserLemma.ma".
-(* INCLUDE
-CPoly_Shift
-*)
+include "fta/CPoly_Shift.ma".
-(* INCLUDE
-CPoly_Contin1
-*)
+include "fta/CPoly_Contin1.ma".
(*#* * FTA for regular polynomials
** The Kneser sequence
(*#* * FTA for regular polynomials
** The Kneser sequence
-inline cic:/CoRN/fta/FTAreg/n.var.
+inline "cic:/CoRN/fta/FTAreg/n.var".
-inline cic:/CoRN/fta/FTAreg/lt0n.var.
+inline "cic:/CoRN/fta/FTAreg/lt0n.var".
(*#*
%\begin{convention}% Let [qK] be a real between 0 and 1, with
(*#*
%\begin{convention}% Let [qK] be a real between 0 and 1, with
Section Kneser_Sequence.
*)
Section Kneser_Sequence.
*)
-inline cic:/CoRN/fta/FTAreg/qK.var.
+inline "cic:/CoRN/fta/FTAreg/qK.var".
+
+inline "cic:/CoRN/fta/FTAreg/zltq.var".
+
+inline "cic:/CoRN/fta/FTAreg/qlt1.var".
-inline cic:/CoRN/fta/FTAreg/zltq.var.
+inline "cic:/CoRN/fta/FTAreg/q_prop.var".
-inline cic:/CoRN/fta/FTAreg/qlt1.var.
+inline "cic:/CoRN/fta/FTAreg/p.var".
-inline cic:/CoRN/fta/FTAreg/q_prop.var.
+inline "cic:/CoRN/fta/FTAreg/mp.var".
-inline cic:/CoRN/fta/FTAreg/p.var.
+inline "cic:/CoRN/fta/FTAreg/c0.var".
-inline cic:/CoRN/fta/FTAreg/mp.var.
+inline "cic:/CoRN/fta/FTAreg/p0ltc0.var".
-inline cic:/CoRN/fta/FTAreg/c0.var.
+inline "cic:/CoRN/fta/FTAreg/Knes_tup.ind".
-inline cic:/CoRN/fta/FTAreg/p0ltc0.var.
+coercion "cic:/matita/CoRN-Decl/fta/FTAreg/z_el.con" 0 (* compounds *).
-inline cic:/CoRN/fta/FTAreg/Knes_tup.ind.
+inline "cic:/CoRN/fta/FTAreg/Knes_tupp.ind".
-inline cic:/CoRN/fta/FTAreg/Knes_tupp.ind.
+coercion "cic:/matita/CoRN-Decl/fta/FTAreg/Kntup.con" 0 (* compounds *).
-inline cic:/CoRN/fta/FTAreg/Knes_fun.con.
+inline "cic:/CoRN/fta/FTAreg/Knes_fun.con".
-inline cic:/CoRN/fta/FTAreg/Knes_fun_it.con.
+inline "cic:/CoRN/fta/FTAreg/Knes_fun_it.con".
-inline cic:/CoRN/fta/FTAreg/sK.con.
+inline "cic:/CoRN/fta/FTAreg/sK.con".
-inline cic:/CoRN/fta/FTAreg/sK_c.con.
+inline "cic:/CoRN/fta/FTAreg/sK_c.con".
-inline cic:/CoRN/fta/FTAreg/sK_c0.con.
+inline "cic:/CoRN/fta/FTAreg/sK_c0.con".
-inline cic:/CoRN/fta/FTAreg/sK_prop1.con.
+inline "cic:/CoRN/fta/FTAreg/sK_prop1.con".
-inline cic:/CoRN/fta/FTAreg/sK_it.con.
+inline "cic:/CoRN/fta/FTAreg/sK_it.con".
-inline cic:/CoRN/fta/FTAreg/sK_prop2.con.
+inline "cic:/CoRN/fta/FTAreg/sK_prop2.con".
(* UNEXPORTED
End Kneser_Sequence.
(* UNEXPORTED
End Kneser_Sequence.
-inline cic:/CoRN/fta/FTAreg/seq_exists.con.
+inline "cic:/CoRN/fta/FTAreg/seq_exists.con".
(* UNEXPORTED
End Seq_Exists_Main.
(* UNEXPORTED
End Seq_Exists_Main.
-inline cic:/CoRN/fta/FTAreg/n.var.
+inline "cic:/CoRN/fta/FTAreg/n.var".
-inline cic:/CoRN/fta/FTAreg/lt0n.var.
+inline "cic:/CoRN/fta/FTAreg/lt0n.var".
-inline cic:/CoRN/fta/FTAreg/q.var.
+inline "cic:/CoRN/fta/FTAreg/q.var".
-inline cic:/CoRN/fta/FTAreg/zleq.var.
+inline "cic:/CoRN/fta/FTAreg/zleq.var".
-inline cic:/CoRN/fta/FTAreg/qlt1.var.
+inline "cic:/CoRN/fta/FTAreg/qlt1.var".
-inline cic:/CoRN/fta/FTAreg/c.var.
+inline "cic:/CoRN/fta/FTAreg/c.var".
-inline cic:/CoRN/fta/FTAreg/zltc.var.
+inline "cic:/CoRN/fta/FTAreg/zltc.var".
-inline cic:/CoRN/fta/FTAreg/q_.con.
+inline "cic:/CoRN/fta/FTAreg/q_.con".
-inline cic:/CoRN/fta/FTAreg/e.var.
+inline "cic:/CoRN/fta/FTAreg/e.var".
-inline cic:/CoRN/fta/FTAreg/zlte.var.
+inline "cic:/CoRN/fta/FTAreg/zlte.var".
-inline cic:/CoRN/fta/FTAreg/N_exists.con.
+inline "cic:/CoRN/fta/FTAreg/N_exists.con".
(* UNEXPORTED
End N_Exists.
(* UNEXPORTED
End N_Exists.
(*#* ** The Kneser sequence is Cauchy in [CC] *)
(*#* ** The Kneser sequence is Cauchy in [CC] *)
-inline cic:/CoRN/fta/FTAreg/n.var.
+inline "cic:/CoRN/fta/FTAreg/n.var".
-inline cic:/CoRN/fta/FTAreg/lt0n.var.
+inline "cic:/CoRN/fta/FTAreg/lt0n.var".
-inline cic:/CoRN/fta/FTAreg/q.var.
+inline "cic:/CoRN/fta/FTAreg/q.var".
-inline cic:/CoRN/fta/FTAreg/zleq.var.
+inline "cic:/CoRN/fta/FTAreg/zleq.var".
-inline cic:/CoRN/fta/FTAreg/qlt1.var.
+inline "cic:/CoRN/fta/FTAreg/qlt1.var".
-inline cic:/CoRN/fta/FTAreg/c.var.
+inline "cic:/CoRN/fta/FTAreg/c.var".
-inline cic:/CoRN/fta/FTAreg/zltc.var.
+inline "cic:/CoRN/fta/FTAreg/zltc.var".
(*#* %\begin{convention}% Let:
- [q_] prove [q[-]One [#] Zero]
(*#* %\begin{convention}% Let:
- [q_] prove [q[-]One [#] Zero]
-inline cic:/CoRN/fta/FTAreg/q_.con.
+inline "cic:/CoRN/fta/FTAreg/q_.con".
-inline cic:/CoRN/fta/FTAreg/nrtq.con.
+inline "cic:/CoRN/fta/FTAreg/nrtq.con".
-inline cic:/CoRN/fta/FTAreg/nrtc.con.
+inline "cic:/CoRN/fta/FTAreg/nrtc.con".
-inline cic:/CoRN/fta/FTAreg/nrtqlt1.con.
+inline "cic:/CoRN/fta/FTAreg/nrtqlt1.con".
-inline cic:/CoRN/fta/FTAreg/nrtq_.con.
+inline "cic:/CoRN/fta/FTAreg/nrtq_.con".
-inline cic:/CoRN/fta/FTAreg/zlt_nrtq.con.
+inline "cic:/CoRN/fta/FTAreg/zlt_nrtq.con".
-inline cic:/CoRN/fta/FTAreg/zlt_nrtc.con.
+inline "cic:/CoRN/fta/FTAreg/zlt_nrtc.con".
-inline cic:/CoRN/fta/FTAreg/nrt_pow.con.
+inline "cic:/CoRN/fta/FTAreg/nrt_pow.con".
-inline cic:/CoRN/fta/FTAreg/abs_pow_ltRe.con.
+inline "cic:/CoRN/fta/FTAreg/abs_pow_ltRe.con".
-inline cic:/CoRN/fta/FTAreg/abs_pow_ltIm.con.
+inline "cic:/CoRN/fta/FTAreg/abs_pow_ltIm.con".
-inline cic:/CoRN/fta/FTAreg/SublemmaRe.con.
+inline "cic:/CoRN/fta/FTAreg/SublemmaRe.con".
-inline cic:/CoRN/fta/FTAreg/SublemmaIm.con.
+inline "cic:/CoRN/fta/FTAreg/SublemmaIm.con".
-inline cic:/CoRN/fta/FTAreg/seq_is_CC_Cauchy.con.
+inline "cic:/CoRN/fta/FTAreg/seq_is_CC_Cauchy.con".
(* UNEXPORTED
End Seq_is_CC_CAuchy.
*)
(* UNEXPORTED
End Seq_is_CC_CAuchy.
*)
-inline cic:/CoRN/fta/FTAreg/FTA_monic.con.
+inline "cic:/CoRN/fta/FTAreg/FTA_monic.con".
-inline cic:/CoRN/fta/FTAreg/FTA_reg.con.
+inline "cic:/CoRN/fta/FTAreg/FTA_reg.con".
set "baseuri" "cic:/matita/CoRN-Decl/fta/KeyLemma".
set "baseuri" "cic:/matita/CoRN-Decl/fta/KeyLemma".
-(* $Id: KeyLemma.v,v 1.5 2004/04/23 10:00:57 lcf Exp $ *)
-
-(* INCLUDE
-ZArith
-*)
+(* $Id: KeyLemma.v,v 1.5 2004/04/23 10:00:57 lcf Exp $ *)
+include "reals/NRootIR.ma".
(*#* printing p3m %\ensuremath{\frac13\hat{\ }}% *)
(*#* printing p3m %\ensuremath{\frac13\hat{\ }}% *)
-inline cic:/CoRN/fta/KeyLemma/a.var.
+inline "cic:/CoRN/fta/KeyLemma/a.var".
-inline cic:/CoRN/fta/KeyLemma/n.var.
+inline "cic:/CoRN/fta/KeyLemma/n.var".
-inline cic:/CoRN/fta/KeyLemma/gt_n_0.var.
+inline "cic:/CoRN/fta/KeyLemma/gt_n_0.var".
-inline cic:/CoRN/fta/KeyLemma/eps.var.
+inline "cic:/CoRN/fta/KeyLemma/eps.var".
-inline cic:/CoRN/fta/KeyLemma/eps_pos.var.
+inline "cic:/CoRN/fta/KeyLemma/eps_pos.var".
-inline cic:/CoRN/fta/KeyLemma/a_nonneg.var.
+inline "cic:/CoRN/fta/KeyLemma/a_nonneg.var".
-inline cic:/CoRN/fta/KeyLemma/a_n_1.var.
+inline "cic:/CoRN/fta/KeyLemma/a_n_1.var".
-inline cic:/CoRN/fta/KeyLemma/a_0.var.
+inline "cic:/CoRN/fta/KeyLemma/a_0.var".
-inline cic:/CoRN/fta/KeyLemma/eps_le_a_0.var.
+inline "cic:/CoRN/fta/KeyLemma/eps_le_a_0.var".
-inline cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con.
+inline "cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con".
-inline cic:/CoRN/fta/KeyLemma/a_0_eps_fuzz.con.
+inline "cic:/CoRN/fta/KeyLemma/a_0_eps_fuzz.con".
-inline cic:/CoRN/fta/KeyLemma/lem_1a.con.
+inline "cic:/CoRN/fta/KeyLemma/lem_1a.con".
-inline cic:/CoRN/fta/KeyLemma/lem_1b.con.
+inline "cic:/CoRN/fta/KeyLemma/lem_1b.con".
-inline cic:/CoRN/fta/KeyLemma/lem_1c.con.
+inline "cic:/CoRN/fta/KeyLemma/lem_1c.con".
-inline cic:/CoRN/fta/KeyLemma/lem_1.con.
+inline "cic:/CoRN/fta/KeyLemma/lem_1.con".
-inline cic:/CoRN/fta/KeyLemma/p3m.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m.con".
-inline cic:/CoRN/fta/KeyLemma/p3m_pos.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_pos.con".
-inline cic:/CoRN/fta/KeyLemma/p3m_S.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_S.con".
(* UNEXPORTED
Hint Resolve p3m_S: algebra.
*)
(* UNEXPORTED
Hint Resolve p3m_S: algebra.
*)
-inline cic:/CoRN/fta/KeyLemma/p3m_P.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_P.con".
-inline cic:/CoRN/fta/KeyLemma/p3m_aux.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_aux.con".
-inline cic:/CoRN/fta/KeyLemma/p3m_pow.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_pow.con".
(* UNEXPORTED
Hint Resolve p3m_aux: algebra.
*)
(* UNEXPORTED
Hint Resolve p3m_aux: algebra.
*)
-inline cic:/CoRN/fta/KeyLemma/p3m_0.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_0.con".
(* UNEXPORTED
Hint Resolve p3m_0: algebra.
*)
(* UNEXPORTED
Hint Resolve p3m_0: algebra.
*)
-inline cic:/CoRN/fta/KeyLemma/third_pos.con.
+inline "cic:/CoRN/fta/KeyLemma/third_pos.con".
(* UNEXPORTED
Hint Resolve third_pos: algebra.
*)
(* UNEXPORTED
Hint Resolve third_pos: algebra.
*)
-inline cic:/CoRN/fta/KeyLemma/third_less_one.con.
+inline "cic:/CoRN/fta/KeyLemma/third_less_one.con".
(* UNEXPORTED
Hint Resolve third_less_one: algebra.
*)
(* UNEXPORTED
Hint Resolve third_less_one: algebra.
*)
-inline cic:/CoRN/fta/KeyLemma/p3m_mon.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_mon.con".
-inline cic:/CoRN/fta/KeyLemma/p3m_mon'.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_mon'.con".
-inline cic:/CoRN/fta/KeyLemma/p3m_small.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_small.con".
-inline cic:/CoRN/fta/KeyLemma/p3m_smaller.con.
+inline "cic:/CoRN/fta/KeyLemma/p3m_smaller.con".
-inline cic:/CoRN/fta/KeyLemma/chfun.con.
+inline "cic:/CoRN/fta/KeyLemma/chfun.con".
-inline cic:/CoRN/fta/KeyLemma/chfun_1.con.
+inline "cic:/CoRN/fta/KeyLemma/chfun_1.con".
-inline cic:/CoRN/fta/KeyLemma/chfun_2.con.
+inline "cic:/CoRN/fta/KeyLemma/chfun_2.con".
-inline cic:/CoRN/fta/KeyLemma/chfun_3.con.
+inline "cic:/CoRN/fta/KeyLemma/chfun_3.con".
-inline cic:/CoRN/fta/KeyLemma/chfun_4.con.
+inline "cic:/CoRN/fta/KeyLemma/chfun_4.con".
-inline cic:/CoRN/fta/KeyLemma/Halfeps.con.
+inline "cic:/CoRN/fta/KeyLemma/Halfeps.con".
-inline cic:/CoRN/fta/KeyLemma/Halfeps_pos.con.
+inline "cic:/CoRN/fta/KeyLemma/Halfeps_pos.con".
-inline cic:/CoRN/fta/KeyLemma/Halfeps_Halfeps.con.
+inline "cic:/CoRN/fta/KeyLemma/Halfeps_Halfeps.con".
(* UNEXPORTED
Hint Resolve Halfeps_Halfeps: algebra.
*)
(* UNEXPORTED
Hint Resolve Halfeps_Halfeps: algebra.
*)
-inline cic:/CoRN/fta/KeyLemma/Halfeps_eps.con.
+inline "cic:/CoRN/fta/KeyLemma/Halfeps_eps.con".
-inline cic:/CoRN/fta/KeyLemma/Halfeps_trans.con.
+inline "cic:/CoRN/fta/KeyLemma/Halfeps_trans.con".
-inline cic:/CoRN/fta/KeyLemma/Key_1a.con.
+inline "cic:/CoRN/fta/KeyLemma/Key_1a.con".
(* UNEXPORTED
Hint Resolve Key_1a: algebra.
*)
(* UNEXPORTED
Hint Resolve Key_1a: algebra.
*)
-inline cic:/CoRN/fta/KeyLemma/Key_1b.con.
+inline "cic:/CoRN/fta/KeyLemma/Key_1b.con".
-inline cic:/CoRN/fta/KeyLemma/Key_1.con.
+inline "cic:/CoRN/fta/KeyLemma/Key_1.con".
-inline cic:/CoRN/fta/KeyLemma/Key_2.con.
+inline "cic:/CoRN/fta/KeyLemma/Key_2.con".
-inline cic:/CoRN/fta/KeyLemma/Key.con.
+inline "cic:/CoRN/fta/KeyLemma/Key.con".
set "baseuri" "cic:/matita/CoRN-Decl/fta/KneserLemma".
set "baseuri" "cic:/matita/CoRN-Decl/fta/KneserLemma".
(* $Id: KneserLemma.v,v 1.7 2004/04/23 10:00:57 lcf Exp $ *)
(*#* printing Smallest %\ensuremath{\frac13^{2n^2+n}}% *)
(*#* printing eta_0 %\ensuremath{\eta_0}% #η<SUB>0</SUB># *)
(* $Id: KneserLemma.v,v 1.7 2004/04/23 10:00:57 lcf Exp $ *)
(*#* printing Smallest %\ensuremath{\frac13^{2n^2+n}}% *)
(*#* printing eta_0 %\ensuremath{\eta_0}% #η<SUB>0</SUB># *)
+include "complex/NRootCC.ma".
+include "complex/AbsCC.ma".
-(* INCLUDE
-MainLemma
-*)
+include "fta/MainLemma.ma".
-inline cic:/CoRN/fta/KneserLemma/b.var.
+inline "cic:/CoRN/fta/KneserLemma/b.var".
-inline cic:/CoRN/fta/KneserLemma/n.var.
+inline "cic:/CoRN/fta/KneserLemma/n.var".
-inline cic:/CoRN/fta/KneserLemma/gt_n_0.var.
+inline "cic:/CoRN/fta/KneserLemma/gt_n_0.var".
-inline cic:/CoRN/fta/KneserLemma/b_0.con.
+inline "cic:/CoRN/fta/KneserLemma/b_0.con".
-inline cic:/CoRN/fta/KneserLemma/b_n.con.
+inline "cic:/CoRN/fta/KneserLemma/b_n.con".
-inline cic:/CoRN/fta/KneserLemma/b_n_1.var.
+inline "cic:/CoRN/fta/KneserLemma/b_n_1.var".
-inline cic:/CoRN/fta/KneserLemma/c.var.
+inline "cic:/CoRN/fta/KneserLemma/c.var".
-inline cic:/CoRN/fta/KneserLemma/b_0_lt_c.var.
+inline "cic:/CoRN/fta/KneserLemma/b_0_lt_c.var".
(*#*
%\begin{convention}% We define the following local abbreviations:
(*#*
%\begin{convention}% We define the following local abbreviations:
-inline cic:/CoRN/fta/KneserLemma/two_n.con.
+inline "cic:/CoRN/fta/KneserLemma/two_n.con".
-inline cic:/CoRN/fta/KneserLemma/Small.con.
+inline "cic:/CoRN/fta/KneserLemma/Small.con".
-inline cic:/CoRN/fta/KneserLemma/Smaller.con.
+inline "cic:/CoRN/fta/KneserLemma/Smaller.con".
-inline cic:/CoRN/fta/KneserLemma/Smallest.con.
+inline "cic:/CoRN/fta/KneserLemma/Smallest.con".
-inline cic:/CoRN/fta/KneserLemma/q.con.
+inline "cic:/CoRN/fta/KneserLemma/q.con".
-inline cic:/CoRN/fta/KneserLemma/b_0'_exists.con.
+inline "cic:/CoRN/fta/KneserLemma/b_0'_exists.con".
-inline cic:/CoRN/fta/KneserLemma/eta_0.con.
+inline "cic:/CoRN/fta/KneserLemma/eta_0.con".
-inline cic:/CoRN/fta/KneserLemma/eta_0_pos.con.
+inline "cic:/CoRN/fta/KneserLemma/eta_0_pos.con".
-inline cic:/CoRN/fta/KneserLemma/eta_exists.con.
+inline "cic:/CoRN/fta/KneserLemma/eta_exists.con".
-inline cic:/CoRN/fta/KneserLemma/eps_exists_1.con.
+inline "cic:/CoRN/fta/KneserLemma/eps_exists_1.con".
(* less_cotransitive_unfolded on
{Zero [<] y[/]x[//]H3[-]Half[*]eps} +
{y[/]x[//]H3[-]Half[*]eps [<] Half[*]eps}. *)
(* less_cotransitive_unfolded on
{Zero [<] y[/]x[//]H3[-]Half[*]eps} +
{y[/]x[//]H3[-]Half[*]eps [<] Half[*]eps}. *)
-inline cic:/CoRN/fta/KneserLemma/eps_exists.con.
+inline "cic:/CoRN/fta/KneserLemma/eps_exists.con".
-inline cic:/CoRN/fta/KneserLemma/a.con.
+inline "cic:/CoRN/fta/KneserLemma/a.con".
-inline cic:/CoRN/fta/KneserLemma/z_exists.con.
+inline "cic:/CoRN/fta/KneserLemma/z_exists.con".
-inline cic:/CoRN/fta/KneserLemma/Kneser_1'.con.
+inline "cic:/CoRN/fta/KneserLemma/Kneser_1'.con".
-inline cic:/CoRN/fta/KneserLemma/Kneser_1''.con.
+inline "cic:/CoRN/fta/KneserLemma/Kneser_1''.con".
-inline cic:/CoRN/fta/KneserLemma/Kneser_1.con.
+inline "cic:/CoRN/fta/KneserLemma/Kneser_1.con".
-inline cic:/CoRN/fta/KneserLemma/Kneser_2a.con.
+inline "cic:/CoRN/fta/KneserLemma/Kneser_2a.con".
-inline cic:/CoRN/fta/KneserLemma/Kneser_2b.con.
+inline "cic:/CoRN/fta/KneserLemma/Kneser_2b.con".
-inline cic:/CoRN/fta/KneserLemma/Kneser_2c.con.
+inline "cic:/CoRN/fta/KneserLemma/Kneser_2c.con".
-inline cic:/CoRN/fta/KneserLemma/Kneser_2.con.
+inline "cic:/CoRN/fta/KneserLemma/Kneser_2.con".
-inline cic:/CoRN/fta/KneserLemma/Kneser_3.con.
+inline "cic:/CoRN/fta/KneserLemma/Kneser_3.con".
(* UNEXPORTED
End Kneser_Lemma.
*)
(* UNEXPORTED
End Kneser_Lemma.
*)
-inline cic:/CoRN/fta/KneserLemma/Kneser.con.
+inline "cic:/CoRN/fta/KneserLemma/Kneser.con".
set "baseuri" "cic:/matita/CoRN-Decl/fta/MainLemma".
set "baseuri" "cic:/matita/CoRN-Decl/fta/MainLemma".
(* $Id: MainLemma.v,v 1.3 2004/04/23 10:00:57 lcf Exp $ *)
(*#* printing two_n %\ensuremath{2n}% #2n# *)
(* $Id: MainLemma.v,v 1.3 2004/04/23 10:00:57 lcf Exp $ *)
(*#* printing two_n %\ensuremath{2n}% #2n# *)
(*#* printing Smaller %\ensuremath{\frac13^{2n^2}}% *)
(*#* printing Smaller %\ensuremath{\frac13^{2n^2}}% *)
-(* INCLUDE
-CSumsReals
-*)
+include "reals/CSumsReals.ma".
-(* INCLUDE
-KeyLemma
-*)
+include "fta/KeyLemma.ma".
-inline cic:/CoRN/fta/MainLemma/a.var.
+inline "cic:/CoRN/fta/MainLemma/a.var".
-inline cic:/CoRN/fta/MainLemma/n.var.
+inline "cic:/CoRN/fta/MainLemma/n.var".
-inline cic:/CoRN/fta/MainLemma/gt_n_0.var.
+inline "cic:/CoRN/fta/MainLemma/gt_n_0.var".
-inline cic:/CoRN/fta/MainLemma/eps.var.
+inline "cic:/CoRN/fta/MainLemma/eps.var".
-inline cic:/CoRN/fta/MainLemma/eps_pos.var.
+inline "cic:/CoRN/fta/MainLemma/eps_pos.var".
-inline cic:/CoRN/fta/MainLemma/a_nonneg.var.
+inline "cic:/CoRN/fta/MainLemma/a_nonneg.var".
-inline cic:/CoRN/fta/MainLemma/a_n_1.var.
+inline "cic:/CoRN/fta/MainLemma/a_n_1.var".
-inline cic:/CoRN/fta/MainLemma/a_0.var.
+inline "cic:/CoRN/fta/MainLemma/a_0.var".
-inline cic:/CoRN/fta/MainLemma/eps_le_a_0.var.
+inline "cic:/CoRN/fta/MainLemma/eps_le_a_0.var".
-inline cic:/CoRN/fta/MainLemma/a_0_pos.con.
+inline "cic:/CoRN/fta/MainLemma/a_0_pos.con".
(*#*
%\begin{convention}% We define the following local abbreviations:
(*#*
%\begin{convention}% We define the following local abbreviations:
-inline cic:/CoRN/fta/MainLemma/two_n.con.
+inline "cic:/CoRN/fta/MainLemma/two_n.con".
-inline cic:/CoRN/fta/MainLemma/Small.con.
+inline "cic:/CoRN/fta/MainLemma/Small.con".
-inline cic:/CoRN/fta/MainLemma/Smaller.con.
+inline "cic:/CoRN/fta/MainLemma/Smaller.con".
-inline cic:/CoRN/fta/MainLemma/Main_1a'.con.
+inline "cic:/CoRN/fta/MainLemma/Main_1a'.con".
-inline cic:/CoRN/fta/MainLemma/Main_1b'.con.
+inline "cic:/CoRN/fta/MainLemma/Main_1b'.con".
-inline cic:/CoRN/fta/MainLemma/Main_1a.con.
+inline "cic:/CoRN/fta/MainLemma/Main_1a.con".
-inline cic:/CoRN/fta/MainLemma/Main_1b.con.
+inline "cic:/CoRN/fta/MainLemma/Main_1b.con".
-inline cic:/CoRN/fta/MainLemma/Main_1.con.
+inline "cic:/CoRN/fta/MainLemma/Main_1.con".
-inline cic:/CoRN/fta/MainLemma/Main_2'.con.
+inline "cic:/CoRN/fta/MainLemma/Main_2'.con".
-inline cic:/CoRN/fta/MainLemma/Main_2.con.
+inline "cic:/CoRN/fta/MainLemma/Main_2.con".
-inline cic:/CoRN/fta/MainLemma/Main_3a.con.
+inline "cic:/CoRN/fta/MainLemma/Main_3a.con".
-inline cic:/CoRN/fta/MainLemma/Main_3.con.
+inline "cic:/CoRN/fta/MainLemma/Main_3.con".
-inline cic:/CoRN/fta/MainLemma/Main.con.
+inline "cic:/CoRN/fta/MainLemma/Main.con".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/COrdLemmas".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/COrdLemmas".
(* $Id: COrdLemmas.v,v 1.2 2004/04/23 10:00:57 lcf Exp $ *)
(* $Id: COrdLemmas.v,v 1.2 2004/04/23 10:00:57 lcf Exp $ *)
-(* INCLUDE
-COrdCauchy
-*)
+include "algebra/COrdCauchy.ma".
(* UNEXPORTED
Section Lemmas.
(* UNEXPORTED
Section Lemmas.
-inline cic:/CoRN/ftc/COrdLemmas/F.var.
+inline "cic:/CoRN/ftc/COrdLemmas/F.var".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_1.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_1.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_2a.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_2a.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_2.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_2.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_3a.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_3a.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_3b.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_3b.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_4a.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_4a.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_4b.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_4b.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_4c.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_4c.con".
-inline cic:/CoRN/ftc/COrdLemmas/om_fun_4d.con.
+inline "cic:/CoRN/ftc/COrdLemmas/om_fun_4d.con".
-inline cic:/CoRN/ftc/COrdLemmas/f.var.
+inline "cic:/CoRN/ftc/COrdLemmas/f.var".
-inline cic:/CoRN/ftc/COrdLemmas/f0.var.
+inline "cic:/CoRN/ftc/COrdLemmas/f0.var".
-inline cic:/CoRN/ftc/COrdLemmas/f_mon.var.
+inline "cic:/CoRN/ftc/COrdLemmas/f_mon.var".
-inline cic:/CoRN/ftc/COrdLemmas/h.var.
+inline "cic:/CoRN/ftc/COrdLemmas/h.var".
-inline cic:/CoRN/ftc/COrdLemmas/Sumx_Sum_Sum
+inline "cic:/CoRN/ftc/COrdLemmas/Sumx_Sum_Sum
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum
+inline "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum
(* UNEXPORTED
End Lemmas.
(* UNEXPORTED
End Lemmas.
-inline cic:/CoRN/ftc/COrdLemmas/f'.con.
+inline "cic:/CoRN/ftc/COrdLemmas/f'.con".
-inline cic:/CoRN/ftc/COrdLemmas/F.var.
+inline "cic:/CoRN/ftc/COrdLemmas/F.var".
-inline cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum'
+inline "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum'
set "baseuri" "cic:/matita/CoRN-Decl/ftc/CalculusTheorems".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/CalculusTheorems".
(* $Id: CalculusTheorems.v,v 1.6 2004/04/23 10:00:57 lcf Exp $ *)
(* $Id: CalculusTheorems.v,v 1.6 2004/04/23 10:00:57 lcf Exp $ *)
-(* INCLUDE
-DiffTactics3
-*)
+include "tactics/DiffTactics3.ma".
(* UNEXPORTED
Opaque Min Max.
(* UNEXPORTED
Opaque Min Max.
(sometimes called Heine continuity).
*)
(sometimes called Heine continuity).
*)
-inline cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_comm_Lim.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_comm_Lim.con".
(*#*
This is a tricky result: if [F] is continuous and positive in both [[a,b]]
and [(b,c]], then it is positive in [[a,c]].
*)
(*#*
This is a tricky result: if [F] is continuous and positive in both [[a,b]]
and [(b,c]], then it is positive in [[a,c]].
*)
-inline cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con".
(*#*
Similar results for increasing functions:
*)
(*#*
Similar results for increasing functions:
*)
-inline cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues.con".
-inline cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues'.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues'.con".
-inline cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues.con".
-inline cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues'.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues'.con".
(*#* More on glueing intervals. *)
(*#* More on glueing intervals. *)
-inline cic:/CoRN/ftc/CalculusTheorems/olor_pos_clor_nonneg.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clor_nonneg.con".
-inline cic:/CoRN/ftc/CalculusTheorems/olor_pos_olcr_nonneg.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/olor_pos_olcr_nonneg.con".
-inline cic:/CoRN/ftc/CalculusTheorems/olor_pos_clcr_nonneg.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clcr_nonneg.con".
(*#*
Any function that has the null function as its derivative must be constant.
*)
(*#*
Any function that has the null function as its derivative must be constant.
*)
-inline cic:/CoRN/ftc/CalculusTheorems/FConst_prop.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/FConst_prop.con".
(*#* As a corollary, two functions with the same derivative must differ
by a constant.
*)
(*#* As a corollary, two functions with the same derivative must differ
by a constant.
*)
-inline cic:/CoRN/ftc/CalculusTheorems/Feq_crit_with_const.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/Feq_crit_with_const.con".
(*#* This yields the following known result: any differential equation
of the form [f'=g] with initial condition [f(a) [=] b] has a unique solution.
*)
(*#* This yields the following known result: any differential equation
of the form [f'=g] with initial condition [f(a) [=] b] has a unique solution.
*)
-inline cic:/CoRN/ftc/CalculusTheorems/Feq_criterium.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/Feq_criterium.con".
(*#*
Finally, a well known result: any function with a (strictly) positive
(*#*
Finally, a well known result: any function with a (strictly) positive
formalization and from the mathematical point of view.
*)
formalization and from the mathematical point of view.
*)
-inline cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less.con".
-inline cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_leEq.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_leEq.con".
-inline cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less'.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less'.con".
(*#* From these results we can finally prove that exponentiation to a
real power preserves the less or equal than relation!
(*#* From these results we can finally prove that exponentiation to a
real power preserves the less or equal than relation!
-inline cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con.
+inline "cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con".
(* UNEXPORTED
End Various_Theorems.
(* UNEXPORTED
End Various_Theorems.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Composition".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Composition".
(* $Id: Composition.v,v 1.4 2004/04/23 10:00:58 lcf Exp $ *)
(* $Id: Composition.v,v 1.4 2004/04/23 10:00:58 lcf Exp $ *)
-(* INCLUDE
-MoreFunctions
-*)
+include "ftc/MoreFunctions.ma".
(* UNEXPORTED
Section Maps_into_Compacts.
(* UNEXPORTED
Section Maps_into_Compacts.
partial functions, and prove some trivial results.
*)
partial functions, and prove some trivial results.
*)
-inline cic:/CoRN/ftc/Composition/F.var.
+inline "cic:/CoRN/ftc/Composition/F.var".
-inline cic:/CoRN/ftc/Composition/G.var.
+inline "cic:/CoRN/ftc/Composition/G.var".
-inline cic:/CoRN/ftc/Composition/a.var.
+inline "cic:/CoRN/ftc/Composition/a.var".
-inline cic:/CoRN/ftc/Composition/b.var.
+inline "cic:/CoRN/ftc/Composition/b.var".
-inline cic:/CoRN/ftc/Composition/Hab.var.
+inline "cic:/CoRN/ftc/Composition/Hab.var".
-inline cic:/CoRN/ftc/Composition/c.var.
+inline "cic:/CoRN/ftc/Composition/c.var".
-inline cic:/CoRN/ftc/Composition/d.var.
+inline "cic:/CoRN/ftc/Composition/d.var".
-inline cic:/CoRN/ftc/Composition/Hcd.var.
+inline "cic:/CoRN/ftc/Composition/Hcd.var".
-inline cic:/CoRN/ftc/Composition/I.con.
+inline "cic:/CoRN/ftc/Composition/I.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/Composition/Hf.var.
+inline "cic:/CoRN/ftc/Composition/Hf.var".
-inline cic:/CoRN/ftc/Composition/maps_into_compacts.con.
+inline "cic:/CoRN/ftc/Composition/maps_into_compacts.con".
-inline cic:/CoRN/ftc/Composition/maps.var.
+inline "cic:/CoRN/ftc/Composition/maps.var".
-inline cic:/CoRN/ftc/Composition/maps_lemma'.con.
+inline "cic:/CoRN/ftc/Composition/maps_lemma'.con".
-inline cic:/CoRN/ftc/Composition/maps_lemma.con.
+inline "cic:/CoRN/ftc/Composition/maps_lemma.con".
-inline cic:/CoRN/ftc/Composition/maps_lemma_less.con.
+inline "cic:/CoRN/ftc/Composition/maps_lemma_less.con".
-inline cic:/CoRN/ftc/Composition/maps_lemma_inc.con.
+inline "cic:/CoRN/ftc/Composition/maps_lemma_inc.con".
(* UNEXPORTED
End Part_Funct.
(* UNEXPORTED
End Part_Funct.
completely characterizes the domain of the composite function.
*)
completely characterizes the domain of the composite function.
*)
-inline cic:/CoRN/ftc/Composition/F.var.
+inline "cic:/CoRN/ftc/Composition/F.var".
-inline cic:/CoRN/ftc/Composition/G.var.
+inline "cic:/CoRN/ftc/Composition/G.var".
-inline cic:/CoRN/ftc/Composition/a.var.
+inline "cic:/CoRN/ftc/Composition/a.var".
-inline cic:/CoRN/ftc/Composition/b.var.
+inline "cic:/CoRN/ftc/Composition/b.var".
-inline cic:/CoRN/ftc/Composition/Hab.var.
+inline "cic:/CoRN/ftc/Composition/Hab.var".
-inline cic:/CoRN/ftc/Composition/c.var.
+inline "cic:/CoRN/ftc/Composition/c.var".
-inline cic:/CoRN/ftc/Composition/d.var.
+inline "cic:/CoRN/ftc/Composition/d.var".
-inline cic:/CoRN/ftc/Composition/Hcd.var.
+inline "cic:/CoRN/ftc/Composition/Hcd.var".
-inline cic:/CoRN/ftc/Composition/Hf.var.
+inline "cic:/CoRN/ftc/Composition/Hf.var".
-inline cic:/CoRN/ftc/Composition/Hg.var.
+inline "cic:/CoRN/ftc/Composition/Hg.var".
-inline cic:/CoRN/ftc/Composition/maps.var.
+inline "cic:/CoRN/ftc/Composition/maps.var".
-inline cic:/CoRN/ftc/Composition/included_comp.con.
+inline "cic:/CoRN/ftc/Composition/included_comp.con".
(* UNEXPORTED
End Mapping.
(* UNEXPORTED
End Mapping.
We now prove that the composition of two continuous partial functions is continuous.
*)
We now prove that the composition of two continuous partial functions is continuous.
*)
-inline cic:/CoRN/ftc/Composition/a.var.
+inline "cic:/CoRN/ftc/Composition/a.var".
-inline cic:/CoRN/ftc/Composition/b.var.
+inline "cic:/CoRN/ftc/Composition/b.var".
-inline cic:/CoRN/ftc/Composition/Hab.var.
+inline "cic:/CoRN/ftc/Composition/Hab.var".
-inline cic:/CoRN/ftc/Composition/I.con.
+inline "cic:/CoRN/ftc/Composition/I.con".
-inline cic:/CoRN/ftc/Composition/c.var.
+inline "cic:/CoRN/ftc/Composition/c.var".
-inline cic:/CoRN/ftc/Composition/d.var.
+inline "cic:/CoRN/ftc/Composition/d.var".
-inline cic:/CoRN/ftc/Composition/Hcd.var.
+inline "cic:/CoRN/ftc/Composition/Hcd.var".
-inline cic:/CoRN/ftc/Composition/F.var.
+inline "cic:/CoRN/ftc/Composition/F.var".
-inline cic:/CoRN/ftc/Composition/G.var.
+inline "cic:/CoRN/ftc/Composition/G.var".
-inline cic:/CoRN/ftc/Composition/contF.var.
+inline "cic:/CoRN/ftc/Composition/contF.var".
-inline cic:/CoRN/ftc/Composition/contG.var.
+inline "cic:/CoRN/ftc/Composition/contG.var".
-inline cic:/CoRN/ftc/Composition/Hmap.var.
+inline "cic:/CoRN/ftc/Composition/Hmap.var".
-inline cic:/CoRN/ftc/Composition/Continuous_I_comp.con.
+inline "cic:/CoRN/ftc/Composition/Continuous_I_comp.con".
(* UNEXPORTED
End Interval_Continuity.
(* UNEXPORTED
End Interval_Continuity.
We now work with the derivative relation and prove the chain rule for partial functions.
*)
We now work with the derivative relation and prove the chain rule for partial functions.
*)
-inline cic:/CoRN/ftc/Composition/F.var.
+inline "cic:/CoRN/ftc/Composition/F.var".
-inline cic:/CoRN/ftc/Composition/F'.var.
+inline "cic:/CoRN/ftc/Composition/F'.var".
-inline cic:/CoRN/ftc/Composition/G.var.
+inline "cic:/CoRN/ftc/Composition/G.var".
-inline cic:/CoRN/ftc/Composition/G'.var.
+inline "cic:/CoRN/ftc/Composition/G'.var".
-inline cic:/CoRN/ftc/Composition/a.var.
+inline "cic:/CoRN/ftc/Composition/a.var".
-inline cic:/CoRN/ftc/Composition/b.var.
+inline "cic:/CoRN/ftc/Composition/b.var".
-inline cic:/CoRN/ftc/Composition/Hab'.var.
+inline "cic:/CoRN/ftc/Composition/Hab'.var".
-inline cic:/CoRN/ftc/Composition/c.var.
+inline "cic:/CoRN/ftc/Composition/c.var".
-inline cic:/CoRN/ftc/Composition/d.var.
+inline "cic:/CoRN/ftc/Composition/d.var".
-inline cic:/CoRN/ftc/Composition/Hcd'.var.
+inline "cic:/CoRN/ftc/Composition/Hcd'.var".
-inline cic:/CoRN/ftc/Composition/Hab.con.
+inline "cic:/CoRN/ftc/Composition/Hab.con".
-inline cic:/CoRN/ftc/Composition/Hcd.con.
+inline "cic:/CoRN/ftc/Composition/Hcd.con".
-inline cic:/CoRN/ftc/Composition/I.con.
+inline "cic:/CoRN/ftc/Composition/I.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/Composition/derF.var.
+inline "cic:/CoRN/ftc/Composition/derF.var".
-inline cic:/CoRN/ftc/Composition/derG.var.
+inline "cic:/CoRN/ftc/Composition/derG.var".
-inline cic:/CoRN/ftc/Composition/Hmap.var.
+inline "cic:/CoRN/ftc/Composition/Hmap.var".
-inline cic:/CoRN/ftc/Composition/included_comp'.con.
+inline "cic:/CoRN/ftc/Composition/included_comp'.con".
-inline cic:/CoRN/ftc/Composition/maps'.con.
+inline "cic:/CoRN/ftc/Composition/maps'.con".
-inline cic:/CoRN/ftc/Composition/Derivative_I_comp.con.
+inline "cic:/CoRN/ftc/Composition/Derivative_I_comp.con".
(*#*
The next lemma will be useful when we move on to differentiability.
*)
(*#*
The next lemma will be useful when we move on to differentiability.
*)
-inline cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con.
+inline "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con".
(* UNEXPORTED
End Derivative.
(* UNEXPORTED
End Derivative.
Finally, we move on to differentiability.
*)
Finally, we move on to differentiability.
*)
-inline cic:/CoRN/ftc/Composition/F.var.
+inline "cic:/CoRN/ftc/Composition/F.var".
-inline cic:/CoRN/ftc/Composition/G.var.
+inline "cic:/CoRN/ftc/Composition/G.var".
-inline cic:/CoRN/ftc/Composition/a.var.
+inline "cic:/CoRN/ftc/Composition/a.var".
-inline cic:/CoRN/ftc/Composition/b.var.
+inline "cic:/CoRN/ftc/Composition/b.var".
-inline cic:/CoRN/ftc/Composition/Hab'.var.
+inline "cic:/CoRN/ftc/Composition/Hab'.var".
-inline cic:/CoRN/ftc/Composition/c.var.
+inline "cic:/CoRN/ftc/Composition/c.var".
-inline cic:/CoRN/ftc/Composition/d.var.
+inline "cic:/CoRN/ftc/Composition/d.var".
-inline cic:/CoRN/ftc/Composition/Hcd'.var.
+inline "cic:/CoRN/ftc/Composition/Hcd'.var".
-inline cic:/CoRN/ftc/Composition/Hab.con.
+inline "cic:/CoRN/ftc/Composition/Hab.con".
-inline cic:/CoRN/ftc/Composition/Hcd.con.
+inline "cic:/CoRN/ftc/Composition/Hcd.con".
-inline cic:/CoRN/ftc/Composition/I.con.
+inline "cic:/CoRN/ftc/Composition/I.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/Composition/diffF.var.
+inline "cic:/CoRN/ftc/Composition/diffF.var".
-inline cic:/CoRN/ftc/Composition/diffG.var.
+inline "cic:/CoRN/ftc/Composition/diffG.var".
-inline cic:/CoRN/ftc/Composition/Hmap.var.
+inline "cic:/CoRN/ftc/Composition/Hmap.var".
-inline cic:/CoRN/ftc/Composition/Diffble_I_comp.con.
+inline "cic:/CoRN/ftc/Composition/Diffble_I_comp.con".
(* UNEXPORTED
End Differentiability.
(* UNEXPORTED
End Differentiability.
-inline cic:/CoRN/ftc/Composition/I.var.
+inline "cic:/CoRN/ftc/Composition/I.var".
-inline cic:/CoRN/ftc/Composition/J.var.
+inline "cic:/CoRN/ftc/Composition/J.var".
-inline cic:/CoRN/ftc/Composition/pI.var.
+inline "cic:/CoRN/ftc/Composition/pI.var".
-inline cic:/CoRN/ftc/Composition/pJ.var.
+inline "cic:/CoRN/ftc/Composition/pJ.var".
-inline cic:/CoRN/ftc/Composition/maps_compacts_into.con.
+inline "cic:/CoRN/ftc/Composition/maps_compacts_into.con".
(*#*
Now everything comes naturally:
*)
(*#*
Now everything comes naturally:
*)
-inline cic:/CoRN/ftc/Composition/comp_inc_lemma.con.
+inline "cic:/CoRN/ftc/Composition/comp_inc_lemma.con".
-inline cic:/CoRN/ftc/Composition/F.var.
+inline "cic:/CoRN/ftc/Composition/F.var".
-inline cic:/CoRN/ftc/Composition/F'.var.
+inline "cic:/CoRN/ftc/Composition/F'.var".
-inline cic:/CoRN/ftc/Composition/G.var.
+inline "cic:/CoRN/ftc/Composition/G.var".
-inline cic:/CoRN/ftc/Composition/G'.var.
+inline "cic:/CoRN/ftc/Composition/G'.var".
-inline cic:/CoRN/ftc/Composition/Hmap.var.
+inline "cic:/CoRN/ftc/Composition/Hmap.var".
-inline cic:/CoRN/ftc/Composition/Continuous_comp.con.
+inline "cic:/CoRN/ftc/Composition/Continuous_comp.con".
-inline cic:/CoRN/ftc/Composition/Hmap'.var.
+inline "cic:/CoRN/ftc/Composition/Hmap'.var".
-inline cic:/CoRN/ftc/Composition/Derivative_comp.con.
+inline "cic:/CoRN/ftc/Composition/Derivative_comp.con".
(* UNEXPORTED
End Generalized_Intervals.
(* UNEXPORTED
End Generalized_Intervals.
Finally, some criteria to prove that a function with a specific domain maps compacts into compacts:
*)
Finally, some criteria to prove that a function with a specific domain maps compacts into compacts:
*)
-inline cic:/CoRN/ftc/Composition/positive_fun.con.
+inline "cic:/CoRN/ftc/Composition/positive_fun.con".
-inline cic:/CoRN/ftc/Composition/negative_fun.con.
+inline "cic:/CoRN/ftc/Composition/negative_fun.con".
-inline cic:/CoRN/ftc/Composition/positive_imp_maps_compacts_into.con.
+inline "cic:/CoRN/ftc/Composition/positive_imp_maps_compacts_into.con".
-inline cic:/CoRN/ftc/Composition/negative_imp_maps_compacts_into.con.
+inline "cic:/CoRN/ftc/Composition/negative_imp_maps_compacts_into.con".
-inline cic:/CoRN/ftc/Composition/Continuous_imp_maps_compacts_into.con.
+inline "cic:/CoRN/ftc/Composition/Continuous_imp_maps_compacts_into.con".
(*#*
As a corollary, we get the generalization of differentiability property.
*)
(*#*
As a corollary, we get the generalization of differentiability property.
*)
-inline cic:/CoRN/ftc/Composition/Diffble_comp.con.
+inline "cic:/CoRN/ftc/Composition/Diffble_comp.con".
(* UNEXPORTED
End Corollaries.
(* UNEXPORTED
End Corollaries.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Continuity".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Continuity".
(* $Id: Continuity.v,v 1.6 2004/04/23 10:00:58 lcf Exp $ *)
(*#* printing Norm_Funct %\ensuremath{\|\cdot\|}% *)
(* $Id: Continuity.v,v 1.6 2004/04/23 10:00:58 lcf Exp $ *)
(*#* printing Norm_Funct %\ensuremath{\|\cdot\|}% *)
+include "reals/NRootIR.ma".
-(* INCLUDE
-FunctSums
-*)
+include "ftc/FunctSums.ma".
(* UNEXPORTED
Section Definitions_and_Basic_Results.
(* UNEXPORTED
Section Definitions_and_Basic_Results.
Here we define continuity and prove some basic properties of continuous functions.
*)
Here we define continuity and prove some basic properties of continuous functions.
*)
-inline cic:/CoRN/ftc/Continuity/a.var.
+inline "cic:/CoRN/ftc/Continuity/a.var".
-inline cic:/CoRN/ftc/Continuity/b.var.
+inline "cic:/CoRN/ftc/Continuity/b.var".
-inline cic:/CoRN/ftc/Continuity/Hab.var.
+inline "cic:/CoRN/ftc/Continuity/Hab.var".
-inline cic:/CoRN/ftc/Continuity/I.con.
+inline "cic:/CoRN/ftc/Continuity/I.con".
-inline cic:/CoRN/ftc/Continuity/F.var.
+inline "cic:/CoRN/ftc/Continuity/F.var".
-inline cic:/CoRN/ftc/Continuity/P.con.
+inline "cic:/CoRN/ftc/Continuity/P.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I.con".
(*#*
For convenience, we distinguish the two properties of continuous functions.
*)
(*#*
For convenience, we distinguish the two properties of continuous functions.
*)
-inline cic:/CoRN/ftc/Continuity/contin_imp_inc.con.
+inline "cic:/CoRN/ftc/Continuity/contin_imp_inc.con".
-inline cic:/CoRN/ftc/Continuity/contin_prop.con.
+inline "cic:/CoRN/ftc/Continuity/contin_prop.con".
(*#*
Assume [F] to be continuous in [I]. Then it has a least upper bound and a greater lower bound on [I].
*)
(*#*
Assume [F] to be continuous in [I]. Then it has a least upper bound and a greater lower bound on [I].
*)
-inline cic:/CoRN/ftc/Continuity/contF.var.
+inline "cic:/CoRN/ftc/Continuity/contF.var".
-inline cic:/CoRN/ftc/Continuity/Hinc'.con.
+inline "cic:/CoRN/ftc/Continuity/Hinc'.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_imp_tb_image.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_imp_tb_image.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_imp_lub.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_imp_lub.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_imp_glb.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_imp_glb.con".
(*#*
We now make this glb and lub into operators.
*)
(*#*
We now make this glb and lub into operators.
*)
-inline cic:/CoRN/ftc/Continuity/lub_funct.con.
+inline "cic:/CoRN/ftc/Continuity/lub_funct.con".
-inline cic:/CoRN/ftc/Continuity/glb_funct.con.
+inline "cic:/CoRN/ftc/Continuity/glb_funct.con".
(*#*
These operators have the expected properties.
*)
(*#*
These operators have the expected properties.
*)
-inline cic:/CoRN/ftc/Continuity/lub_is_lub.con.
+inline "cic:/CoRN/ftc/Continuity/lub_is_lub.con".
-inline cic:/CoRN/ftc/Continuity/glb_is_glb.con.
+inline "cic:/CoRN/ftc/Continuity/glb_is_glb.con".
-inline cic:/CoRN/ftc/Continuity/glb_prop.con.
+inline "cic:/CoRN/ftc/Continuity/glb_prop.con".
-inline cic:/CoRN/ftc/Continuity/lub_prop.con.
+inline "cic:/CoRN/ftc/Continuity/lub_prop.con".
(*#*
The norm of a function is defined as being the supremum of its absolute value; that is equivalent to the following definition (which is often more convenient to use).
*)
(*#*
The norm of a function is defined as being the supremum of its absolute value; that is equivalent to the following definition (which is often more convenient to use).
*)
-inline cic:/CoRN/ftc/Continuity/Norm_Funct.con.
+inline "cic:/CoRN/ftc/Continuity/Norm_Funct.con".
(*#*
The norm effectively bounds the absolute value of a function.
*)
(*#*
The norm effectively bounds the absolute value of a function.
*)
-inline cic:/CoRN/ftc/Continuity/norm_bnd_AbsIR.con.
+inline "cic:/CoRN/ftc/Continuity/norm_bnd_AbsIR.con".
(*#*
The following is another way of characterizing the norm:
*)
(*#*
The following is another way of characterizing the norm:
*)
-inline cic:/CoRN/ftc/Continuity/Continuous_I_imp_abs_lub.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_imp_abs_lub.con".
(*#*
We now prove some basic properties of the norm---namely that it is positive, and that it provides a least upper bound for the absolute value of its argument.
*)
(*#*
We now prove some basic properties of the norm---namely that it is positive, and that it provides a least upper bound for the absolute value of its argument.
*)
-inline cic:/CoRN/ftc/Continuity/positive_norm.con.
+inline "cic:/CoRN/ftc/Continuity/positive_norm.con".
-inline cic:/CoRN/ftc/Continuity/norm_fun_lub.con.
+inline "cic:/CoRN/ftc/Continuity/norm_fun_lub.con".
-inline cic:/CoRN/ftc/Continuity/leEq_Norm_Funct.con.
+inline "cic:/CoRN/ftc/Continuity/leEq_Norm_Funct.con".
-inline cic:/CoRN/ftc/Continuity/less_Norm_Funct.con.
+inline "cic:/CoRN/ftc/Continuity/less_Norm_Funct.con".
(* UNEXPORTED
End Definitions_and_Basic_Results.
(* UNEXPORTED
End Definitions_and_Basic_Results.
We now state and prove some results about continuous functions. Assume that [I] is included in the domain of both [F] and [G].
*)
We now state and prove some results about continuous functions. Assume that [I] is included in the domain of both [F] and [G].
*)
-inline cic:/CoRN/ftc/Continuity/a.var.
+inline "cic:/CoRN/ftc/Continuity/a.var".
-inline cic:/CoRN/ftc/Continuity/b.var.
+inline "cic:/CoRN/ftc/Continuity/b.var".
-inline cic:/CoRN/ftc/Continuity/Hab.var.
+inline "cic:/CoRN/ftc/Continuity/Hab.var".
-inline cic:/CoRN/ftc/Continuity/I.con.
+inline "cic:/CoRN/ftc/Continuity/I.con".
-inline cic:/CoRN/ftc/Continuity/F.var.
+inline "cic:/CoRN/ftc/Continuity/F.var".
-inline cic:/CoRN/ftc/Continuity/G.var.
+inline "cic:/CoRN/ftc/Continuity/G.var".
-inline cic:/CoRN/ftc/Continuity/P.con.
+inline "cic:/CoRN/ftc/Continuity/P.con".
-inline cic:/CoRN/ftc/Continuity/Q.con.
+inline "cic:/CoRN/ftc/Continuity/Q.con".
-inline cic:/CoRN/ftc/Continuity/incF.var.
+inline "cic:/CoRN/ftc/Continuity/incF.var".
-inline cic:/CoRN/ftc/Continuity/incG.var.
+inline "cic:/CoRN/ftc/Continuity/incG.var".
(*#*
The first result does not require the function to be continuous; however, its preconditions are easily verified by continuous functions, which justifies its inclusion in this section.
*)
(*#*
The first result does not require the function to be continuous; however, its preconditions are easily verified by continuous functions, which justifies its inclusion in this section.
*)
-inline cic:/CoRN/ftc/Continuity/cont_no_sign_change.con.
+inline "cic:/CoRN/ftc/Continuity/cont_no_sign_change.con".
-inline cic:/CoRN/ftc/Continuity/cont_no_sign_change_pos.con.
+inline "cic:/CoRN/ftc/Continuity/cont_no_sign_change_pos.con".
-inline cic:/CoRN/ftc/Continuity/cont_no_sign_change_neg.con.
+inline "cic:/CoRN/ftc/Continuity/cont_no_sign_change_neg.con".
(*#*
Being continuous is an extensional property.
*)
(*#*
Being continuous is an extensional property.
*)
-inline cic:/CoRN/ftc/Continuity/Continuous_I_wd.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_wd.con".
(*#*
A continuous function remains continuous if you restrict its domain.
*)
(*#*
A continuous function remains continuous if you restrict its domain.
*)
-inline cic:/CoRN/ftc/Continuity/included_imp_contin.con.
+inline "cic:/CoRN/ftc/Continuity/included_imp_contin.con".
(*#*
Constant functions and identity are continuous.
*)
(*#*
Constant functions and identity are continuous.
*)
-inline cic:/CoRN/ftc/Continuity/Continuous_I_const.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_const.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_id.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_id.con".
(*#*
Assume [F] and [G] are continuous in [I]. Then functions derived from these through algebraic operations are also continuous, provided (in the case of reciprocal and division) some extra conditions are met.
*)
(*#*
Assume [F] and [G] are continuous in [I]. Then functions derived from these through algebraic operations are also continuous, provided (in the case of reciprocal and division) some extra conditions are met.
*)
-inline cic:/CoRN/ftc/Continuity/contF.var.
+inline "cic:/CoRN/ftc/Continuity/contF.var".
-inline cic:/CoRN/ftc/Continuity/contG.var.
+inline "cic:/CoRN/ftc/Continuity/contG.var".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_plus.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_inv.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_inv.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_mult.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_mult.con".
(* UNEXPORTED
Opaque AbsIR Max.
(* UNEXPORTED
Opaque AbsIR Max.
Transparent AbsIR Max.
*)
Transparent AbsIR Max.
*)
-inline cic:/CoRN/ftc/Continuity/Continuous_I_max.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_max.con".
-inline cic:/CoRN/ftc/Continuity/Hg'.var.
+inline "cic:/CoRN/ftc/Continuity/Hg'.var".
-inline cic:/CoRN/ftc/Continuity/Hg''.var.
+inline "cic:/CoRN/ftc/Continuity/Hg''.var".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_recip.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_recip.con".
(* UNEXPORTED
End Local_Results.
(* UNEXPORTED
End Local_Results.
-inline cic:/CoRN/ftc/Continuity/a.var.
+inline "cic:/CoRN/ftc/Continuity/a.var".
-inline cic:/CoRN/ftc/Continuity/b.var.
+inline "cic:/CoRN/ftc/Continuity/b.var".
-inline cic:/CoRN/ftc/Continuity/Hab.var.
+inline "cic:/CoRN/ftc/Continuity/Hab.var".
-inline cic:/CoRN/ftc/Continuity/I.con.
+inline "cic:/CoRN/ftc/Continuity/I.con".
-inline cic:/CoRN/ftc/Continuity/F.var.
+inline "cic:/CoRN/ftc/Continuity/F.var".
-inline cic:/CoRN/ftc/Continuity/G.var.
+inline "cic:/CoRN/ftc/Continuity/G.var".
-inline cic:/CoRN/ftc/Continuity/P.con.
+inline "cic:/CoRN/ftc/Continuity/P.con".
-inline cic:/CoRN/ftc/Continuity/Q.con.
+inline "cic:/CoRN/ftc/Continuity/Q.con".
-inline cic:/CoRN/ftc/Continuity/contF.var.
+inline "cic:/CoRN/ftc/Continuity/contF.var".
-inline cic:/CoRN/ftc/Continuity/contG.var.
+inline "cic:/CoRN/ftc/Continuity/contG.var".
(*#*
The corresponding properties for subtraction, division and
(*#*
The corresponding properties for subtraction, division and
product and constant functions.
*)
product and constant functions.
*)
-inline cic:/CoRN/ftc/Continuity/Continuous_I_minus.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_minus.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_scal.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_scal.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_nth.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_nth.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_min.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_min.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_abs.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con".
-inline cic:/CoRN/ftc/Continuity/Hg'.var.
+inline "cic:/CoRN/ftc/Continuity/Hg'.var".
-inline cic:/CoRN/ftc/Continuity/Hg''.var.
+inline "cic:/CoRN/ftc/Continuity/Hg''.var".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_div.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_div.con".
(* UNEXPORTED
End Corolaries.
(* UNEXPORTED
End Corolaries.
We finally prove that the sum of an arbitrary family of continuous functions is still a continuous function.
*)
We finally prove that the sum of an arbitrary family of continuous functions is still a continuous function.
*)
-inline cic:/CoRN/ftc/Continuity/a.var.
+inline "cic:/CoRN/ftc/Continuity/a.var".
-inline cic:/CoRN/ftc/Continuity/b.var.
+inline "cic:/CoRN/ftc/Continuity/b.var".
-inline cic:/CoRN/ftc/Continuity/Hab.var.
+inline "cic:/CoRN/ftc/Continuity/Hab.var".
-inline cic:/CoRN/ftc/Continuity/Hab'.var.
+inline "cic:/CoRN/ftc/Continuity/Hab'.var".
-inline cic:/CoRN/ftc/Continuity/I.con.
+inline "cic:/CoRN/ftc/Continuity/I.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_Sum0.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_Sum0.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_Sumx.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_Sumx.con".
-inline cic:/CoRN/ftc/Continuity/Continuous_I_Sum.con.
+inline "cic:/CoRN/ftc/Continuity/Continuous_I_Sum.con".
For practical purposes, these characterization results are useful:
*)
For practical purposes, these characterization results are useful:
*)
-inline cic:/CoRN/ftc/Continuity/lub_charact.con.
+inline "cic:/CoRN/ftc/Continuity/lub_charact.con".
-inline cic:/CoRN/ftc/Continuity/glb_charact.con.
+inline "cic:/CoRN/ftc/Continuity/glb_charact.con".
(*#*
The following result is also extremely useful, as it allows us to set a lower bound on the glb of a function.
*)
(*#*
The following result is also extremely useful, as it allows us to set a lower bound on the glb of a function.
*)
-inline cic:/CoRN/ftc/Continuity/leEq_glb.con.
+inline "cic:/CoRN/ftc/Continuity/leEq_glb.con".
(*#*
The norm is also an extensional property.
*)
(*#*
The norm is also an extensional property.
*)
-inline cic:/CoRN/ftc/Continuity/Norm_Funct_wd.con.
+inline "cic:/CoRN/ftc/Continuity/Norm_Funct_wd.con".
(*#*
The value of the norm is covariant with the length of the interval.
*)
(*#*
The value of the norm is covariant with the length of the interval.
*)
-inline cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con.
+inline "cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Derivative".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Derivative".
(* $Id: Derivative.v,v 1.7 2004/04/23 10:00:58 lcf Exp $ *)
(* $Id: Derivative.v,v 1.7 2004/04/23 10:00:58 lcf Exp $ *)
-(* INCLUDE
-Continuity
-*)
+include "ftc/Continuity.ma".
(* UNEXPORTED
Section Definitions.
(* UNEXPORTED
Section Definitions.
-inline cic:/CoRN/ftc/Derivative/a.var.
+inline "cic:/CoRN/ftc/Derivative/a.var".
-inline cic:/CoRN/ftc/Derivative/b.var.
+inline "cic:/CoRN/ftc/Derivative/b.var".
-inline cic:/CoRN/ftc/Derivative/Hab'.var.
+inline "cic:/CoRN/ftc/Derivative/Hab'.var".
-inline cic:/CoRN/ftc/Derivative/Hab.con.
+inline "cic:/CoRN/ftc/Derivative/Hab.con".
-inline cic:/CoRN/ftc/Derivative/I.con.
+inline "cic:/CoRN/ftc/Derivative/I.con".
-inline cic:/CoRN/ftc/Derivative/F.var.
+inline "cic:/CoRN/ftc/Derivative/F.var".
-inline cic:/CoRN/ftc/Derivative/P.con.
+inline "cic:/CoRN/ftc/Derivative/P.con".
-inline cic:/CoRN/ftc/Derivative/Derivative_I.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
(*#* **Basic Properties
*)
(*#* **Basic Properties
*)
-inline cic:/CoRN/ftc/Derivative/a.var.
+inline "cic:/CoRN/ftc/Derivative/a.var".
-inline cic:/CoRN/ftc/Derivative/b.var.
+inline "cic:/CoRN/ftc/Derivative/b.var".
-inline cic:/CoRN/ftc/Derivative/Hab'.var.
+inline "cic:/CoRN/ftc/Derivative/Hab'.var".
-inline cic:/CoRN/ftc/Derivative/Hab.con.
+inline "cic:/CoRN/ftc/Derivative/Hab.con".
-inline cic:/CoRN/ftc/Derivative/I.con.
+inline "cic:/CoRN/ftc/Derivative/I.con".
Like we did for equality, we begin by stating a lemma that makes proofs of derivation easier in practice.
*)
Like we did for equality, we begin by stating a lemma that makes proofs of derivation easier in practice.
*)
-inline cic:/CoRN/ftc/Derivative/Derivative_I_char.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I_char.con".
Derivative is a well defined relation; we will make this explicit for both arguments:
*)
Derivative is a well defined relation; we will make this explicit for both arguments:
*)
-inline cic:/CoRN/ftc/Derivative/F.var.
+inline "cic:/CoRN/ftc/Derivative/F.var".
-inline cic:/CoRN/ftc/Derivative/G.var.
+inline "cic:/CoRN/ftc/Derivative/G.var".
-inline cic:/CoRN/ftc/Derivative/H.var.
+inline "cic:/CoRN/ftc/Derivative/H.var".
-inline cic:/CoRN/ftc/Derivative/P.con.
+inline "cic:/CoRN/ftc/Derivative/P.con".
-inline cic:/CoRN/ftc/Derivative/Q.con.
+inline "cic:/CoRN/ftc/Derivative/Q.con".
-inline cic:/CoRN/ftc/Derivative/R.con.
+inline "cic:/CoRN/ftc/Derivative/R.con".
-inline cic:/CoRN/ftc/Derivative/Derivative_I_wdl.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I_wdl.con".
-inline cic:/CoRN/ftc/Derivative/Derivative_I_wdr.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I_wdr.con".
-inline cic:/CoRN/ftc/Derivative/Derivative_I_unique_lemma.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I_unique_lemma.con".
-inline cic:/CoRN/ftc/Derivative/Derivative_I_unique.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I_unique.con".
(*#*
Finally, the set where we are considering the relation is included in the domain of both functions.
*)
(*#*
Finally, the set where we are considering the relation is included in the domain of both functions.
*)
-inline cic:/CoRN/ftc/Derivative/derivative_imp_inc.con.
+inline "cic:/CoRN/ftc/Derivative/derivative_imp_inc.con".
-inline cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con.
+inline "cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con".
(*#*
Any function that is or has a derivative is continuous.
*)
(*#*
Any function that is or has a derivative is continuous.
*)
-inline cic:/CoRN/ftc/Derivative/Hab''.var.
+inline "cic:/CoRN/ftc/Derivative/Hab''.var".
-inline cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con.
+inline "cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con".
-inline cic:/CoRN/ftc/Derivative/deriv_imp_contin_I.con.
+inline "cic:/CoRN/ftc/Derivative/deriv_imp_contin_I.con".
(* UNEXPORTED
End Basic_Properties.
(* UNEXPORTED
End Basic_Properties.
If [G] is the derivative of [F] in a given interval, then [G] is also the derivative of [F] in any smaller interval.
*)
If [G] is the derivative of [F] in a given interval, then [G] is also the derivative of [F] in any smaller interval.
*)
-inline cic:/CoRN/ftc/Derivative/included_imp_deriv.con.
+inline "cic:/CoRN/ftc/Derivative/included_imp_deriv.con".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/DerivativeOps".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/DerivativeOps".
(* $Id: DerivativeOps.v,v 1.3 2004/04/23 10:00:58 lcf Exp $ *)
(* $Id: DerivativeOps.v,v 1.3 2004/04/23 10:00:58 lcf Exp $ *)
-(* INCLUDE
-Derivative
-*)
+include "ftc/Derivative.ma".
(* UNEXPORTED
Section Lemmas.
(* UNEXPORTED
Section Lemmas.
We begin with some technical stuff that will be necessary for division.
*)
We begin with some technical stuff that will be necessary for division.
*)
-inline cic:/CoRN/ftc/DerivativeOps/a.var.
+inline "cic:/CoRN/ftc/DerivativeOps/a.var".
-inline cic:/CoRN/ftc/DerivativeOps/b.var.
+inline "cic:/CoRN/ftc/DerivativeOps/b.var".
-inline cic:/CoRN/ftc/DerivativeOps/Hab.var.
+inline "cic:/CoRN/ftc/DerivativeOps/Hab.var".
-inline cic:/CoRN/ftc/DerivativeOps/I.con.
+inline "cic:/CoRN/ftc/DerivativeOps/I.con".
-inline cic:/CoRN/ftc/DerivativeOps/F.var.
+inline "cic:/CoRN/ftc/DerivativeOps/F.var".
-inline cic:/CoRN/ftc/DerivativeOps/P.con.
+inline "cic:/CoRN/ftc/DerivativeOps/P.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/DerivativeOps/Fbnd.var.
+inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var".
-inline cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con.
+inline "cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con".
(* UNEXPORTED
End Lemmas.
(* UNEXPORTED
End Lemmas.
We can now derive all the usual rules for deriving constant and identity functions, sums, inverses and products of functions with a known derivative.
*)
We can now derive all the usual rules for deriving constant and identity functions, sums, inverses and products of functions with a known derivative.
*)
-inline cic:/CoRN/ftc/DerivativeOps/a.var.
+inline "cic:/CoRN/ftc/DerivativeOps/a.var".
-inline cic:/CoRN/ftc/DerivativeOps/b.var.
+inline "cic:/CoRN/ftc/DerivativeOps/b.var".
-inline cic:/CoRN/ftc/DerivativeOps/Hab'.var.
+inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var".
-inline cic:/CoRN/ftc/DerivativeOps/Hab.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Hab.con".
-inline cic:/CoRN/ftc/DerivativeOps/I.con.
+inline "cic:/CoRN/ftc/DerivativeOps/I.con".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_const.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_const.con".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con".
-inline cic:/CoRN/ftc/DerivativeOps/F.var.
+inline "cic:/CoRN/ftc/DerivativeOps/F.var".
-inline cic:/CoRN/ftc/DerivativeOps/F'.var.
+inline "cic:/CoRN/ftc/DerivativeOps/F'.var".
-inline cic:/CoRN/ftc/DerivativeOps/G.var.
+inline "cic:/CoRN/ftc/DerivativeOps/G.var".
-inline cic:/CoRN/ftc/DerivativeOps/G'.var.
+inline "cic:/CoRN/ftc/DerivativeOps/G'.var".
-inline cic:/CoRN/ftc/DerivativeOps/derF.var.
+inline "cic:/CoRN/ftc/DerivativeOps/derF.var".
-inline cic:/CoRN/ftc/DerivativeOps/derG.var.
+inline "cic:/CoRN/ftc/DerivativeOps/derG.var".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_inv.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_inv.con".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_mult.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_mult.con".
(*#*
As was the case for continuity, the rule for the reciprocal function has a side condition.
(*#*
As was the case for continuity, the rule for the reciprocal function has a side condition.
-inline cic:/CoRN/ftc/DerivativeOps/Fbnd.var.
+inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con".
(* UNEXPORTED
End Local_Results.
(* UNEXPORTED
End Local_Results.
-inline cic:/CoRN/ftc/DerivativeOps/a.var.
+inline "cic:/CoRN/ftc/DerivativeOps/a.var".
-inline cic:/CoRN/ftc/DerivativeOps/b.var.
+inline "cic:/CoRN/ftc/DerivativeOps/b.var".
-inline cic:/CoRN/ftc/DerivativeOps/Hab'.var.
+inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var".
-inline cic:/CoRN/ftc/DerivativeOps/Hab.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Hab.con".
-inline cic:/CoRN/ftc/DerivativeOps/I.con.
+inline "cic:/CoRN/ftc/DerivativeOps/I.con".
-inline cic:/CoRN/ftc/DerivativeOps/F.var.
+inline "cic:/CoRN/ftc/DerivativeOps/F.var".
-inline cic:/CoRN/ftc/DerivativeOps/F'.var.
+inline "cic:/CoRN/ftc/DerivativeOps/F'.var".
-inline cic:/CoRN/ftc/DerivativeOps/G.var.
+inline "cic:/CoRN/ftc/DerivativeOps/G.var".
-inline cic:/CoRN/ftc/DerivativeOps/G'.var.
+inline "cic:/CoRN/ftc/DerivativeOps/G'.var".
-inline cic:/CoRN/ftc/DerivativeOps/derF.var.
+inline "cic:/CoRN/ftc/DerivativeOps/derF.var".
-inline cic:/CoRN/ftc/DerivativeOps/derG.var.
+inline "cic:/CoRN/ftc/DerivativeOps/derG.var".
(*#*
From this lemmas the rules for the other algebraic operations follow directly.
*)
(*#*
From this lemmas the rules for the other algebraic operations follow directly.
*)
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_minus.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_minus.con".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_scal.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_scal.con".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con".
-inline cic:/CoRN/ftc/DerivativeOps/Gbnd.var.
+inline "cic:/CoRN/ftc/DerivativeOps/Gbnd.var".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con".
(* UNEXPORTED
End Corolaries.
(* UNEXPORTED
End Corolaries.
induction using the constant and addition rules.
*)
induction using the constant and addition rules.
*)
-inline cic:/CoRN/ftc/DerivativeOps/a.var.
+inline "cic:/CoRN/ftc/DerivativeOps/a.var".
-inline cic:/CoRN/ftc/DerivativeOps/b.var.
+inline "cic:/CoRN/ftc/DerivativeOps/b.var".
-inline cic:/CoRN/ftc/DerivativeOps/Hab.var.
+inline "cic:/CoRN/ftc/DerivativeOps/Hab.var".
-inline cic:/CoRN/ftc/DerivativeOps/Hab'.var.
+inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var".
-inline cic:/CoRN/ftc/DerivativeOps/I.con.
+inline "cic:/CoRN/ftc/DerivativeOps/I.con".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum0.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum0.con".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sumx.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sumx.con".
-inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum.con.
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum.con".
(* UNEXPORTED
End Derivative_Sums.
(* UNEXPORTED
End Derivative_Sums.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Differentiability".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Differentiability".
(* $Id: Differentiability.v,v 1.5 2004/04/20 22:38:49 hinderer Exp $ *)
(* $Id: Differentiability.v,v 1.5 2004/04/20 22:38:49 hinderer Exp $ *)
-(* INCLUDE
-PartInterval
-*)
+include "ftc/PartInterval.ma".
-(* INCLUDE
-DerivativeOps
-*)
+include "ftc/DerivativeOps.ma".
(* UNEXPORTED
Section Definitions.
(* UNEXPORTED
Section Definitions.
-inline cic:/CoRN/ftc/Differentiability/Diffble_I.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
A function differentiable in [[a,b]] is differentiable in every proper compact subinterval of [[a,b]].
*)
A function differentiable in [[a,b]] is differentiable in every proper compact subinterval of [[a,b]].
*)
-inline cic:/CoRN/ftc/Differentiability/included_imp_diffble.con.
+inline "cic:/CoRN/ftc/Differentiability/included_imp_diffble.con".
(*#*
A function differentiable in an interval is everywhere defined in that interval.
*)
(*#*
A function differentiable in an interval is everywhere defined in that interval.
*)
-inline cic:/CoRN/ftc/Differentiability/a.var.
+inline "cic:/CoRN/ftc/Differentiability/a.var".
-inline cic:/CoRN/ftc/Differentiability/b.var.
+inline "cic:/CoRN/ftc/Differentiability/b.var".
-inline cic:/CoRN/ftc/Differentiability/Hab'.var.
+inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
-inline cic:/CoRN/ftc/Differentiability/Hab.con.
+inline "cic:/CoRN/ftc/Differentiability/Hab.con".
-inline cic:/CoRN/ftc/Differentiability/I.con.
+inline "cic:/CoRN/ftc/Differentiability/I.con".
-inline cic:/CoRN/ftc/Differentiability/diffble_imp_inc.con.
+inline "cic:/CoRN/ftc/Differentiability/diffble_imp_inc.con".
(*#*
If a function has a derivative in an interval then it is differentiable in that interval.
*)
(*#*
If a function has a derivative in an interval then it is differentiable in that interval.
*)
-inline cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con.
+inline "cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con".
(* UNEXPORTED
End Local_Properties.
(* UNEXPORTED
End Local_Properties.
All the algebraic results carry on.
*)
All the algebraic results carry on.
*)
-inline cic:/CoRN/ftc/Differentiability/a.var.
+inline "cic:/CoRN/ftc/Differentiability/a.var".
-inline cic:/CoRN/ftc/Differentiability/b.var.
+inline "cic:/CoRN/ftc/Differentiability/b.var".
-inline cic:/CoRN/ftc/Differentiability/Hab'.var.
+inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
-inline cic:/CoRN/ftc/Differentiability/Hab.con.
+inline "cic:/CoRN/ftc/Differentiability/Hab.con".
-inline cic:/CoRN/ftc/Differentiability/I.con.
+inline "cic:/CoRN/ftc/Differentiability/I.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_const.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_const.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_id.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_id.con".
(* UNEXPORTED
End Constants.
(* UNEXPORTED
End Constants.
Section Well_Definedness.
*)
Section Well_Definedness.
*)
-inline cic:/CoRN/ftc/Differentiability/F.var.
+inline "cic:/CoRN/ftc/Differentiability/F.var".
-inline cic:/CoRN/ftc/Differentiability/H.var.
+inline "cic:/CoRN/ftc/Differentiability/H.var".
-inline cic:/CoRN/ftc/Differentiability/diffF.var.
+inline "cic:/CoRN/ftc/Differentiability/diffF.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con".
(* UNEXPORTED
End Well_Definedness.
*)
(* UNEXPORTED
End Well_Definedness.
*)
-inline cic:/CoRN/ftc/Differentiability/F.var.
+inline "cic:/CoRN/ftc/Differentiability/F.var".
-inline cic:/CoRN/ftc/Differentiability/G.var.
+inline "cic:/CoRN/ftc/Differentiability/G.var".
-inline cic:/CoRN/ftc/Differentiability/diffF.var.
+inline "cic:/CoRN/ftc/Differentiability/diffF.var".
-inline cic:/CoRN/ftc/Differentiability/diffG.var.
+inline "cic:/CoRN/ftc/Differentiability/diffG.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_inv.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_inv.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con".
-inline cic:/CoRN/ftc/Differentiability/Gbnd.var.
+inline "cic:/CoRN/ftc/Differentiability/Gbnd.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con".
(* UNEXPORTED
End Operations.
(* UNEXPORTED
End Operations.
-inline cic:/CoRN/ftc/Differentiability/a.var.
+inline "cic:/CoRN/ftc/Differentiability/a.var".
-inline cic:/CoRN/ftc/Differentiability/b.var.
+inline "cic:/CoRN/ftc/Differentiability/b.var".
-inline cic:/CoRN/ftc/Differentiability/Hab'.var.
+inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
-inline cic:/CoRN/ftc/Differentiability/Hab.con.
+inline "cic:/CoRN/ftc/Differentiability/Hab.con".
-inline cic:/CoRN/ftc/Differentiability/I.con.
+inline "cic:/CoRN/ftc/Differentiability/I.con".
-inline cic:/CoRN/ftc/Differentiability/F.var.
+inline "cic:/CoRN/ftc/Differentiability/F.var".
-inline cic:/CoRN/ftc/Differentiability/G.var.
+inline "cic:/CoRN/ftc/Differentiability/G.var".
-inline cic:/CoRN/ftc/Differentiability/diffF.var.
+inline "cic:/CoRN/ftc/Differentiability/diffF.var".
-inline cic:/CoRN/ftc/Differentiability/diffG.var.
+inline "cic:/CoRN/ftc/Differentiability/diffG.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con".
-inline cic:/CoRN/ftc/Differentiability/Gbnd.var.
+inline "cic:/CoRN/ftc/Differentiability/Gbnd.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_div.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con".
(* UNEXPORTED
End Corollaries.
(* UNEXPORTED
End Corollaries.
induction using the constant and addition rules.
*)
induction using the constant and addition rules.
*)
-inline cic:/CoRN/ftc/Differentiability/a.var.
+inline "cic:/CoRN/ftc/Differentiability/a.var".
-inline cic:/CoRN/ftc/Differentiability/b.var.
+inline "cic:/CoRN/ftc/Differentiability/b.var".
-inline cic:/CoRN/ftc/Differentiability/Hab'.var.
+inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_Sumx.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sumx.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con".
(* UNEXPORTED
End Other_Properties.
(* UNEXPORTED
End Other_Properties.
-inline cic:/CoRN/ftc/Differentiability/diffble_imp_contin_I.con.
+inline "cic:/CoRN/ftc/Differentiability/diffble_imp_contin_I.con".
(* UNEXPORTED
Hint Immediate included_imp_contin deriv_imp_contin_I deriv_imp_contin'_I
(* UNEXPORTED
Hint Immediate included_imp_contin deriv_imp_contin_I deriv_imp_contin'_I
set "baseuri" "cic:/matita/CoRN-Decl/ftc/FTC".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/FTC".
(* $Id: FTC.v,v 1.5 2004/04/23 10:00:58 lcf Exp $ *)
(*#* printing [-S-] %\ensuremath{\int}% #∫# *)
(* $Id: FTC.v,v 1.5 2004/04/23 10:00:58 lcf Exp $ *)
(*#* printing [-S-] %\ensuremath{\int}% #∫# *)
-(* INCLUDE
-MoreIntegrals
-*)
+include "ftc/MoreIntegrals.ma".
-(* INCLUDE
-CalculusTheorems
-*)
+include "ftc/CalculusTheorems.ma".
(* UNEXPORTED
Opaque Min.
(* UNEXPORTED
Opaque Min.
-inline cic:/CoRN/ftc/FTC/I.var.
+inline "cic:/CoRN/ftc/FTC/I.var".
-inline cic:/CoRN/ftc/FTC/F.var.
+inline "cic:/CoRN/ftc/FTC/F.var".
-inline cic:/CoRN/ftc/FTC/contF.var.
+inline "cic:/CoRN/ftc/FTC/contF.var".
-inline cic:/CoRN/ftc/FTC/a.var.
+inline "cic:/CoRN/ftc/FTC/a.var".
-inline cic:/CoRN/ftc/FTC/Ha.var.
+inline "cic:/CoRN/ftc/FTC/Ha.var".
-inline cic:/CoRN/ftc/FTC/prim_lemma.con.
+inline "cic:/CoRN/ftc/FTC/prim_lemma.con".
-inline cic:/CoRN/ftc/FTC/Fprim_strext.con.
+inline "cic:/CoRN/ftc/FTC/Fprim_strext.con".
-inline cic:/CoRN/ftc/FTC/Fprim.con.
+inline "cic:/CoRN/ftc/FTC/Fprim.con".
(* UNEXPORTED
End Indefinite_Integral.
(* UNEXPORTED
End Indefinite_Integral.
-inline cic:/CoRN/ftc/FTC/J.var.
+inline "cic:/CoRN/ftc/FTC/J.var".
-inline cic:/CoRN/ftc/FTC/F.var.
+inline "cic:/CoRN/ftc/FTC/F.var".
-inline cic:/CoRN/ftc/FTC/contF.var.
+inline "cic:/CoRN/ftc/FTC/contF.var".
-inline cic:/CoRN/ftc/FTC/x0.var.
+inline "cic:/CoRN/ftc/FTC/x0.var".
-inline cic:/CoRN/ftc/FTC/Hx0.var.
+inline "cic:/CoRN/ftc/FTC/Hx0.var".
-inline cic:/CoRN/ftc/FTC/G.con.
+inline "cic:/CoRN/ftc/FTC/G.con".
-inline cic:/CoRN/ftc/FTC/Continuous_prim.con.
+inline "cic:/CoRN/ftc/FTC/Continuous_prim.con".
(*#*
The derivative of [G] is simply [F].
*)
(*#*
The derivative of [G] is simply [F].
*)
-inline cic:/CoRN/ftc/FTC/pJ.var.
+inline "cic:/CoRN/ftc/FTC/pJ.var".
-inline cic:/CoRN/ftc/FTC/FTC1.con.
+inline "cic:/CoRN/ftc/FTC/FTC1.con".
(*#*
Any other function [G0] with derivative [F] must differ from [G] by a constant.
*)
(*#*
Any other function [G0] with derivative [F] must differ from [G] by a constant.
*)
-inline cic:/CoRN/ftc/FTC/G0.var.
+inline "cic:/CoRN/ftc/FTC/G0.var".
-inline cic:/CoRN/ftc/FTC/derG0.var.
+inline "cic:/CoRN/ftc/FTC/derG0.var".
-inline cic:/CoRN/ftc/FTC/FTC2.con.
+inline "cic:/CoRN/ftc/FTC/FTC2.con".
(*#*
The following is another statement of the Fundamental Theorem of Calculus, also known as Barrow's rule.
(*#*
The following is another statement of the Fundamental Theorem of Calculus, also known as Barrow's rule.
-inline cic:/CoRN/ftc/FTC/G0_inc.con.
+inline "cic:/CoRN/ftc/FTC/G0_inc.con".
-inline cic:/CoRN/ftc/FTC/Barrow.con.
+inline "cic:/CoRN/ftc/FTC/Barrow.con".
commutes with the indefinite integral.
*)
commutes with the indefinite integral.
*)
-inline cic:/CoRN/ftc/FTC/J.var.
+inline "cic:/CoRN/ftc/FTC/J.var".
-inline cic:/CoRN/ftc/FTC/f.var.
+inline "cic:/CoRN/ftc/FTC/f.var".
-inline cic:/CoRN/ftc/FTC/F.var.
+inline "cic:/CoRN/ftc/FTC/F.var".
-inline cic:/CoRN/ftc/FTC/contf.var.
+inline "cic:/CoRN/ftc/FTC/contf.var".
-inline cic:/CoRN/ftc/FTC/contF.var.
+inline "cic:/CoRN/ftc/FTC/contF.var".
(* UNEXPORTED
Section Compact.
(* UNEXPORTED
Section Compact.
-inline cic:/CoRN/ftc/FTC/a.var.
+inline "cic:/CoRN/ftc/FTC/a.var".
-inline cic:/CoRN/ftc/FTC/b.var.
+inline "cic:/CoRN/ftc/FTC/b.var".
-inline cic:/CoRN/ftc/FTC/Hab.var.
+inline "cic:/CoRN/ftc/FTC/Hab.var".
-inline cic:/CoRN/ftc/FTC/contIf.var.
+inline "cic:/CoRN/ftc/FTC/contIf.var".
-inline cic:/CoRN/ftc/FTC/contIF.var.
+inline "cic:/CoRN/ftc/FTC/contIF.var".
-inline cic:/CoRN/ftc/FTC/convF.var.
+inline "cic:/CoRN/ftc/FTC/convF.var".
-inline cic:/CoRN/ftc/FTC/x0.var.
+inline "cic:/CoRN/ftc/FTC/x0.var".
-inline cic:/CoRN/ftc/FTC/Hx0.var.
+inline "cic:/CoRN/ftc/FTC/Hx0.var".
-inline cic:/CoRN/ftc/FTC/Hx0'.var.
+inline "cic:/CoRN/ftc/FTC/Hx0'.var".
-inline cic:/CoRN/ftc/FTC/g.con.
+inline "cic:/CoRN/ftc/FTC/g.con".
-inline cic:/CoRN/ftc/FTC/G.con.
+inline "cic:/CoRN/ftc/FTC/G.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/FTC/contg.var.
+inline "cic:/CoRN/ftc/FTC/contg.var".
-inline cic:/CoRN/ftc/FTC/contG.var.
+inline "cic:/CoRN/ftc/FTC/contG.var".
-inline cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con.
+inline "cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con".
(* UNEXPORTED
End Compact.
(* UNEXPORTED
End Compact.
And now we can generalize it step by step.
*)
And now we can generalize it step by step.
*)
-inline cic:/CoRN/ftc/FTC/limit_of_integral.con.
+inline "cic:/CoRN/ftc/FTC/limit_of_integral.con".
-inline cic:/CoRN/ftc/FTC/limit_of_Integral.con.
+inline "cic:/CoRN/ftc/FTC/limit_of_Integral.con".
(* UNEXPORTED
Section General.
(* UNEXPORTED
Section General.
-inline cic:/CoRN/ftc/FTC/convF.var.
+inline "cic:/CoRN/ftc/FTC/convF.var".
-inline cic:/CoRN/ftc/FTC/x0.var.
+inline "cic:/CoRN/ftc/FTC/x0.var".
-inline cic:/CoRN/ftc/FTC/Hx0.var.
+inline "cic:/CoRN/ftc/FTC/Hx0.var".
-inline cic:/CoRN/ftc/FTC/g.con.
+inline "cic:/CoRN/ftc/FTC/g.con".
-inline cic:/CoRN/ftc/FTC/G.con.
+inline "cic:/CoRN/ftc/FTC/G.con".
-inline cic:/CoRN/ftc/FTC/contg.var.
+inline "cic:/CoRN/ftc/FTC/contg.var".
-inline cic:/CoRN/ftc/FTC/contG.var.
+inline "cic:/CoRN/ftc/FTC/contG.var".
-inline cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con.
+inline "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con".
(* UNEXPORTED
End General.
(* UNEXPORTED
End General.
-inline cic:/CoRN/ftc/FTC/J.var.
+inline "cic:/CoRN/ftc/FTC/J.var".
-inline cic:/CoRN/ftc/FTC/pJ.var.
+inline "cic:/CoRN/ftc/FTC/pJ.var".
-inline cic:/CoRN/ftc/FTC/f.var.
+inline "cic:/CoRN/ftc/FTC/f.var".
-inline cic:/CoRN/ftc/FTC/g.var.
+inline "cic:/CoRN/ftc/FTC/g.var".
-inline cic:/CoRN/ftc/FTC/F.var.
+inline "cic:/CoRN/ftc/FTC/F.var".
-inline cic:/CoRN/ftc/FTC/G.var.
+inline "cic:/CoRN/ftc/FTC/G.var".
-inline cic:/CoRN/ftc/FTC/contf.var.
+inline "cic:/CoRN/ftc/FTC/contf.var".
-inline cic:/CoRN/ftc/FTC/contF.var.
+inline "cic:/CoRN/ftc/FTC/contF.var".
-inline cic:/CoRN/ftc/FTC/convF.var.
+inline "cic:/CoRN/ftc/FTC/convF.var".
-inline cic:/CoRN/ftc/FTC/contg.var.
+inline "cic:/CoRN/ftc/FTC/contg.var".
-inline cic:/CoRN/ftc/FTC/contG.var.
+inline "cic:/CoRN/ftc/FTC/contG.var".
-inline cic:/CoRN/ftc/FTC/convG.var.
+inline "cic:/CoRN/ftc/FTC/convG.var".
-inline cic:/CoRN/ftc/FTC/derf.var.
+inline "cic:/CoRN/ftc/FTC/derf.var".
-inline cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con.
+inline "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con".
(* UNEXPORTED
End Limit_of_Derivative_Seq.
(* UNEXPORTED
End Limit_of_Derivative_Seq.
As a very important case of this result, we get a rule for deriving series.
*)
As a very important case of this result, we get a rule for deriving series.
*)
-inline cic:/CoRN/ftc/FTC/J.var.
+inline "cic:/CoRN/ftc/FTC/J.var".
-inline cic:/CoRN/ftc/FTC/pJ.var.
+inline "cic:/CoRN/ftc/FTC/pJ.var".
-inline cic:/CoRN/ftc/FTC/f.var.
+inline "cic:/CoRN/ftc/FTC/f.var".
-inline cic:/CoRN/ftc/FTC/g.var.
+inline "cic:/CoRN/ftc/FTC/g.var".
-inline cic:/CoRN/ftc/FTC/convF.var.
+inline "cic:/CoRN/ftc/FTC/convF.var".
-inline cic:/CoRN/ftc/FTC/convG.var.
+inline "cic:/CoRN/ftc/FTC/convG.var".
-inline cic:/CoRN/ftc/FTC/derF.var.
+inline "cic:/CoRN/ftc/FTC/derF.var".
-inline cic:/CoRN/ftc/FTC/Derivative_FSeries.con.
+inline "cic:/CoRN/ftc/FTC/Derivative_FSeries.con".
(* UNEXPORTED
End Derivative_Series.
(* UNEXPORTED
End Derivative_Series.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSequence".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSequence".
(* $Id: FunctSequence.v,v 1.5 2004/04/23 10:00:58 lcf Exp $ *)
(* $Id: FunctSequence.v,v 1.5 2004/04/23 10:00:58 lcf Exp $ *)
-(* INCLUDE
-Continuity
-*)
+include "ftc/Continuity.ma".
-(* INCLUDE
-PartInterval
-*)
+include "ftc/PartInterval.ma".
(* UNEXPORTED
Section Definitions.
(* UNEXPORTED
Section Definitions.
-inline cic:/CoRN/ftc/FunctSequence/a.var.
+inline "cic:/CoRN/ftc/FunctSequence/a.var".
-inline cic:/CoRN/ftc/FunctSequence/b.var.
+inline "cic:/CoRN/ftc/FunctSequence/b.var".
-inline cic:/CoRN/ftc/FunctSequence/Hab.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
-inline cic:/CoRN/ftc/FunctSequence/I.con.
+inline "cic:/CoRN/ftc/FunctSequence/I.con".
-inline cic:/CoRN/ftc/FunctSequence/f.var.
+inline "cic:/CoRN/ftc/FunctSequence/f.var".
-inline cic:/CoRN/ftc/FunctSequence/F.var.
+inline "cic:/CoRN/ftc/FunctSequence/F.var".
-inline cic:/CoRN/ftc/FunctSequence/contf.var.
+inline "cic:/CoRN/ftc/FunctSequence/contf.var".
-inline cic:/CoRN/ftc/FunctSequence/contF.var.
+inline "cic:/CoRN/ftc/FunctSequence/contF.var".
-inline cic:/CoRN/ftc/FunctSequence/incf.con.
+inline "cic:/CoRN/ftc/FunctSequence/incf.con".
-inline cic:/CoRN/ftc/FunctSequence/incF.con.
+inline "cic:/CoRN/ftc/FunctSequence/incF.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_seq'.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2.con".
(*#*
These definitions are all shown to be equivalent.
*)
(*#*
These definitions are all shown to be equivalent.
*)
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq'.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq'.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq'.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq'.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq2.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq2.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_seq.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_seq.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_norm.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_norm.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_norm_seq.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_norm_seq.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq'.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq'.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq1.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq1.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq1.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq1.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq.con".
(*#*
A Cauchy sequence of functions is pointwise a Cauchy sequence.
*)
(*#*
A Cauchy sequence of functions is pointwise a Cauchy sequence.
*)
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
Section More_Definitions.
*)
Section More_Definitions.
*)
-inline cic:/CoRN/ftc/FunctSequence/a.var.
+inline "cic:/CoRN/ftc/FunctSequence/a.var".
-inline cic:/CoRN/ftc/FunctSequence/b.var.
+inline "cic:/CoRN/ftc/FunctSequence/b.var".
-inline cic:/CoRN/ftc/FunctSequence/Hab.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
-inline cic:/CoRN/ftc/FunctSequence/I.con.
+inline "cic:/CoRN/ftc/FunctSequence/I.con".
-inline cic:/CoRN/ftc/FunctSequence/f.var.
+inline "cic:/CoRN/ftc/FunctSequence/f.var".
-inline cic:/CoRN/ftc/FunctSequence/contf.var.
+inline "cic:/CoRN/ftc/FunctSequence/contf.var".
(*#*
We can also say that [f] is simply convergent if it converges to some
(*#*
We can also say that [f] is simply convergent if it converges to some
partial functions, for reasons which were already explained.
*)
partial functions, for reasons which were already explained.
*)
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_seq.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq.con".
(*#*
It is useful to extract the limit as a partial function:
(*#*
It is useful to extract the limit as a partial function:
-inline cic:/CoRN/ftc/FunctSequence/H.var.
+inline "cic:/CoRN/ftc/FunctSequence/H.var".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con".
(* UNEXPORTED
End More_Definitions.
(* UNEXPORTED
End More_Definitions.
This section contains a number of technical results stating mainly that being a Cauchy sequence or converging to some limit is a property of the sequence itself and independent of the proofs we supply of its continuity or the continuity of its limit.
*)
This section contains a number of technical results stating mainly that being a Cauchy sequence or converging to some limit is a property of the sequence itself and independent of the proofs we supply of its continuity or the continuity of its limit.
*)
-inline cic:/CoRN/ftc/FunctSequence/a.var.
+inline "cic:/CoRN/ftc/FunctSequence/a.var".
-inline cic:/CoRN/ftc/FunctSequence/b.var.
+inline "cic:/CoRN/ftc/FunctSequence/b.var".
-inline cic:/CoRN/ftc/FunctSequence/Hab.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
-inline cic:/CoRN/ftc/FunctSequence/I.con.
+inline "cic:/CoRN/ftc/FunctSequence/I.con".
-inline cic:/CoRN/ftc/FunctSequence/f.var.
+inline "cic:/CoRN/ftc/FunctSequence/f.var".
-inline cic:/CoRN/ftc/FunctSequence/contf.var.
+inline "cic:/CoRN/ftc/FunctSequence/contf.var".
-inline cic:/CoRN/ftc/FunctSequence/contf0.var.
+inline "cic:/CoRN/ftc/FunctSequence/contf0.var".
-inline cic:/CoRN/ftc/FunctSequence/F.var.
+inline "cic:/CoRN/ftc/FunctSequence/F.var".
-inline cic:/CoRN/ftc/FunctSequence/contF.var.
+inline "cic:/CoRN/ftc/FunctSequence/contF.var".
-inline cic:/CoRN/ftc/FunctSequence/contF0.var.
+inline "cic:/CoRN/ftc/FunctSequence/contF0.var".
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wd.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wd.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_wd.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_wd.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_wd.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_wd.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq_wd.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq_wd.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_wd.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_wd.con".
(* UNEXPORTED
End Irrelevance_of_Proofs.
(* UNEXPORTED
End Irrelevance_of_Proofs.
Section More_Proof_Irrelevance.
*)
Section More_Proof_Irrelevance.
*)
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_seq_wd.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq_wd.con".
(* UNEXPORTED
End More_Proof_Irrelevance.
(* UNEXPORTED
End More_Proof_Irrelevance.
defined with respect to functional equality in the interval [[a,b]].
*)
defined with respect to functional equality in the interval [[a,b]].
*)
-inline cic:/CoRN/ftc/FunctSequence/a.var.
+inline "cic:/CoRN/ftc/FunctSequence/a.var".
-inline cic:/CoRN/ftc/FunctSequence/b.var.
+inline "cic:/CoRN/ftc/FunctSequence/b.var".
-inline cic:/CoRN/ftc/FunctSequence/Hab.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
-inline cic:/CoRN/ftc/FunctSequence/I.con.
+inline "cic:/CoRN/ftc/FunctSequence/I.con".
-inline cic:/CoRN/ftc/FunctSequence/f.var.
+inline "cic:/CoRN/ftc/FunctSequence/f.var".
-inline cic:/CoRN/ftc/FunctSequence/g.var.
+inline "cic:/CoRN/ftc/FunctSequence/g.var".
-inline cic:/CoRN/ftc/FunctSequence/contf.var.
+inline "cic:/CoRN/ftc/FunctSequence/contf.var".
-inline cic:/CoRN/ftc/FunctSequence/contf0.var.
+inline "cic:/CoRN/ftc/FunctSequence/contf0.var".
-inline cic:/CoRN/ftc/FunctSequence/contg.var.
+inline "cic:/CoRN/ftc/FunctSequence/contg.var".
-inline cic:/CoRN/ftc/FunctSequence/contg0.var.
+inline "cic:/CoRN/ftc/FunctSequence/contg0.var".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con".
-inline cic:/CoRN/ftc/FunctSequence/F.var.
+inline "cic:/CoRN/ftc/FunctSequence/F.var".
-inline cic:/CoRN/ftc/FunctSequence/G.var.
+inline "cic:/CoRN/ftc/FunctSequence/G.var".
-inline cic:/CoRN/ftc/FunctSequence/contF.var.
+inline "cic:/CoRN/ftc/FunctSequence/contF.var".
-inline cic:/CoRN/ftc/FunctSequence/contF0.var.
+inline "cic:/CoRN/ftc/FunctSequence/contF0.var".
-inline cic:/CoRN/ftc/FunctSequence/contG.var.
+inline "cic:/CoRN/ftc/FunctSequence/contG.var".
-inline cic:/CoRN/ftc/FunctSequence/contG0.var.
+inline "cic:/CoRN/ftc/FunctSequence/contG0.var".
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl'.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl'.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr'.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr'.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_wd.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_wd.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_cont_Lim.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_cont_Lim.con".
-inline cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq.con.
+inline "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq.con".
-inline cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq.con.
+inline "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq.con".
(*#*
More interesting is the fact that a convergent sequence of functions converges pointwise as a sequence of real numbers.
*)
(*#*
More interesting is the fact that a convergent sequence of functions converges pointwise as a sequence of real numbers.
*)
-inline cic:/CoRN/ftc/FunctSequence/fun_conv_imp_seq_conv.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_conv_imp_seq_conv.con".
(*#*
And a sequence of real numbers converges iff the corresponding sequence of constant functions converges to the corresponding constant function.
*)
(*#*
And a sequence of real numbers converges iff the corresponding sequence of constant functions converges to the corresponding constant function.
*)
-inline cic:/CoRN/ftc/FunctSequence/seq_conv_imp_fun_conv.con.
+inline "cic:/CoRN/ftc/FunctSequence/seq_conv_imp_fun_conv.con".
(* UNEXPORTED
End More_Properties.
(* UNEXPORTED
End More_Properties.
We now study how convergence is affected by algebraic operations, and some algebraic properties of the limit function.
*)
We now study how convergence is affected by algebraic operations, and some algebraic properties of the limit function.
*)
-inline cic:/CoRN/ftc/FunctSequence/a.var.
+inline "cic:/CoRN/ftc/FunctSequence/a.var".
-inline cic:/CoRN/ftc/FunctSequence/b.var.
+inline "cic:/CoRN/ftc/FunctSequence/b.var".
-inline cic:/CoRN/ftc/FunctSequence/Hab.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
-inline cic:/CoRN/ftc/FunctSequence/I.con.
+inline "cic:/CoRN/ftc/FunctSequence/I.con".
-inline cic:/CoRN/ftc/FunctSequence/f.var.
+inline "cic:/CoRN/ftc/FunctSequence/f.var".
-inline cic:/CoRN/ftc/FunctSequence/g.var.
+inline "cic:/CoRN/ftc/FunctSequence/g.var".
-inline cic:/CoRN/ftc/FunctSequence/contf.var.
+inline "cic:/CoRN/ftc/FunctSequence/contf.var".
-inline cic:/CoRN/ftc/FunctSequence/contg.var.
+inline "cic:/CoRN/ftc/FunctSequence/contg.var".
(*#*
First, the limit function is unique.
*)
(*#*
First, the limit function is unique.
*)
-inline cic:/CoRN/ftc/FunctSequence/FLim_unique.con.
+inline "cic:/CoRN/ftc/FunctSequence/FLim_unique.con".
(*#* Constant sequences (not sequences of constant functions!) always converge.
*)
(*#* Constant sequences (not sequences of constant functions!) always converge.
*)
-inline cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_const.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_const.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_const.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_const.con".
(*#*
We now prove that if two sequences converge than their sum (difference, product) also converge to the sum (difference, product) of their limits.
*)
(*#*
We now prove that if two sequences converge than their sum (difference, product) also converge to the sum (difference, product) of their limits.
*)
-inline cic:/CoRN/ftc/FunctSequence/F.var.
+inline "cic:/CoRN/ftc/FunctSequence/F.var".
-inline cic:/CoRN/ftc/FunctSequence/G.var.
+inline "cic:/CoRN/ftc/FunctSequence/G.var".
-inline cic:/CoRN/ftc/FunctSequence/contF.var.
+inline "cic:/CoRN/ftc/FunctSequence/contF.var".
-inline cic:/CoRN/ftc/FunctSequence/contG.var.
+inline "cic:/CoRN/ftc/FunctSequence/contG.var".
-inline cic:/CoRN/ftc/FunctSequence/convF.var.
+inline "cic:/CoRN/ftc/FunctSequence/convF.var".
-inline cic:/CoRN/ftc/FunctSequence/convG.var.
+inline "cic:/CoRN/ftc/FunctSequence/convG.var".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/FunctSequence/incf.con.
+inline "cic:/CoRN/ftc/FunctSequence/incf.con".
-inline cic:/CoRN/ftc/FunctSequence/incg.con.
+inline "cic:/CoRN/ftc/FunctSequence/incg.con".
-inline cic:/CoRN/ftc/FunctSequence/incF.con.
+inline "cic:/CoRN/ftc/FunctSequence/incF.con".
-inline cic:/CoRN/ftc/FunctSequence/incG.con.
+inline "cic:/CoRN/ftc/FunctSequence/incG.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus'.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus'.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus'.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus'.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult'.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult'.con".
(* UNEXPORTED
End Algebraic_Properties.
(* UNEXPORTED
End Algebraic_Properties.
Section More_Algebraic_Properties.
*)
Section More_Algebraic_Properties.
*)
-inline cic:/CoRN/ftc/FunctSequence/a.var.
+inline "cic:/CoRN/ftc/FunctSequence/a.var".
-inline cic:/CoRN/ftc/FunctSequence/b.var.
+inline "cic:/CoRN/ftc/FunctSequence/b.var".
-inline cic:/CoRN/ftc/FunctSequence/Hab.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
-inline cic:/CoRN/ftc/FunctSequence/I.con.
+inline "cic:/CoRN/ftc/FunctSequence/I.con".
-inline cic:/CoRN/ftc/FunctSequence/f.var.
+inline "cic:/CoRN/ftc/FunctSequence/f.var".
-inline cic:/CoRN/ftc/FunctSequence/g.var.
+inline "cic:/CoRN/ftc/FunctSequence/g.var".
-inline cic:/CoRN/ftc/FunctSequence/contf.var.
+inline "cic:/CoRN/ftc/FunctSequence/contf.var".
-inline cic:/CoRN/ftc/FunctSequence/contg.var.
+inline "cic:/CoRN/ftc/FunctSequence/contg.var".
(*#*
The same is true if we don't make the limits explicit.
(*#*
The same is true if we don't make the limits explicit.
-inline cic:/CoRN/ftc/FunctSequence/Hf.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hf.var".
-inline cic:/CoRN/ftc/FunctSequence/Hg.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hg.var".
-inline cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_plus.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_plus.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_minus.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_minus.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_mult.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_mult.con".
(* UNEXPORTED
End More_Algebraic_Properties.
(* UNEXPORTED
End More_Algebraic_Properties.
Section Still_More_Algebraic_Properties.
*)
Section Still_More_Algebraic_Properties.
*)
-inline cic:/CoRN/ftc/FunctSequence/a.var.
+inline "cic:/CoRN/ftc/FunctSequence/a.var".
-inline cic:/CoRN/ftc/FunctSequence/b.var.
+inline "cic:/CoRN/ftc/FunctSequence/b.var".
-inline cic:/CoRN/ftc/FunctSequence/Hab.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
-inline cic:/CoRN/ftc/FunctSequence/I.con.
+inline "cic:/CoRN/ftc/FunctSequence/I.con".
-inline cic:/CoRN/ftc/FunctSequence/f.var.
+inline "cic:/CoRN/ftc/FunctSequence/f.var".
-inline cic:/CoRN/ftc/FunctSequence/contf.var.
+inline "cic:/CoRN/ftc/FunctSequence/contf.var".
-inline cic:/CoRN/ftc/FunctSequence/Hf.var.
+inline "cic:/CoRN/ftc/FunctSequence/Hf.var".
(*#*
As a corollary, we get the analogous property for the sequence of algebraic inverse functions.
*)
(*#*
As a corollary, we get the analogous property for the sequence of algebraic inverse functions.
*)
-inline cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_inv.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_inv.con".
-inline cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_inv.con.
+inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_inv.con".
(* UNEXPORTED
End Still_More_Algebraic_Properties.
(* UNEXPORTED
End Still_More_Algebraic_Properties.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSeries".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSeries".
(* $Id: FunctSeries.v,v 1.6 2004/04/23 10:00:58 lcf Exp $ *)
(* $Id: FunctSeries.v,v 1.6 2004/04/23 10:00:58 lcf Exp $ *)
-(* INCLUDE
-FunctSequence
-*)
+include "ftc/FunctSequence.ma".
+include "reals/Series.ma".
(*#* printing fun_seq_part_sum %\ensuremath{\sum^n}% #∑<sup>n</sup># *)
(*#* printing fun_seq_part_sum %\ensuremath{\sum^n}% #∑<sup>n</sup># *)
convergence is simply the convergence of the sequence of partial sums.
*)
convergence is simply the convergence of the sequence of partial sums.
*)
-inline cic:/CoRN/ftc/FunctSeries/a.var.
+inline "cic:/CoRN/ftc/FunctSeries/a.var".
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+inline "cic:/CoRN/ftc/FunctSeries/b.var".
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
-inline cic:/CoRN/ftc/FunctSeries/I.con.
+inline "cic:/CoRN/ftc/FunctSeries/I.con".
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+inline "cic:/CoRN/ftc/FunctSeries/f.var".
-inline cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con".
-inline cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con".
-inline cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con".
(*#*
For what comes up next we need to know that the convergence of a
(*#*
For what comes up next we need to know that the convergence of a
-inline cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con".
(*#* We then define the sum of the series as being the pointwise sum of
the corresponding series.
(*#* We then define the sum of the series as being the pointwise sum of
the corresponding series.
-inline cic:/CoRN/ftc/FunctSeries/H.var.
+inline "cic:/CoRN/ftc/FunctSeries/H.var".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/FunctSeries/contf.con.
+inline "cic:/CoRN/ftc/FunctSeries/contf.con".
-inline cic:/CoRN/ftc/FunctSeries/incf.con.
+inline "cic:/CoRN/ftc/FunctSeries/incf.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
Section More_Definitions.
*)
Section More_Definitions.
*)
-inline cic:/CoRN/ftc/FunctSeries/a.var.
+inline "cic:/CoRN/ftc/FunctSeries/a.var".
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+inline "cic:/CoRN/ftc/FunctSeries/b.var".
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+inline "cic:/CoRN/ftc/FunctSeries/f.var".
(*#* A series can also be absolutely convergent. *)
(*#* A series can also be absolutely convergent. *)
-inline cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con".
(* UNEXPORTED
End More_Definitions.
(* UNEXPORTED
End More_Definitions.
All of these are analogous to the properties for series of real numbers, so we won't comment much about them.
*)
All of these are analogous to the properties for series of real numbers, so we won't comment much about them.
*)
-inline cic:/CoRN/ftc/FunctSeries/a.var.
+inline "cic:/CoRN/ftc/FunctSeries/a.var".
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+inline "cic:/CoRN/ftc/FunctSeries/b.var".
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
-inline cic:/CoRN/ftc/FunctSeries/I.con.
+inline "cic:/CoRN/ftc/FunctSeries/I.con".
-inline cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con".
-inline cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con.
+inline "cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con".
-inline cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con".
-inline cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con.
+inline "cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con".
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+inline "cic:/CoRN/ftc/FunctSeries/f.var".
-inline cic:/CoRN/ftc/FunctSeries/g.var.
+inline "cic:/CoRN/ftc/FunctSeries/g.var".
-inline cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con".
-inline cic:/CoRN/ftc/FunctSeries/convF.var.
+inline "cic:/CoRN/ftc/FunctSeries/convF.var".
-inline cic:/CoRN/ftc/FunctSeries/convG.var.
+inline "cic:/CoRN/ftc/FunctSeries/convG.var".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con".
-inline cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con.
+inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con".
-inline cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con.
+inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con".
(*#*
%\begin{convention}% Let [c:IR].
%\end{convention}%
*)
(*#*
%\begin{convention}% Let [c:IR].
%\end{convention}%
*)
-inline cic:/CoRN/ftc/FunctSeries/c.var.
+inline "cic:/CoRN/ftc/FunctSeries/c.var".
-inline cic:/CoRN/ftc/FunctSeries/H.var.
+inline "cic:/CoRN/ftc/FunctSeries/H.var".
-inline cic:/CoRN/ftc/FunctSeries/contH.var.
+inline "cic:/CoRN/ftc/FunctSeries/contH.var".
-inline cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con.
+inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con".
(* UNEXPORTED
End Operations.
(* UNEXPORTED
End Operations.
Section More_Operations.
*)
Section More_Operations.
*)
-inline cic:/CoRN/ftc/FunctSeries/a.var.
+inline "cic:/CoRN/ftc/FunctSeries/a.var".
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+inline "cic:/CoRN/ftc/FunctSeries/b.var".
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
-inline cic:/CoRN/ftc/FunctSeries/I.con.
+inline "cic:/CoRN/ftc/FunctSeries/I.con".
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+inline "cic:/CoRN/ftc/FunctSeries/f.var".
-inline cic:/CoRN/ftc/FunctSeries/convF.var.
+inline "cic:/CoRN/ftc/FunctSeries/convF.var".
-inline cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con.
+inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con".
(* UNEXPORTED
End More_Operations.
(* UNEXPORTED
End More_Operations.
Section Other_Results.
*)
Section Other_Results.
*)
-inline cic:/CoRN/ftc/FunctSeries/a.var.
+inline "cic:/CoRN/ftc/FunctSeries/a.var".
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+inline "cic:/CoRN/ftc/FunctSeries/b.var".
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+inline "cic:/CoRN/ftc/FunctSeries/f.var".
-inline cic:/CoRN/ftc/FunctSeries/convF.var.
+inline "cic:/CoRN/ftc/FunctSeries/convF.var".
(*#*
The following relate the sum series with the limit of the sequence of
(*#*
The following relate the sum series with the limit of the sequence of
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con".
-inline cic:/CoRN/ftc/FunctSeries/fun_series_conv.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_series_conv.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con".
-inline cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con.
+inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con".
(* UNEXPORTED
End Other_Results.
(* UNEXPORTED
End Other_Results.
Most of the convergence criteria for series of real numbers carry over to series of real-valued functions, so again we just present them without comments.
*)
Most of the convergence criteria for series of real numbers carry over to series of real-valued functions, so again we just present them without comments.
*)
-inline cic:/CoRN/ftc/FunctSeries/a.var.
+inline "cic:/CoRN/ftc/FunctSeries/a.var".
-inline cic:/CoRN/ftc/FunctSeries/b.var.
+inline "cic:/CoRN/ftc/FunctSeries/b.var".
-inline cic:/CoRN/ftc/FunctSeries/Hab.var.
+inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
-inline cic:/CoRN/ftc/FunctSeries/I.con.
+inline "cic:/CoRN/ftc/FunctSeries/I.con".
-inline cic:/CoRN/ftc/FunctSeries/f.var.
+inline "cic:/CoRN/ftc/FunctSeries/f.var".
-inline cic:/CoRN/ftc/FunctSeries/contF.var.
+inline "cic:/CoRN/ftc/FunctSeries/contF.var".
(* UNEXPORTED
Opaque Frestr.
(* UNEXPORTED
Opaque Frestr.
Opaque fun_seq_part_sum.
*)
Opaque fun_seq_part_sum.
*)
-inline cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con".
(* UNEXPORTED
Transparent FAbs.
*)
(* UNEXPORTED
Transparent FAbs.
*)
-inline cic:/CoRN/ftc/FunctSeries/fun_comparison.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_comparison.con".
-inline cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con.
+inline "cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con".
(* UNEXPORTED
Opaque FAbs.
*)
(* UNEXPORTED
Opaque FAbs.
*)
-inline cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con.
+inline "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con".
(* UNEXPORTED
End Convergence_Criteria.
(* UNEXPORTED
End Convergence_Criteria.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSums".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSums".
(* $Id: FunctSums.v,v 1.5 2004/04/23 10:00:59 lcf Exp $ *)
(*#* printing FSum0 %\ensuremath{\sum_0}% #∑<sub>0</sub># *)
(* $Id: FunctSums.v,v 1.5 2004/04/23 10:00:59 lcf Exp $ *)
(*#* printing FSum0 %\ensuremath{\sum_0}% #∑<sub>0</sub># *)
(*#* printing FSumx %\ensuremath{\sum'}% #∑'&*)
(*#* printing FSumx %\ensuremath{\sum'}% #∑'&*)
-(* INCLUDE
-CSumsReals
-*)
+include "reals/CSumsReals.ma".
-(* INCLUDE
-PartFunEquality
-*)
+include "ftc/PartFunEquality.ma".
-inline cic:/CoRN/ftc/FunctSums/FSum0.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum0.con".
-inline cic:/CoRN/ftc/FunctSums/FSum.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum.con".
(*#*
Although [FSum] is here defined directly, it has the same relationship
(*#*
Although [FSum] is here defined directly, it has the same relationship
-inline cic:/CoRN/ftc/FunctSums/FSum_FSum0.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_FSum0.con".
-inline cic:/CoRN/ftc/FunctSums/FSum0_wd.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum0_wd.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_one.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_one.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_FSum.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_FSum.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_first.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_first.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_last.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_last.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_last'.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_last'.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_wd.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_wd.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_plus_FSum.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_plus_FSum.con".
-inline cic:/CoRN/ftc/FunctSums/inv_FSum.con.
+inline "cic:/CoRN/ftc/FunctSums/inv_FSum.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_minus_FSum.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_minus_FSum.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_wd'.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_wd'.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_resp_less.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_resp_less.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_resp_leEq.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_resp_leEq.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_comm_scal.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_comm_scal.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_comm_scal'.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_comm_scal'.con".
(*#*
Also important is the case when we have a finite family
(*#*
Also important is the case when we have a finite family
to use the [FSumx] operator.
*)
to use the [FSumx] operator.
*)
-inline cic:/CoRN/ftc/FunctSums/FSumx.con.
+inline "cic:/CoRN/ftc/FunctSums/FSumx.con".
(*#*
This operator is well defined, as expected.
*)
(*#*
This operator is well defined, as expected.
*)
-inline cic:/CoRN/ftc/FunctSums/FSumx_wd.con.
+inline "cic:/CoRN/ftc/FunctSums/FSumx_wd.con".
-inline cic:/CoRN/ftc/FunctSums/FSumx_wd'.con.
+inline "cic:/CoRN/ftc/FunctSums/FSumx_wd'.con".
(*#*
As was already the case for [Sumx], in many cases we will need to
(*#*
As was already the case for [Sumx], in many cases we will need to
function $f_i$#f<sub>i</sub>#.
*)
function $f_i$#f<sub>i</sub>#.
*)
-inline cic:/CoRN/ftc/FunctSums/ext_fun_seq.con.
+inline "cic:/CoRN/ftc/FunctSums/ext_fun_seq.con".
-inline cic:/CoRN/ftc/FunctSums/ext_fun_seq'.con.
+inline "cic:/CoRN/ftc/FunctSums/ext_fun_seq'.con".
(* UNEXPORTED
Implicit Arguments ext_fun_seq [n].
(* UNEXPORTED
Implicit Arguments ext_fun_seq [n].
Under these assumptions, we can characterize the domain and the value of the sum function from the domains and values of the summands:
*)
Under these assumptions, we can characterize the domain and the value of the sum function from the domains and values of the summands:
*)
-inline cic:/CoRN/ftc/FunctSums/FSumx_pred.con.
+inline "cic:/CoRN/ftc/FunctSums/FSumx_pred.con".
-inline cic:/CoRN/ftc/FunctSums/FSumx_pred'.con.
+inline "cic:/CoRN/ftc/FunctSums/FSumx_pred'.con".
-inline cic:/CoRN/ftc/FunctSums/FSumx_char.con.
+inline "cic:/CoRN/ftc/FunctSums/FSumx_char.con".
(*#*
As we did for arbitrary groups, it is often useful to rewrite this sums as ordinary sums.
*)
(*#*
As we did for arbitrary groups, it is often useful to rewrite this sums as ordinary sums.
*)
-inline cic:/CoRN/ftc/FunctSums/FSumx_to_FSum.con.
+inline "cic:/CoRN/ftc/FunctSums/FSumx_to_FSum.con".
-inline cic:/CoRN/ftc/FunctSums/FSumx_lt.con.
+inline "cic:/CoRN/ftc/FunctSums/FSumx_lt.con".
-inline cic:/CoRN/ftc/FunctSums/FSumx_le.con.
+inline "cic:/CoRN/ftc/FunctSums/FSumx_le.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_FSumx_to_FSum.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_FSumx_to_FSum.con".
(*#*
Some useful lemmas follow.
*)
(*#*
Some useful lemmas follow.
*)
-inline cic:/CoRN/ftc/FunctSums/FSum0_0.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum0_0.con".
-inline cic:/CoRN/ftc/FunctSums/FSum0_S.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum0_S.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_0.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_0.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_S.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_S.con".
-inline cic:/CoRN/ftc/FunctSums/FSum_FSum0'.con.
+inline "cic:/CoRN/ftc/FunctSums/FSum_FSum0'.con".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Integral".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Integral".
(* $Id: Integral.v,v 1.10 2004/04/23 10:00:59 lcf Exp $ *)
(* $Id: Integral.v,v 1.10 2004/04/23 10:00:59 lcf Exp $ *)
-(* INCLUDE
-RefLemma
-*)
+include "ftc/RefLemma.ma".
(*#* printing integral %\ensuremath{\int_I}% #∫<sub>I</sub># *)
(*#* printing integral %\ensuremath{\int_I}% #∫<sub>I</sub># *)
-inline cic:/CoRN/ftc/Integral/Sumx_wd_weird.con.
+inline "cic:/CoRN/ftc/Integral/Sumx_wd_weird.con".
-inline cic:/CoRN/ftc/Integral/Sumx_weird_lemma.con.
+inline "cic:/CoRN/ftc/Integral/Sumx_weird_lemma.con".
(* UNEXPORTED
End Lemmas.
(* UNEXPORTED
End Lemmas.
-inline cic:/CoRN/ftc/Integral/a.var.
+inline "cic:/CoRN/ftc/Integral/a.var".
-inline cic:/CoRN/ftc/Integral/b.var.
+inline "cic:/CoRN/ftc/Integral/b.var".
-inline cic:/CoRN/ftc/Integral/Hab.var.
+inline "cic:/CoRN/ftc/Integral/Hab.var".
-inline cic:/CoRN/ftc/Integral/I.con.
+inline "cic:/CoRN/ftc/Integral/I.con".
-inline cic:/CoRN/ftc/Integral/F.var.
+inline "cic:/CoRN/ftc/Integral/F.var".
-inline cic:/CoRN/ftc/Integral/contF.var.
+inline "cic:/CoRN/ftc/Integral/contF.var".
-inline cic:/CoRN/ftc/Integral/contF'.con.
+inline "cic:/CoRN/ftc/Integral/contF'.con".
-inline cic:/CoRN/ftc/Integral/integral_seq.con.
+inline "cic:/CoRN/ftc/Integral/integral_seq.con".
-inline cic:/CoRN/ftc/Integral/Cauchy_Darboux_Seq.con.
+inline "cic:/CoRN/ftc/Integral/Cauchy_Darboux_Seq.con".
-inline cic:/CoRN/ftc/Integral/integral.con.
+inline "cic:/CoRN/ftc/Integral/integral.con".
(* UNEXPORTED
End Darboux_Sum.
(* UNEXPORTED
End Darboux_Sum.
-inline cic:/CoRN/ftc/Integral/n.var.
+inline "cic:/CoRN/ftc/Integral/n.var".
-inline cic:/CoRN/ftc/Integral/P.var.
+inline "cic:/CoRN/ftc/Integral/P.var".
-inline cic:/CoRN/ftc/Integral/e.var.
+inline "cic:/CoRN/ftc/Integral/e.var".
-inline cic:/CoRN/ftc/Integral/He.var.
+inline "cic:/CoRN/ftc/Integral/He.var".
-inline cic:/CoRN/ftc/Integral/d.con.
+inline "cic:/CoRN/ftc/Integral/d.con".
-inline cic:/CoRN/ftc/Integral/HmeshP.var.
+inline "cic:/CoRN/ftc/Integral/HmeshP.var".
-inline cic:/CoRN/ftc/Integral/fP.var.
+inline "cic:/CoRN/ftc/Integral/fP.var".
-inline cic:/CoRN/ftc/Integral/HfP.var.
+inline "cic:/CoRN/ftc/Integral/HfP.var".
-inline cic:/CoRN/ftc/Integral/HfP'.var.
+inline "cic:/CoRN/ftc/Integral/HfP'.var".
-inline cic:/CoRN/ftc/Integral/incF.var.
+inline "cic:/CoRN/ftc/Integral/incF.var".
-inline cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con.
+inline "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con".
(* UNEXPORTED
End Integral_Thm.
(* UNEXPORTED
End Integral_Thm.
The usual extensionality and strong extensionality results hold.
*)
The usual extensionality and strong extensionality results hold.
*)
-inline cic:/CoRN/ftc/Integral/a.var.
+inline "cic:/CoRN/ftc/Integral/a.var".
-inline cic:/CoRN/ftc/Integral/b.var.
+inline "cic:/CoRN/ftc/Integral/b.var".
-inline cic:/CoRN/ftc/Integral/Hab.var.
+inline "cic:/CoRN/ftc/Integral/Hab.var".
-inline cic:/CoRN/ftc/Integral/I.con.
+inline "cic:/CoRN/ftc/Integral/I.con".
Section Well_Definedness.
*)
Section Well_Definedness.
*)
-inline cic:/CoRN/ftc/Integral/F.var.
+inline "cic:/CoRN/ftc/Integral/F.var".
-inline cic:/CoRN/ftc/Integral/G.var.
+inline "cic:/CoRN/ftc/Integral/G.var".
-inline cic:/CoRN/ftc/Integral/contF.var.
+inline "cic:/CoRN/ftc/Integral/contF.var".
-inline cic:/CoRN/ftc/Integral/contG.var.
+inline "cic:/CoRN/ftc/Integral/contG.var".
-inline cic:/CoRN/ftc/Integral/integral_strext.con.
+inline "cic:/CoRN/ftc/Integral/integral_strext.con".
-inline cic:/CoRN/ftc/Integral/integral_strext'.con.
+inline "cic:/CoRN/ftc/Integral/integral_strext'.con".
-inline cic:/CoRN/ftc/Integral/integral_wd.con.
+inline "cic:/CoRN/ftc/Integral/integral_wd.con".
-inline cic:/CoRN/ftc/Integral/integral_wd'.con.
+inline "cic:/CoRN/ftc/Integral/integral_wd'.con".
(* UNEXPORTED
End Well_Definedness.
(* UNEXPORTED
End Well_Definedness.
The integral is a linear and monotonous function; in order to prove these facts we also need the important equalities $\int_a^bdx=b-a$#∫<sub>a</sub><sup>b</sup>dx=b-a# and $\int_a^af(x)dx=0$#∫<sub>a</sub><sup>a</sup>=0#.
*)
The integral is a linear and monotonous function; in order to prove these facts we also need the important equalities $\int_a^bdx=b-a$#∫<sub>a</sub><sup>b</sup>dx=b-a# and $\int_a^af(x)dx=0$#∫<sub>a</sub><sup>a</sup>=0#.
*)
-inline cic:/CoRN/ftc/Integral/integral_one.con.
+inline "cic:/CoRN/ftc/Integral/integral_one.con".
-inline cic:/CoRN/ftc/Integral/F.var.
+inline "cic:/CoRN/ftc/Integral/F.var".
-inline cic:/CoRN/ftc/Integral/G.var.
+inline "cic:/CoRN/ftc/Integral/G.var".
-inline cic:/CoRN/ftc/Integral/contF.var.
+inline "cic:/CoRN/ftc/Integral/contF.var".
-inline cic:/CoRN/ftc/Integral/contG.var.
+inline "cic:/CoRN/ftc/Integral/contG.var".
-inline cic:/CoRN/ftc/Integral/integral_comm_scal.con.
+inline "cic:/CoRN/ftc/Integral/integral_comm_scal.con".
-inline cic:/CoRN/ftc/Integral/integral_plus.con.
+inline "cic:/CoRN/ftc/Integral/integral_plus.con".
(* UNEXPORTED
Transparent Even_Partition.
*)
(* UNEXPORTED
Transparent Even_Partition.
*)
-inline cic:/CoRN/ftc/Integral/integral_empty.con.
+inline "cic:/CoRN/ftc/Integral/integral_empty.con".
(* UNEXPORTED
End Linearity_and_Monotonicity.
(* UNEXPORTED
End Linearity_and_Monotonicity.
Section Linearity_and_Monotonicity'.
*)
Section Linearity_and_Monotonicity'.
*)
-inline cic:/CoRN/ftc/Integral/F.var.
+inline "cic:/CoRN/ftc/Integral/F.var".
-inline cic:/CoRN/ftc/Integral/G.var.
+inline "cic:/CoRN/ftc/Integral/G.var".
-inline cic:/CoRN/ftc/Integral/contF.var.
+inline "cic:/CoRN/ftc/Integral/contF.var".
-inline cic:/CoRN/ftc/Integral/contG.var.
+inline "cic:/CoRN/ftc/Integral/contG.var".
(*#*
%\begin{convention}% Let [alpha, beta : IR] and assume that
(*#*
%\begin{convention}% Let [alpha, beta : IR] and assume that
-inline cic:/CoRN/ftc/Integral/alpha.var.
+inline "cic:/CoRN/ftc/Integral/alpha.var".
-inline cic:/CoRN/ftc/Integral/beta.var.
+inline "cic:/CoRN/ftc/Integral/beta.var".
-inline cic:/CoRN/ftc/Integral/h.con.
+inline "cic:/CoRN/ftc/Integral/h.con".
-inline cic:/CoRN/ftc/Integral/contH.var.
+inline "cic:/CoRN/ftc/Integral/contH.var".
-inline cic:/CoRN/ftc/Integral/linear_integral.con.
+inline "cic:/CoRN/ftc/Integral/linear_integral.con".
(* UNEXPORTED
Opaque nring.
*)
(* UNEXPORTED
Opaque nring.
*)
-inline cic:/CoRN/ftc/Integral/monotonous_integral.con.
+inline "cic:/CoRN/ftc/Integral/monotonous_integral.con".
(* UNEXPORTED
Transparent nring.
(* UNEXPORTED
Transparent nring.
-inline cic:/CoRN/ftc/Integral/F.var.
+inline "cic:/CoRN/ftc/Integral/F.var".
-inline cic:/CoRN/ftc/Integral/G.var.
+inline "cic:/CoRN/ftc/Integral/G.var".
-inline cic:/CoRN/ftc/Integral/contF.var.
+inline "cic:/CoRN/ftc/Integral/contF.var".
-inline cic:/CoRN/ftc/Integral/contG.var.
+inline "cic:/CoRN/ftc/Integral/contG.var".
(*#*
As corollaries we can calculate integrals of group operations applied to functions.
*)
(*#*
As corollaries we can calculate integrals of group operations applied to functions.
*)
-inline cic:/CoRN/ftc/Integral/integral_const.con.
+inline "cic:/CoRN/ftc/Integral/integral_const.con".
-inline cic:/CoRN/ftc/Integral/integral_minus.con.
+inline "cic:/CoRN/ftc/Integral/integral_minus.con".
-inline cic:/CoRN/ftc/Integral/integral_inv.con.
+inline "cic:/CoRN/ftc/Integral/integral_inv.con".
(*#*
We can also bound integrals by bounding the integrated functions.
*)
(*#*
We can also bound integrals by bounding the integrated functions.
*)
-inline cic:/CoRN/ftc/Integral/lb_integral.con.
+inline "cic:/CoRN/ftc/Integral/lb_integral.con".
-inline cic:/CoRN/ftc/Integral/ub_integral.con.
+inline "cic:/CoRN/ftc/Integral/ub_integral.con".
-inline cic:/CoRN/ftc/Integral/integral_leEq_norm.con.
+inline "cic:/CoRN/ftc/Integral/integral_leEq_norm.con".
(* UNEXPORTED
End Corollaries.
(* UNEXPORTED
End Corollaries.
-inline cic:/CoRN/ftc/Integral/F.var.
+inline "cic:/CoRN/ftc/Integral/F.var".
-inline cic:/CoRN/ftc/Integral/c.var.
+inline "cic:/CoRN/ftc/Integral/c.var".
-inline cic:/CoRN/ftc/Integral/Hac.var.
+inline "cic:/CoRN/ftc/Integral/Hac.var".
-inline cic:/CoRN/ftc/Integral/Hcb.var.
+inline "cic:/CoRN/ftc/Integral/Hcb.var".
-inline cic:/CoRN/ftc/Integral/Hab'.var.
+inline "cic:/CoRN/ftc/Integral/Hab'.var".
-inline cic:/CoRN/ftc/Integral/Hac'.var.
+inline "cic:/CoRN/ftc/Integral/Hac'.var".
-inline cic:/CoRN/ftc/Integral/Hcb'.var.
+inline "cic:/CoRN/ftc/Integral/Hcb'.var".
(* UNEXPORTED
Section Partition_Join.
(* UNEXPORTED
Section Partition_Join.
-inline cic:/CoRN/ftc/Integral/n.var.
+inline "cic:/CoRN/ftc/Integral/n.var".
-inline cic:/CoRN/ftc/Integral/m.var.
+inline "cic:/CoRN/ftc/Integral/m.var".
-inline cic:/CoRN/ftc/Integral/P.var.
+inline "cic:/CoRN/ftc/Integral/P.var".
-inline cic:/CoRN/ftc/Integral/Q.var.
+inline "cic:/CoRN/ftc/Integral/Q.var".
-inline cic:/CoRN/ftc/Integral/partition_join_aux.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_aux.con".
-inline cic:/CoRN/ftc/Integral/partition_join_fun.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_fun.con".
-inline cic:/CoRN/ftc/Integral/pjf_1.con.
+inline "cic:/CoRN/ftc/Integral/pjf_1.con".
-inline cic:/CoRN/ftc/Integral/pjf_2.con.
+inline "cic:/CoRN/ftc/Integral/pjf_2.con".
-inline cic:/CoRN/ftc/Integral/pjf_2'.con.
+inline "cic:/CoRN/ftc/Integral/pjf_2'.con".
-inline cic:/CoRN/ftc/Integral/pjf_3.con.
+inline "cic:/CoRN/ftc/Integral/pjf_3.con".
-inline cic:/CoRN/ftc/Integral/partition_join_prf1.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_prf1.con".
-inline cic:/CoRN/ftc/Integral/partition_join_prf2.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_prf2.con".
-inline cic:/CoRN/ftc/Integral/partition_join_start.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_start.con".
-inline cic:/CoRN/ftc/Integral/partition_join_finish.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_finish.con".
-inline cic:/CoRN/ftc/Integral/partition_join.con.
+inline "cic:/CoRN/ftc/Integral/partition_join.con".
-inline cic:/CoRN/ftc/Integral/fP.var.
+inline "cic:/CoRN/ftc/Integral/fP.var".
-inline cic:/CoRN/ftc/Integral/HfP.var.
+inline "cic:/CoRN/ftc/Integral/HfP.var".
-inline cic:/CoRN/ftc/Integral/HfP'.var.
+inline "cic:/CoRN/ftc/Integral/HfP'.var".
-inline cic:/CoRN/ftc/Integral/fQ.var.
+inline "cic:/CoRN/ftc/Integral/fQ.var".
-inline cic:/CoRN/ftc/Integral/HfQ.var.
+inline "cic:/CoRN/ftc/Integral/HfQ.var".
-inline cic:/CoRN/ftc/Integral/HfQ'.var.
+inline "cic:/CoRN/ftc/Integral/HfQ'.var".
-inline cic:/CoRN/ftc/Integral/partition_join_aux'.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_aux'.con".
-inline cic:/CoRN/ftc/Integral/partition_join_pts.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_pts.con".
-inline cic:/CoRN/ftc/Integral/pjp_1.con.
+inline "cic:/CoRN/ftc/Integral/pjp_1.con".
-inline cic:/CoRN/ftc/Integral/pjp_2.con.
+inline "cic:/CoRN/ftc/Integral/pjp_2.con".
-inline cic:/CoRN/ftc/Integral/pjp_3.con.
+inline "cic:/CoRN/ftc/Integral/pjp_3.con".
-inline cic:/CoRN/ftc/Integral/partition_join_Pts_in_partition.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_Pts_in_partition.con".
-inline cic:/CoRN/ftc/Integral/partition_join_Pts_wd.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_Pts_wd.con".
(* UNEXPORTED
Opaque partition_join.
(* UNEXPORTED
Opaque partition_join.
-inline cic:/CoRN/ftc/Integral/partition_join_Sum_lemma.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_Sum_lemma.con".
-inline cic:/CoRN/ftc/Integral/partition_join_mesh.con.
+inline "cic:/CoRN/ftc/Integral/partition_join_mesh.con".
(* UNEXPORTED
End Partition_Join.
(* UNEXPORTED
End Partition_Join.
Opaque Even_Partition.
*)
Opaque Even_Partition.
*)
-inline cic:/CoRN/ftc/Integral/integral_plus_integral.con.
+inline "cic:/CoRN/ftc/Integral/integral_plus_integral.con".
(* UNEXPORTED
End Integral_Sum.
(* UNEXPORTED
End Integral_Sum.
The following are simple consequences of this result and of previous ones.
*)
The following are simple consequences of this result and of previous ones.
*)
-inline cic:/CoRN/ftc/Integral/integral_less_norm.con.
+inline "cic:/CoRN/ftc/Integral/integral_less_norm.con".
-inline cic:/CoRN/ftc/Integral/integral_gt_zero.con.
+inline "cic:/CoRN/ftc/Integral/integral_gt_zero.con".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/IntervalFunct".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/IntervalFunct".
(* $Id: IntervalFunct.v,v 1.5 2004/04/08 15:28:06 lcf Exp $ *)
(* $Id: IntervalFunct.v,v 1.5 2004/04/08 15:28:06 lcf Exp $ *)
-(* INCLUDE
-PartFunEquality
-*)
+include "ftc/PartFunEquality.ma".
(* UNEXPORTED
Section Operations.
(* UNEXPORTED
Section Operations.
-inline cic:/CoRN/ftc/IntervalFunct/a.var.
+inline "cic:/CoRN/ftc/IntervalFunct/a.var".
-inline cic:/CoRN/ftc/IntervalFunct/b.var.
+inline "cic:/CoRN/ftc/IntervalFunct/b.var".
-inline cic:/CoRN/ftc/IntervalFunct/Hab.var.
+inline "cic:/CoRN/ftc/IntervalFunct/Hab.var".
-inline cic:/CoRN/ftc/IntervalFunct/I.con.
+inline "cic:/CoRN/ftc/IntervalFunct/I.con".
-inline cic:/CoRN/ftc/IntervalFunct/f.var.
+inline "cic:/CoRN/ftc/IntervalFunct/f.var".
-inline cic:/CoRN/ftc/IntervalFunct/g.var.
+inline "cic:/CoRN/ftc/IntervalFunct/g.var".
(* UNEXPORTED
Section Const.
(* UNEXPORTED
Section Const.
-inline cic:/CoRN/ftc/IntervalFunct/c.var.
+inline "cic:/CoRN/ftc/IntervalFunct/c.var".
-inline cic:/CoRN/ftc/IntervalFunct/IConst_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IConst_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IConst.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IConst.con".
(* UNEXPORTED
End Const.
*)
(* UNEXPORTED
End Const.
*)
-inline cic:/CoRN/ftc/IntervalFunct/IId_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IId_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IId.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IId.con".
(*#*
Next, we define addition, algebraic inverse, subtraction and product of functions.
*)
(*#*
Next, we define addition, algebraic inverse, subtraction and product of functions.
*)
-inline cic:/CoRN/ftc/IntervalFunct/IPlus_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IPlus_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IPlus.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IPlus.con".
-inline cic:/CoRN/ftc/IntervalFunct/IInv_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IInv_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IInv.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IInv.con".
-inline cic:/CoRN/ftc/IntervalFunct/IMinus_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IMinus_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IMinus.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IMinus.con".
-inline cic:/CoRN/ftc/IntervalFunct/IMult_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IMult_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IMult.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IMult.con".
(* UNEXPORTED
Section Nth_Power.
(* UNEXPORTED
Section Nth_Power.
Exponentiation to a natural power [n] is also useful.
*)
Exponentiation to a natural power [n] is also useful.
*)
-inline cic:/CoRN/ftc/IntervalFunct/n.var.
+inline "cic:/CoRN/ftc/IntervalFunct/n.var".
-inline cic:/CoRN/ftc/IntervalFunct/INth_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/INth_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/INth.con.
+inline "cic:/CoRN/ftc/IntervalFunct/INth.con".
(* UNEXPORTED
End Nth_Power.
(* UNEXPORTED
End Nth_Power.
-inline cic:/CoRN/ftc/IntervalFunct/Hg.var.
+inline "cic:/CoRN/ftc/IntervalFunct/Hg.var".
-inline cic:/CoRN/ftc/IntervalFunct/IRecip_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IRecip_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IRecip.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IRecip.con".
-inline cic:/CoRN/ftc/IntervalFunct/IDiv_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IDiv_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IDiv.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IDiv.con".
(* UNEXPORTED
End Recip_Div.
(* UNEXPORTED
End Recip_Div.
Absolute value will also be needed at some point.
*)
Absolute value will also be needed at some point.
*)
-inline cic:/CoRN/ftc/IntervalFunct/IAbs_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IAbs_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IAbs.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IAbs.con".
(* UNEXPORTED
End Operations.
(* UNEXPORTED
End Operations.
-inline cic:/CoRN/ftc/IntervalFunct/a.var.
+inline "cic:/CoRN/ftc/IntervalFunct/a.var".
-inline cic:/CoRN/ftc/IntervalFunct/b.var.
+inline "cic:/CoRN/ftc/IntervalFunct/b.var".
-inline cic:/CoRN/ftc/IntervalFunct/Hab.var.
+inline "cic:/CoRN/ftc/IntervalFunct/Hab.var".
-inline cic:/CoRN/ftc/IntervalFunct/I.con.
+inline "cic:/CoRN/ftc/IntervalFunct/I.con".
-inline cic:/CoRN/ftc/IntervalFunct/a'.var.
+inline "cic:/CoRN/ftc/IntervalFunct/a'.var".
-inline cic:/CoRN/ftc/IntervalFunct/b'.var.
+inline "cic:/CoRN/ftc/IntervalFunct/b'.var".
-inline cic:/CoRN/ftc/IntervalFunct/Hab'.var.
+inline "cic:/CoRN/ftc/IntervalFunct/Hab'.var".
-inline cic:/CoRN/ftc/IntervalFunct/I'.con.
+inline "cic:/CoRN/ftc/IntervalFunct/I'.con".
-inline cic:/CoRN/ftc/IntervalFunct/f.var.
+inline "cic:/CoRN/ftc/IntervalFunct/f.var".
-inline cic:/CoRN/ftc/IntervalFunct/g.var.
+inline "cic:/CoRN/ftc/IntervalFunct/g.var".
-inline cic:/CoRN/ftc/IntervalFunct/Hfg.var.
+inline "cic:/CoRN/ftc/IntervalFunct/Hfg.var".
-inline cic:/CoRN/ftc/IntervalFunct/IComp_strext.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IComp_strext.con".
-inline cic:/CoRN/ftc/IntervalFunct/IComp.con.
+inline "cic:/CoRN/ftc/IntervalFunct/IComp.con".
(* UNEXPORTED
End Composition.
(* UNEXPORTED
End Composition.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreFunSeries".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreFunSeries".
(* $Id: MoreFunSeries.v,v 1.4 2004/04/23 10:00:59 lcf Exp $ *)
(* $Id: MoreFunSeries.v,v 1.4 2004/04/23 10:00:59 lcf Exp $ *)
-(* INCLUDE
-FunctSeries
-*)
+include "ftc/FunctSeries.ma".
-(* INCLUDE
-MoreFunctions
-*)
+include "ftc/MoreFunctions.ma".
(*#* printing FSeries_Sum %\ensuremath{\sum_{\infty}}% #∑'<sub>∞</sub># *)
(*#* printing FSeries_Sum %\ensuremath{\sum_{\infty}}% #∑'<sub>∞</sub># *)
but the ones which do we simply adapt in the usual way.
*)
but the ones which do we simply adapt in the usual way.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/F.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/F.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contf.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contF.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_IR.con".
(*#*
The equivalences between these definitions still hold.
*)
(*#*
The equivalences between these definitions still hold.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq'_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq'_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_seq2_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_seq2_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_seq_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_seq_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
Limit is defined and works in the same way as before.
*)
Limit is defined and works in the same way as before.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contf.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
-inline cic:/CoRN/ftc/MoreFunSeries/conv.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv.var".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con".
(* UNEXPORTED
End More_Definitions.
(* UNEXPORTED
End More_Definitions.
Proofs are irrelevant as before---they just have to be present.
*)
Proofs are irrelevant as before---they just have to be present.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contf.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contf0.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contf0.var".
-inline cic:/CoRN/ftc/MoreFunSeries/F.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/F.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contF.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contF0.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contF0.var".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wd_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wd_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_wd_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_wd_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con".
(* UNEXPORTED
End Irrelevance_of_Proofs.
(* UNEXPORTED
End Irrelevance_of_Proofs.
Section More_Properties.
*)
Section More_Properties.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/g.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/g.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contf.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contf0.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contf0.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contg.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contg.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contg0.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contg0.var".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/F.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/F.var".
-inline cic:/CoRN/ftc/MoreFunSeries/G.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/G.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contF.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contF0.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contF0.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contG.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contG.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contG0.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contG0.var".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl'_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl'_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr'_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr'_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_cont_Lim_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_cont_Lim_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con".
(* UNEXPORTED
End More_Properties.
(* UNEXPORTED
End More_Properties.
Algebraic operations still work well.
*)
Algebraic operations still work well.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/g.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/g.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contf.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contg.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contg.var".
-inline cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_wd_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_wd_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/F.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/F.var".
-inline cic:/CoRN/ftc/MoreFunSeries/G.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/G.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contF.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contG.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contG.var".
-inline cic:/CoRN/ftc/MoreFunSeries/convF.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/convF.var".
-inline cic:/CoRN/ftc/MoreFunSeries/convG.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/convG.var".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus'_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus'_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus'_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus'_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con".
(* UNEXPORTED
End Algebraic_Properties.
(* UNEXPORTED
End Algebraic_Properties.
If we work with the limit function things fit in just as well.
*)
If we work with the limit function things fit in just as well.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/g.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/g.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contf.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contg.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contg.var".
-inline cic:/CoRN/ftc/MoreFunSeries/Hf.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/Hf.var".
-inline cic:/CoRN/ftc/MoreFunSeries/Hg.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/Hg.var".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_plus.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_plus.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_inv_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_inv_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_inv.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_inv.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_minus.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_minus.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con".
(* UNEXPORTED
End More_Algebraic_Properties.
(* UNEXPORTED
End More_Algebraic_Properties.
Finally, we define a mapping between sequences of real numbers and sequences of (constant) functions and prove that convergence is preserved.
*)
Finally, we define a mapping between sequences of real numbers and sequences of (constant) functions and prove that convergence is preserved.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/seq_to_funseq.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/seq_to_funseq.con".
-inline cic:/CoRN/ftc/MoreFunSeries/funseq_conv.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/funseq_conv.con".
(*#*
Another interesting fact: if a sequence of constant functions converges then it must converge to a constant function.
*)
(*#*
Another interesting fact: if a sequence of constant functions converges then it must converge to a constant function.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con".
Convergence is defined as expected---through convergence in every compact interval.
*)
Convergence is defined as expected---through convergence in every compact interval.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/H.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/H.var".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_series_inc_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_inc_IR.con".
(*#* Assume [h(x)] is the pointwise series of [f(x)] *)
(* begin hide *)
(*#* Assume [h(x)] is the pointwise series of [f(x)] *)
(* begin hide *)
-inline cic:/CoRN/ftc/MoreFunSeries/h.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/h.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_strext_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_strext_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con".
(* UNEXPORTED
End Series_Definitions.
(* UNEXPORTED
End Series_Definitions.
Section More_Series_Definitions.
*)
Section More_Series_Definitions.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
(*#*
Absolute convergence still exists.
*)
(*#*
Absolute convergence still exists.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con".
(* UNEXPORTED
End More_Series_Definitions.
(* UNEXPORTED
End More_Series_Definitions.
As before, any series converges to its sum.
*)
As before, any series converges to its sum.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con".
-inline cic:/CoRN/ftc/MoreFunSeries/convergent_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_inc.con".
-inline cic:/CoRN/ftc/MoreFunSeries/convergent_imp_Continuous.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_Continuous.con".
-inline cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con".
(* UNEXPORTED
End Convergence_Results.
(* UNEXPORTED
End Convergence_Results.
Convergence is well defined and preserved by operations.
*)
Convergence is well defined and preserved by operations.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_const_series_Sum_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_const_series_Sum_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/g.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/g.var".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/convF.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/convF.var".
-inline cic:/CoRN/ftc/MoreFunSeries/convG.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/convG.var".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_wd'.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_wd'.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus_conv.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus_conv.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv_conv.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv_conv.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus_conv.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus_conv.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con".
(*#*
%\begin{convention}% Let [c:IR] and [H:PartIR] be continuous in [J].
%\end{convention}%
*)
(*#*
%\begin{convention}% Let [c:IR] and [H:PartIR] be continuous in [J].
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunSeries/c.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/c.var".
-inline cic:/CoRN/ftc/MoreFunSeries/H.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/H.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contH.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contH.var".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con".
-inline cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con".
(* UNEXPORTED
End Operations.
(* UNEXPORTED
End Operations.
comparison test (in both versions) and the ratio test.
*)
comparison test (in both versions) and the ratio test.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/contF.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_comparison_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_comparison_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/abs_imp_conv_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/abs_imp_conv_IR.con".
-inline cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con".
(* UNEXPORTED
End Convergence_Criteria.
(* UNEXPORTED
End Convergence_Criteria.
position. This does not affect convergence or the sum of the series.
*)
position. This does not affect convergence or the sum of the series.
*)
-inline cic:/CoRN/ftc/MoreFunSeries/J.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
-inline cic:/CoRN/ftc/MoreFunSeries/f.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
-inline cic:/CoRN/ftc/MoreFunSeries/convF.var.
+inline "cic:/CoRN/ftc/MoreFunSeries/convF.var".
-inline cic:/CoRN/ftc/MoreFunSeries/insert_series.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/insert_series.con".
-inline cic:/CoRN/ftc/MoreFunSeries/insert_series_cont.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_cont.con".
-inline cic:/CoRN/ftc/MoreFunSeries/insert_series_sum_char.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum_char.con".
-inline cic:/CoRN/ftc/MoreFunSeries/insert_series_conv.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_conv.con".
-inline cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con.
+inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con".
(* UNEXPORTED
End Insert_Series.
(* UNEXPORTED
End Insert_Series.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreFunctions".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreFunctions".
(* $Id: MoreFunctions.v,v 1.5 2004/04/20 22:38:50 hinderer Exp $ *)
(*#* printing FNorm %\ensuremath{\|\cdot\|_{\infty}}% *)
(* $Id: MoreFunctions.v,v 1.5 2004/04/20 22:38:50 hinderer Exp $ *)
(*#* printing FNorm %\ensuremath{\|\cdot\|_{\infty}}% *)
-(* INCLUDE
-MoreIntervals
-*)
+include "ftc/MoreIntervals.ma".
(* UNEXPORTED
Opaque Min Max.
(* UNEXPORTED
Opaque Min Max.
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con".
(*#*
%\begin{convention}% Assume that [I] is compact and [F] is continuous in [I].
%\end{convention}%
*)
(*#*
%\begin{convention}% Assume that [I] is compact and [F] is continuous in [I].
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunctions/cI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/cI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/contF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
-inline cic:/CoRN/ftc/MoreFunctions/continuous_compact.con.
+inline "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con".
-inline cic:/CoRN/ftc/MoreFunctions/Hinc.var.
+inline "cic:/CoRN/ftc/MoreFunctions/Hinc.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_I_imp_tb_image.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_I_imp_tb_image.con".
-inline cic:/CoRN/ftc/MoreFunctions/FNorm.con.
+inline "cic:/CoRN/ftc/MoreFunctions/FNorm.con".
-inline cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con.
+inline "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con".
(* UNEXPORTED
End Basic_Results.
(* UNEXPORTED
End Basic_Results.
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con".
-inline cic:/CoRN/ftc/MoreFunctions/contF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
-inline cic:/CoRN/ftc/MoreFunctions/contG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contG.var".
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Continuous.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Continuous.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Continuous.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Continuous.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_const.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_const.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_id.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_id.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_plus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_inv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_inv.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_minus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_minus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_mult.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_mult.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_nth.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_nth.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_scal.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_scal.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con".
(* UNEXPORTED
End Other_Results.
(* UNEXPORTED
End Other_Results.
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/cI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/cI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/contF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
-inline cic:/CoRN/ftc/MoreFunctions/contG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contG.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_div.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con".
-inline cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con".
(* UNEXPORTED
End Corollaries.
(* UNEXPORTED
End Corollaries.
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con".
(*#*
%\begin{convention}% Assume [f] is a sequence of continuous functions.
%\end{convention}%
*)
(*#*
%\begin{convention}% Assume [f] is a sequence of continuous functions.
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunctions/f.var.
+inline "cic:/CoRN/ftc/MoreFunctions/f.var".
-inline cic:/CoRN/ftc/MoreFunctions/contF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con".
-inline cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con".
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/H.var.
+inline "cic:/CoRN/ftc/MoreFunctions/H.var".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_wdr.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_wdr.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_unique.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_unique.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc'.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc'.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con".
(* UNEXPORTED
End Basic_Properties.
(* UNEXPORTED
End Basic_Properties.
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
(*#*
%\begin{convention}% Assume that [F'] and [G'] are derivatives of [F] and [G], respectively, in [I].
%\end{convention}%
*)
(*#*
%\begin{convention}% Assume that [F'] and [G'] are derivatives of [F] and [G], respectively, in [I].
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/F'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F'.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/G'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G'.var".
-inline cic:/CoRN/ftc/MoreFunctions/derF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
-inline cic:/CoRN/ftc/MoreFunctions/derG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derG.var".
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_const.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_const.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_id.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_id.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_plus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_inv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_inv.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_minus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_minus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_mult.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_mult.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_scal.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_scal.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_nth.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_nth.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con".
(* UNEXPORTED
End More_Results.
(* UNEXPORTED
End More_Results.
Section More_Corollaries.
*)
Section More_Corollaries.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/F'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F'.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/G'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G'.var".
-inline cic:/CoRN/ftc/MoreFunctions/derF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
-inline cic:/CoRN/ftc/MoreFunctions/derG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derG.var".
-inline cic:/CoRN/ftc/MoreFunctions/Gbnd.var.
+inline "cic:/CoRN/ftc/MoreFunctions/Gbnd.var".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_div.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con".
(* UNEXPORTED
End More_Corollaries.
(* UNEXPORTED
End More_Corollaries.
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con".
-inline cic:/CoRN/ftc/MoreFunctions/f.var.
+inline "cic:/CoRN/ftc/MoreFunctions/f.var".
-inline cic:/CoRN/ftc/MoreFunctions/f'.var.
+inline "cic:/CoRN/ftc/MoreFunctions/f'.var".
-inline cic:/CoRN/ftc/MoreFunctions/derF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con".
(* UNEXPORTED
End More_Sums.
(* UNEXPORTED
End More_Sums.
Mutatis mutandis for differentiability.
*)
Mutatis mutandis for differentiability.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffG.var".
(*#*
%\begin{convention}% Assume [F] and [G] are differentiable in [I].
%\end{convention}%
*)
(*#*
%\begin{convention}% Assume [F] and [G] are differentiable in [I].
%\end{convention}%
*)
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_const.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_const.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_id.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_id.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_plus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_inv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_inv.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_minus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_minus.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_mult.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_mult.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_nth.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_nth.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con".
(* UNEXPORTED
End Diffble_Basic_Properties.
(* UNEXPORTED
End Diffble_Basic_Properties.
Section Diffble_Corollaries.
*)
Section Diffble_Corollaries.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/G.var.
+inline "cic:/CoRN/ftc/MoreFunctions/G.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffG.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffG.var".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_div.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_Sum0.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum0.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con".
(* UNEXPORTED
End Diffble_Corollaries.
(* UNEXPORTED
End Diffble_Corollaries.
Higher order derivatives pose more interesting problems. It turns out that it really becomes necessary to generalize our [n_deriv] operator to any interval.
*)
Higher order derivatives pose more interesting problems. It turns out that it really becomes necessary to generalize our [n_deriv] operator to any interval.
*)
-inline cic:/CoRN/ftc/MoreFunctions/I.var.
+inline "cic:/CoRN/ftc/MoreFunctions/I.var".
-inline cic:/CoRN/ftc/MoreFunctions/pI.var.
+inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
(* UNEXPORTED
Section Definitions.
(* UNEXPORTED
Section Definitions.
-inline cic:/CoRN/ftc/MoreFunctions/n.var.
+inline "cic:/CoRN/ftc/MoreFunctions/n.var".
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_char
- (* begin hide *).con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_char
+ (* begin hide *).con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_strext.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_strext.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
All the usual results hold.
*)
All the usual results hold.
*)
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_n_wd.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_n_wd.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdr.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdr.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdl.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdl.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_unique.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_unique.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble.con".
-inline cic:/CoRN/ftc/MoreFunctions/le_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/le_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_le.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_le.con".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_inc.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc'.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc'.con".
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con".
(* UNEXPORTED
End Basic_Results.
(* UNEXPORTED
End Basic_Results.
Some new results hold, too:
*)
Some new results hold, too:
*)
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_Feq.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_Feq.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_lemma.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_lemma.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_S.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_S.con".
-inline cic:/CoRN/ftc/MoreFunctions/N_Deriv_plus.con.
+inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_plus.con".
(*#*
Some useful characterization results.
*)
(*#*
Some useful characterization results.
*)
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con".
(* UNEXPORTED
End More_Results.
(* UNEXPORTED
End More_Results.
As a special case we get a differentiation operator%\ldots%#...#
*)
As a special case we get a differentiation operator%\ldots%#...#
*)
-inline cic:/CoRN/ftc/MoreFunctions/F.var.
+inline "cic:/CoRN/ftc/MoreFunctions/F.var".
-inline cic:/CoRN/ftc/MoreFunctions/diffF.var.
+inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
-inline cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con".
-inline cic:/CoRN/ftc/MoreFunctions/Deriv.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Deriv.con".
(* UNEXPORTED
End Derivating_Diffble.
(* UNEXPORTED
End Derivating_Diffble.
%\ldots%#...# for which the expected property also holds.
*)
%\ldots%#...# for which the expected property also holds.
*)
-inline cic:/CoRN/ftc/MoreFunctions/Deriv_lemma.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Deriv_lemma.con".
(*#*
Some more interesting properties.
*)
(*#*
Some more interesting properties.
*)
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_1.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_1.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_chain.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_chain.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con".
-inline cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con.
+inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con".
(* UNEXPORTED
End Corollaries.
(* UNEXPORTED
End Corollaries.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreIntegrals".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreIntegrals".
(* $Id: MoreIntegrals.v,v 1.6 2004/04/23 10:00:59 lcf Exp $ *)
(* $Id: MoreIntegrals.v,v 1.6 2004/04/23 10:00:59 lcf Exp $ *)
-(* INCLUDE
-Integral
-*)
+include "ftc/Integral.ma".
-(* INCLUDE
-MoreFunctions
-*)
+include "ftc/MoreFunctions.ma".
(* UNEXPORTED
Section Lemmas.
(* UNEXPORTED
Section Lemmas.
Before we define the new integral we need to some trivial interval inclusions.
*)
Before we define the new integral we need to some trivial interval inclusions.
*)
-inline cic:/CoRN/ftc/MoreIntegrals/a.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
-inline cic:/CoRN/ftc/MoreIntegrals/b.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hab.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
-inline cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con".
-inline cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_rht.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_rht.con".
(* UNEXPORTED
End Lemmas.
(* UNEXPORTED
End Lemmas.
-inline cic:/CoRN/ftc/MoreIntegrals/a.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
-inline cic:/CoRN/ftc/MoreIntegrals/b.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hab.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
-inline cic:/CoRN/ftc/MoreIntegrals/F.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/F.var".
-inline cic:/CoRN/ftc/MoreIntegrals/HF.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/HF.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_inc2.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_inc2.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_integral.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_integral.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
new ones, too. We begin with (strong) extensionality.
*)
new ones, too. We begin with (strong) extensionality.
*)
-inline cic:/CoRN/ftc/MoreIntegrals/a.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
-inline cic:/CoRN/ftc/MoreIntegrals/b.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hab.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
-inline cic:/CoRN/ftc/MoreIntegrals/F.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/F.var".
-inline cic:/CoRN/ftc/MoreIntegrals/G.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/G.var".
-inline cic:/CoRN/ftc/MoreIntegrals/contF.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/contF.var".
-inline cic:/CoRN/ftc/MoreIntegrals/contG.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/contG.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_strext'.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_strext'.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_wd.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_wd.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_wd'.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_wd'.con".
(*#*
The integral is a linear operator.
*)
(*#*
The integral is a linear operator.
*)
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_const.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_const.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_comm_scal.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_comm_scal.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_plus.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_plus.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_inv.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_inv.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_minus.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_minus.con".
-inline cic:/CoRN/ftc/MoreIntegrals/linear_Integral.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/linear_Integral.con".
(*#*
If the endpoints are equal then the integral vanishes.
*)
(*#*
If the endpoints are equal then the integral vanishes.
*)
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_empty.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_empty.con".
(*#*
And the norm provides an upper bound for the absolute value of the integral.
*)
(*#*
And the norm provides an upper bound for the absolute value of the integral.
*)
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con".
(* UNEXPORTED
End Properties_of_Integral.
(* UNEXPORTED
End Properties_of_Integral.
Two other ways of stating the addition law for domains.
*)
Two other ways of stating the addition law for domains.
*)
-inline cic:/CoRN/ftc/MoreIntegrals/integral_plus_Integral.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/integral_plus_Integral.con".
-inline cic:/CoRN/ftc/MoreIntegrals/integral_plus_integral'.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/integral_plus_integral'.con".
(*#*
And now we can prove the addition law for domains with our general operator.
(*#*
And now we can prove the addition law for domains with our general operator.
-inline cic:/CoRN/ftc/MoreIntegrals/a.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
-inline cic:/CoRN/ftc/MoreIntegrals/b.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
-inline cic:/CoRN/ftc/MoreIntegrals/c.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/c.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hab'.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hab'.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hac'.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hac'.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hcb'.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hcb'.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Habc'.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Habc'.var".
-inline cic:/CoRN/ftc/MoreIntegrals/F.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/F.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hab.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hac.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hac.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hcb.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hcb.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Habc.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Habc.var".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/MoreIntegrals/le_abc_ab.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_ab.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_abc_ac.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_ac.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_abc_cb.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_cb.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_abc_a.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_a.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_abc_b.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_b.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_abc_c.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_c.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_ab_a.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_ab_a.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_cb_c.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_cb_c.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_ac_a.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_ac_a.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_ab_b.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_ab_b.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_cb_b.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_cb_b.con".
-inline cic:/CoRN/ftc/MoreIntegrals/le_ac_c.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/le_ac_c.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Habc_abc.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Habc_abc.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Habc_ab.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Habc_ab.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Habc_ac.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Habc_ac.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Habc_cb.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Habc_cb.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Habc_a.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Habc_a.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Habc_b.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Habc_b.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Habc_c.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Habc_c.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_plus_Integral.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_plus_Integral.con".
(*#*
Notice that, unlike in the classical case, an extra hypothesis (the
(*#*
Notice that, unlike in the classical case, an extra hypothesis (the
-inline cic:/CoRN/ftc/MoreIntegrals/a.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
-inline cic:/CoRN/ftc/MoreIntegrals/b.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
-inline cic:/CoRN/ftc/MoreIntegrals/Hab.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
-inline cic:/CoRN/ftc/MoreIntegrals/F.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/F.var".
-inline cic:/CoRN/ftc/MoreIntegrals/contF.var.
+inline "cic:/CoRN/ftc/MoreIntegrals/contF.var".
(*#* As a corollary, we get the following rule: *)
(*#* As a corollary, we get the following rule: *)
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_op.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_op.con".
(*#* Finally, some miscellaneous results: *)
(*#* Finally, some miscellaneous results: *)
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_less_norm.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_less_norm.con".
-inline cic:/CoRN/ftc/MoreIntegrals/ub_Integral.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/ub_Integral.con".
(* UNEXPORTED
End Corollaries.
*)
(* UNEXPORTED
End Corollaries.
*)
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_ap_zero.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_ap_zero.con".
-inline cic:/CoRN/ftc/MoreIntegrals/Integral_eq_zero.con.
+inline "cic:/CoRN/ftc/MoreIntegrals/Integral_eq_zero.con".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreIntervals".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreIntervals".
(* $Id: MoreIntervals.v,v 1.6 2004/04/23 10:00:59 lcf Exp $ *)
(* $Id: MoreIntervals.v,v 1.6 2004/04/23 10:00:59 lcf Exp $ *)
-(* INCLUDE
-NthDerivative
-*)
+include "ftc/NthDerivative.ma".
(* UNEXPORTED
Opaque Min Max.
(* UNEXPORTED
Opaque Min Max.
-inline cic:/CoRN/ftc/MoreIntervals/interval.ind.
+inline "cic:/CoRN/ftc/MoreIntervals/interval.ind".
(*#*
To each interval a predicate (set) is assigned by the following map:
*)
(*#*
To each interval a predicate (set) is assigned by the following map:
*)
-inline cic:/CoRN/ftc/MoreIntervals/iprop.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop.con".
+coercion "cic:/matita/CoRN-Decl/ftc/MoreIntervals/iprop.con" 0 (* compounds *).
+
finite and compact in the obvious way.
*)
finite and compact in the obvious way.
*)
-inline cic:/CoRN/ftc/MoreIntervals/nonvoid.con.
+inline "cic:/CoRN/ftc/MoreIntervals/nonvoid.con".
-inline cic:/CoRN/ftc/MoreIntervals/proper.con.
+inline "cic:/CoRN/ftc/MoreIntervals/proper.con".
-inline cic:/CoRN/ftc/MoreIntervals/finite.con.
+inline "cic:/CoRN/ftc/MoreIntervals/finite.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_.con".
(*#* Finite intervals have a left end and a right end. *)
(*#* Finite intervals have a left end and a right end. *)
-inline cic:/CoRN/ftc/MoreIntervals/left_end.con.
+inline "cic:/CoRN/ftc/MoreIntervals/left_end.con".
-inline cic:/CoRN/ftc/MoreIntervals/right_end.con.
+inline "cic:/CoRN/ftc/MoreIntervals/right_end.con".
(*#*
Some trivia: compact intervals are finite; proper intervals are nonvoid; an interval is nonvoid iff it contains some point.
*)
(*#*
Some trivia: compact intervals are finite; proper intervals are nonvoid; an interval is nonvoid iff it contains some point.
*)
-inline cic:/CoRN/ftc/MoreIntervals/compact_finite.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_finite.con".
-inline cic:/CoRN/ftc/MoreIntervals/proper_nonvoid.con.
+inline "cic:/CoRN/ftc/MoreIntervals/proper_nonvoid.con".
-inline cic:/CoRN/ftc/MoreIntervals/nonvoid_point.con.
+inline "cic:/CoRN/ftc/MoreIntervals/nonvoid_point.con".
-inline cic:/CoRN/ftc/MoreIntervals/nonvoid_char.con.
+inline "cic:/CoRN/ftc/MoreIntervals/nonvoid_char.con".
(*#*
For practical reasons it helps to define left end and right end of compact intervals.
*)
(*#*
For practical reasons it helps to define left end and right end of compact intervals.
*)
-inline cic:/CoRN/ftc/MoreIntervals/Lend.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Lend.con".
-inline cic:/CoRN/ftc/MoreIntervals/Rend.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Rend.con".
(*#* In a compact interval, the left end is always less than or equal
to the right end.
*)
(*#* In a compact interval, the left end is always less than or equal
to the right end.
*)
-inline cic:/CoRN/ftc/MoreIntervals/Lend_leEq_Rend.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Lend_leEq_Rend.con".
(*#*
Some nice characterizations of inclusion:
*)
(*#*
Some nice characterizations of inclusion:
*)
-inline cic:/CoRN/ftc/MoreIntervals/compact_included.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_included.con".
-inline cic:/CoRN/ftc/MoreIntervals/included_interval'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/included_interval'.con".
-inline cic:/CoRN/ftc/MoreIntervals/included_interval.con.
+inline "cic:/CoRN/ftc/MoreIntervals/included_interval.con".
(*#*
A weirder inclusion result.
*)
(*#*
A weirder inclusion result.
*)
-inline cic:/CoRN/ftc/MoreIntervals/included3_interval.con.
+inline "cic:/CoRN/ftc/MoreIntervals/included3_interval.con".
(*#*
Finally, all intervals are characterized by well defined predicates.
*)
(*#*
Finally, all intervals are characterized by well defined predicates.
*)
-inline cic:/CoRN/ftc/MoreIntervals/iprop_wd.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_wd.con".
(* UNEXPORTED
End Intervals.
(* UNEXPORTED
End Intervals.
-inline cic:/CoRN/ftc/MoreIntervals/P.var.
+inline "cic:/CoRN/ftc/MoreIntervals/P.var".
-inline cic:/CoRN/ftc/MoreIntervals/wdP.var.
+inline "cic:/CoRN/ftc/MoreIntervals/wdP.var".
-inline cic:/CoRN/ftc/MoreIntervals/x.var.
+inline "cic:/CoRN/ftc/MoreIntervals/x.var".
-inline cic:/CoRN/ftc/MoreIntervals/Hx.var.
+inline "cic:/CoRN/ftc/MoreIntervals/Hx.var".
-inline cic:/CoRN/ftc/MoreIntervals/compact_single.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_single.con".
(*#*
This interval contains [x] and only (elements equal to) [x]; furthermore, for every (well-defined) [P], if $x\in P$#x∈P# then $[x,x]\subseteq P$#[x,x]⊆P#.
*)
(*#*
This interval contains [x] and only (elements equal to) [x]; furthermore, for every (well-defined) [P], if $x\in P$#x∈P# then $[x,x]\subseteq P$#[x,x]⊆P#.
*)
-inline cic:/CoRN/ftc/MoreIntervals/compact_single_prop.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_single_prop.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_single_pt.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_single_pt.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_single_inc.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_single_inc.con".
(* UNEXPORTED
End Single_Compact_Interval.
(* UNEXPORTED
End Single_Compact_Interval.
The special case of intervals is worth singling out, as one of the hypothesis becomes a theorem.
*)
The special case of intervals is worth singling out, as one of the hypothesis becomes a theorem.
*)
-inline cic:/CoRN/ftc/MoreIntervals/compact_single_iprop.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_single_iprop.con".
(*#*
Now for more interesting and important results.
(*#*
Now for more interesting and important results.
-inline cic:/CoRN/ftc/MoreIntervals/cip1'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip1'.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip1''.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip1''.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip1'''.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip1'''.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip1''''.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip1''''.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip2.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip2.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip2'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip2'.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip2''.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip2''.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip2'''.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip2'''.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip3.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip3.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip3'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip3'.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip3''.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip3''.con".
-inline cic:/CoRN/ftc/MoreIntervals/cip3'''.con.
+inline "cic:/CoRN/ftc/MoreIntervals/cip3'''.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_in_interval.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval.con".
-inline cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval.con.
+inline "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval.con".
-inline cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval'.con".
-inline cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval.con.
+inline "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval'.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc1.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc1.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc2.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc2.con".
(*#*
If [x [=] y] then the construction yields the same interval whether we
(*#*
If [x [=] y] then the construction yields the same interval whether we
definition rather than as an existential formula.
*)
definition rather than as an existential formula.
*)
-inline cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd1.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd1.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd2.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd2.con".
(*#*
We can make an analogous construction for two points.
*)
(*#*
We can make an analogous construction for two points.
*)
-inline cic:/CoRN/ftc/MoreIntervals/compact_in_interval2.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval2.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval2.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval2.con".
-inline cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2.con.
+inline "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2.con".
-inline cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2'.con".
-inline cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval2.con.
+inline "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval2.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x'.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y'.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc1.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc1.con".
-inline cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc2.con.
+inline "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc2.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_lft.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_lft.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_lft.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_lft.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_rht.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_rht.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_rht.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_rht.con".
(* UNEXPORTED
End Proper_Compact_with_One_or_Two_Points.
(* UNEXPORTED
End Proper_Compact_with_One_or_Two_Points.
Compact intervals are exactly compact intervals(!).
*)
Compact intervals are exactly compact intervals(!).
*)
-inline cic:/CoRN/ftc/MoreIntervals/interval_compact_inc.con.
+inline "cic:/CoRN/ftc/MoreIntervals/interval_compact_inc.con".
-inline cic:/CoRN/ftc/MoreIntervals/compact_interval_inc.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_interval_inc.con".
(*#*
A generalization of the previous results: if $[a,b]\subseteq J$#[a,b]⊆J#
(*#*
A generalization of the previous results: if $[a,b]\subseteq J$#[a,b]⊆J#
$[a,b]\subseteq[a',b']\subseteq J$#[a,b]⊆[a',b']⊆J#.
*)
$[a,b]\subseteq[a',b']\subseteq J$#[a,b]⊆[a',b']⊆J#.
*)
-inline cic:/CoRN/ftc/MoreIntervals/compact_proper_in_interval.con.
+inline "cic:/CoRN/ftc/MoreIntervals/compact_proper_in_interval.con".
(* UNEXPORTED
End Compact_Constructions.
(* UNEXPORTED
End Compact_Constructions.
-inline cic:/CoRN/ftc/MoreIntervals/n.var.
+inline "cic:/CoRN/ftc/MoreIntervals/n.var".
-inline cic:/CoRN/ftc/MoreIntervals/I.var.
+inline "cic:/CoRN/ftc/MoreIntervals/I.var".
-inline cic:/CoRN/ftc/MoreIntervals/Continuous.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Continuous.con".
-inline cic:/CoRN/ftc/MoreIntervals/Derivative.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Derivative.con".
-inline cic:/CoRN/ftc/MoreIntervals/Diffble.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Diffble.con".
-inline cic:/CoRN/ftc/MoreIntervals/Derivative_n.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Derivative_n.con".
-inline cic:/CoRN/ftc/MoreIntervals/Diffble_n.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Diffble_n.con".
(* UNEXPORTED
End Functions.
(* UNEXPORTED
End Functions.
In the case of compact intervals, this definitions collapse to the old ones.
*)
In the case of compact intervals, this definitions collapse to the old ones.
*)
-inline cic:/CoRN/ftc/MoreIntervals/Continuous_Int.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Continuous_Int.con".
-inline cic:/CoRN/ftc/MoreIntervals/Int_Continuous.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Int_Continuous.con".
-inline cic:/CoRN/ftc/MoreIntervals/Derivative_Int.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Derivative_Int.con".
-inline cic:/CoRN/ftc/MoreIntervals/Int_Derivative.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Int_Derivative.con".
-inline cic:/CoRN/ftc/MoreIntervals/Diffble_Int.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Diffble_Int.con".
-inline cic:/CoRN/ftc/MoreIntervals/Int_Diffble.con.
+inline "cic:/CoRN/ftc/MoreIntervals/Int_Diffble.con".
(* UNEXPORTED
End Reflexivity_Properties.
(* UNEXPORTED
End Reflexivity_Properties.
Interestingly, inclusion and equality in an interval are also characterizable in a similar way:
*)
Interestingly, inclusion and equality in an interval are also characterizable in a similar way:
*)
-inline cic:/CoRN/ftc/MoreIntervals/included_imp_inc.con.
+inline "cic:/CoRN/ftc/MoreIntervals/included_imp_inc.con".
-inline cic:/CoRN/ftc/MoreIntervals/included_Feq''.con.
+inline "cic:/CoRN/ftc/MoreIntervals/included_Feq''.con".
-inline cic:/CoRN/ftc/MoreIntervals/included_Feq'.con.
+inline "cic:/CoRN/ftc/MoreIntervals/included_Feq'.con".
(* UNEXPORTED
End Lemmas.
(* UNEXPORTED
End Lemmas.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/NthDerivative".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/NthDerivative".
(* $Id: NthDerivative.v,v 1.5 2004/04/20 22:38:50 hinderer Exp $ *)
(* $Id: NthDerivative.v,v 1.5 2004/04/20 22:38:50 hinderer Exp $ *)
-(* INCLUDE
-Differentiability
-*)
+include "ftc/Differentiability.ma".
(* UNEXPORTED
Section Nth_Derivative.
(* UNEXPORTED
Section Nth_Derivative.
We first define what we mean by the derivative of order [n] of a function.
*)
We first define what we mean by the derivative of order [n] of a function.
*)
-inline cic:/CoRN/ftc/NthDerivative/a.var.
+inline "cic:/CoRN/ftc/NthDerivative/a.var".
-inline cic:/CoRN/ftc/NthDerivative/b.var.
+inline "cic:/CoRN/ftc/NthDerivative/b.var".
-inline cic:/CoRN/ftc/NthDerivative/Hab'.var.
+inline "cic:/CoRN/ftc/NthDerivative/Hab'.var".
-inline cic:/CoRN/ftc/NthDerivative/Hab.con.
+inline "cic:/CoRN/ftc/NthDerivative/Hab.con".
-inline cic:/CoRN/ftc/NthDerivative/I.con.
+inline "cic:/CoRN/ftc/NthDerivative/I.con".
-inline cic:/CoRN/ftc/NthDerivative/Derivative_I_n.con.
+inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n.con".
(*#*
Unlike first order differentiability, for our definition to be
(*#*
Unlike first order differentiability, for our definition to be
[Derivative_I_n] relation.
*)
[Derivative_I_n] relation.
*)
-inline cic:/CoRN/ftc/NthDerivative/Diffble_I_n.con.
+inline "cic:/CoRN/ftc/NthDerivative/Diffble_I_n.con".
(* UNEXPORTED
End Nth_Derivative.
(* UNEXPORTED
End Nth_Derivative.
These are the expected extensionality and uniqueness results.
*)
These are the expected extensionality and uniqueness results.
*)
-inline cic:/CoRN/ftc/NthDerivative/a.var.
+inline "cic:/CoRN/ftc/NthDerivative/a.var".
-inline cic:/CoRN/ftc/NthDerivative/b.var.
+inline "cic:/CoRN/ftc/NthDerivative/b.var".
-inline cic:/CoRN/ftc/NthDerivative/Hab'.var.
+inline "cic:/CoRN/ftc/NthDerivative/Hab'.var".
-inline cic:/CoRN/ftc/NthDerivative/Hab.con.
+inline "cic:/CoRN/ftc/NthDerivative/Hab.con".
-inline cic:/CoRN/ftc/NthDerivative/I.con.
+inline "cic:/CoRN/ftc/NthDerivative/I.con".
-inline cic:/CoRN/ftc/NthDerivative/Diffble_I_n_wd.con.
+inline "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_wd.con".
-inline cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdr.con.
+inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdr.con".
-inline cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdl.con.
+inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdl.con".
-inline cic:/CoRN/ftc/NthDerivative/Derivative_I_n_unique.con.
+inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_unique.con".
(* UNEXPORTED
End Trivia.
(* UNEXPORTED
End Trivia.
definition of [Diffble_I_n].
*)
definition of [Diffble_I_n].
*)
-inline cic:/CoRN/ftc/NthDerivative/a.var.
+inline "cic:/CoRN/ftc/NthDerivative/a.var".
-inline cic:/CoRN/ftc/NthDerivative/b.var.
+inline "cic:/CoRN/ftc/NthDerivative/b.var".
-inline cic:/CoRN/ftc/NthDerivative/Hab'.var.
+inline "cic:/CoRN/ftc/NthDerivative/Hab'.var".
-inline cic:/CoRN/ftc/NthDerivative/Hab.con.
+inline "cic:/CoRN/ftc/NthDerivative/Hab.con".
-inline cic:/CoRN/ftc/NthDerivative/I.con.
+inline "cic:/CoRN/ftc/NthDerivative/I.con".
We begin by showing that having a higher order derivative implies being differentiable.
*)
We begin by showing that having a higher order derivative implies being differentiable.
*)
-inline cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_diffble.con.
+inline "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_diffble.con".
-inline cic:/CoRN/ftc/NthDerivative/deriv_n_imp_diffble.con.
+inline "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_diffble.con".
(*#*
If a function is [n] times differentiable then it is also [m] times differentiable for every [m] less or equal than [n].
*)
(*#*
If a function is [n] times differentiable then it is also [m] times differentiable for every [m] less or equal than [n].
*)
-inline cic:/CoRN/ftc/NthDerivative/le_imp_Diffble_I.con.
+inline "cic:/CoRN/ftc/NthDerivative/le_imp_Diffble_I.con".
(*#*
The next result consolidates our intuition that a function is [n]
(*#*
The next result consolidates our intuition that a function is [n]
-inline cic:/CoRN/ftc/NthDerivative/Diffble_I_imp_le.con.
+inline "cic:/CoRN/ftc/NthDerivative/Diffble_I_imp_le.con".
(*#*
As expected, an [n] times differentiable in [[a,b]] function must be
defined in that interval.
*)
(*#*
As expected, an [n] times differentiable in [[a,b]] function must be
defined in that interval.
*)
-inline cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_inc.con.
+inline "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_inc.con".
(*#*
Also, the notions of derivative and differentiability are related as expected.
*)
(*#*
Also, the notions of derivative and differentiability are related as expected.
*)
-inline cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_deriv_n.con.
+inline "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_deriv_n.con".
-inline cic:/CoRN/ftc/NthDerivative/deriv_n_imp_Diffble_I_n.con.
+inline "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_Diffble_I_n.con".
(*#*
From this we can prove that if [F] has an nth order derivative in
[[a,b]] then both [F] and its derivative are defined in that interval.
*)
(*#*
From this we can prove that if [F] has an nth order derivative in
[[a,b]] then both [F] and its derivative are defined in that interval.
*)
-inline cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc.con.
+inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc.con".
-inline cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc'.con.
+inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc'.con".
(* UNEXPORTED
Section aux.
(* UNEXPORTED
Section aux.
-inline cic:/CoRN/ftc/NthDerivative/F.var.
+inline "cic:/CoRN/ftc/NthDerivative/F.var".
-inline cic:/CoRN/ftc/NthDerivative/diffF.var.
+inline "cic:/CoRN/ftc/NthDerivative/diffF.var".
-inline cic:/CoRN/ftc/NthDerivative/diffFn.var.
+inline "cic:/CoRN/ftc/NthDerivative/diffFn.var".
-inline cic:/CoRN/ftc/NthDerivative/deriv_1_deriv.con.
+inline "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv.con".
-inline cic:/CoRN/ftc/NthDerivative/deriv_1_deriv'.con.
+inline "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv'.con".
As usual, nth order derivability is preserved by shrinking the interval.
*)
As usual, nth order derivability is preserved by shrinking the interval.
*)
-inline cic:/CoRN/ftc/NthDerivative/included_imp_deriv_n.con.
+inline "cic:/CoRN/ftc/NthDerivative/included_imp_deriv_n.con".
-inline cic:/CoRN/ftc/NthDerivative/included_imp_diffble_n.con.
+inline "cic:/CoRN/ftc/NthDerivative/included_imp_diffble_n.con".
(*#*
And finally we have an addition rule for the order of the derivative.
*)
(*#*
And finally we have an addition rule for the order of the derivative.
*)
-inline cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con.
+inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con".
(* UNEXPORTED
End Basic_Results.
(* UNEXPORTED
End Basic_Results.
-inline cic:/CoRN/ftc/NthDerivative/a.var.
+inline "cic:/CoRN/ftc/NthDerivative/a.var".
-inline cic:/CoRN/ftc/NthDerivative/b.var.
+inline "cic:/CoRN/ftc/NthDerivative/b.var".
-inline cic:/CoRN/ftc/NthDerivative/Hab'.var.
+inline "cic:/CoRN/ftc/NthDerivative/Hab'.var".
-inline cic:/CoRN/ftc/NthDerivative/Hab.con.
+inline "cic:/CoRN/ftc/NthDerivative/Hab.con".
-inline cic:/CoRN/ftc/NthDerivative/I.con.
+inline "cic:/CoRN/ftc/NthDerivative/I.con".
as an existential quantification of the nth derivative relation.
*)
as an existential quantification of the nth derivative relation.
*)
-inline cic:/CoRN/ftc/NthDerivative/n_deriv_I.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_deriv_I.con".
(*#*
This operator is well defined and works as expected.
*)
(*#*
This operator is well defined and works as expected.
*)
-inline cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd.con".
-inline cic:/CoRN/ftc/NthDerivative/n_deriv_lemma.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_deriv_lemma.con".
-inline cic:/CoRN/ftc/NthDerivative/n_deriv_inc.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_deriv_inc.con".
-inline cic:/CoRN/ftc/NthDerivative/n_deriv_inc'.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_deriv_inc'.con".
(*#*
Some basic properties of this operation.
*)
(*#*
Some basic properties of this operation.
*)
-inline cic:/CoRN/ftc/NthDerivative/n_Sn_deriv.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_Sn_deriv.con".
-inline cic:/CoRN/ftc/NthDerivative/n_deriv_plus.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_deriv_plus.con".
(* UNEXPORTED
End More_Results.
(* UNEXPORTED
End More_Results.
Some not so basic properties of this operation (needed in rather specific situations).
*)
Some not so basic properties of this operation (needed in rather specific situations).
*)
-inline cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd'.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd'.con".
-inline cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd''.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd''.con".
-inline cic:/CoRN/ftc/NthDerivative/n_deriv_I_strext'.con.
+inline "cic:/CoRN/ftc/NthDerivative/n_deriv_I_strext'.con".
(* UNEXPORTED
End More_on_n_deriv.
(* UNEXPORTED
End More_on_n_deriv.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/PartFunEquality".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/PartFunEquality".
(* $Id: PartFunEquality.v,v 1.8 2004/04/23 10:00:59 lcf Exp $ *)
(*#* printing Feq %\ensuremath{\approx}% #≈# *)
(* $Id: PartFunEquality.v,v 1.8 2004/04/23 10:00:59 lcf Exp $ *)
(*#* printing Feq %\ensuremath{\approx}% #≈# *)
-(* INCLUDE
-Intervals
-*)
+include "reals/Intervals.ma".
-(* INCLUDE
-DiffTactics1
-*)
+include "tactics/DiffTactics1.ma".
(* UNEXPORTED
Section Definitions.
(* UNEXPORTED
Section Definitions.
definition makes this possible.
*)
definition makes this possible.
*)
-inline cic:/CoRN/ftc/PartFunEquality/subset.con.
+inline "cic:/CoRN/ftc/PartFunEquality/subset.con".
(*#*
The core of our work will revolve around the following fundamental
(*#*
The core of our work will revolve around the following fundamental
with proving the main properties of this equality relation.
*)
with proving the main properties of this equality relation.
*)
-inline cic:/CoRN/ftc/PartFunEquality/Feq.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq.con".
(*#*
Notice that, because the quantification over the proofs is universal,
(*#*
Notice that, because the quantification over the proofs is universal,
-inline cic:/CoRN/ftc/PartFunEquality/I.var.
+inline "cic:/CoRN/ftc/PartFunEquality/I.var".
-inline cic:/CoRN/ftc/PartFunEquality/F.var.
+inline "cic:/CoRN/ftc/PartFunEquality/F.var".
-inline cic:/CoRN/ftc/PartFunEquality/G.var.
+inline "cic:/CoRN/ftc/PartFunEquality/G.var".
-inline cic:/CoRN/ftc/PartFunEquality/P.con.
+inline "cic:/CoRN/ftc/PartFunEquality/P.con".
-inline cic:/CoRN/ftc/PartFunEquality/Q.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Q.con".
-inline cic:/CoRN/ftc/PartFunEquality/R.var.
+inline "cic:/CoRN/ftc/PartFunEquality/R.var".
(*#*
We start with two lemmas which make it much easier to prove and use
this definition:
*)
(*#*
We start with two lemmas which make it much easier to prove and use
this definition:
*)
-inline cic:/CoRN/ftc/PartFunEquality/eq_imp_Feq.con.
+inline "cic:/CoRN/ftc/PartFunEquality/eq_imp_Feq.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con".
-inline cic:/CoRN/ftc/PartFunEquality/included_IR.con.
+inline "cic:/CoRN/ftc/PartFunEquality/included_IR.con".
(* UNEXPORTED
End Equality_Results.
(* UNEXPORTED
End Equality_Results.
If two function coincide on a given subset then they coincide in any smaller subset.
*)
If two function coincide on a given subset then they coincide in any smaller subset.
*)
-inline cic:/CoRN/ftc/PartFunEquality/included_Feq.con.
+inline "cic:/CoRN/ftc/PartFunEquality/included_Feq.con".
(* UNEXPORTED
End Some_More.
(* UNEXPORTED
End Some_More.
-inline cic:/CoRN/ftc/PartFunEquality/I.var.
+inline "cic:/CoRN/ftc/PartFunEquality/I.var".
-inline cic:/CoRN/ftc/PartFunEquality/F.var.
+inline "cic:/CoRN/ftc/PartFunEquality/F.var".
-inline cic:/CoRN/ftc/PartFunEquality/P.con.
+inline "cic:/CoRN/ftc/PartFunEquality/P.con".
-inline cic:/CoRN/ftc/PartFunEquality/bnd_away_zero.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero.con".
(*#*
If [F] is bounded away from zero in [I] then [F] is necessarily apart from zero in [I]; also this means that [I] is included in the domain of [{1/}F].
(*#*
If [F] is bounded away from zero in [I] then [F] is necessarily apart from zero in [I]; also this means that [I] is included in the domain of [{1/}F].
-inline cic:/CoRN/ftc/PartFunEquality/Hf.var.
+inline "cic:/CoRN/ftc/PartFunEquality/Hf.var".
-inline cic:/CoRN/ftc/PartFunEquality/bnd_imp_ap_zero.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_ap_zero.con".
-inline cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con".
-inline cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
-inline cic:/CoRN/ftc/PartFunEquality/F.var.
+inline "cic:/CoRN/ftc/PartFunEquality/F.var".
-inline cic:/CoRN/ftc/PartFunEquality/P.var.
+inline "cic:/CoRN/ftc/PartFunEquality/P.var".
-inline cic:/CoRN/ftc/PartFunEquality/Q.var.
+inline "cic:/CoRN/ftc/PartFunEquality/Q.var".
-inline cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con.
+inline "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con".
-inline cic:/CoRN/ftc/PartFunEquality/FRestr_bnd.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd.con".
(*#*
A function is said to be bounded away from zero everywhere if it is bounded away from zero in every compact subinterval of its domain; a similar definition is made for arbitrary sets, which will be necessary for future work.
*)
(*#*
A function is said to be bounded away from zero everywhere if it is bounded away from zero in every compact subinterval of its domain; a similar definition is made for arbitrary sets, which will be necessary for future work.
*)
-inline cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_everywhere.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_everywhere.con".
-inline cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_in_P.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_in_P.con".
(*#*
An immediate consequence:
*)
(*#*
An immediate consequence:
*)
-inline cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con".
-inline cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con".
(* UNEXPORTED
End Away_from_Zero.
(* UNEXPORTED
End Away_from_Zero.
-inline cic:/CoRN/ftc/PartFunEquality/I.var.
+inline "cic:/CoRN/ftc/PartFunEquality/I.var".
(* UNEXPORTED
Section Feq_Equivalence.
*)
(* UNEXPORTED
Section Feq_Equivalence.
*)
-inline cic:/CoRN/ftc/PartFunEquality/F.var.
+inline "cic:/CoRN/ftc/PartFunEquality/F.var".
-inline cic:/CoRN/ftc/PartFunEquality/G.var.
+inline "cic:/CoRN/ftc/PartFunEquality/G.var".
-inline cic:/CoRN/ftc/PartFunEquality/H.var.
+inline "cic:/CoRN/ftc/PartFunEquality/H.var".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con".
(* UNEXPORTED
End Feq_Equivalence.
(* UNEXPORTED
End Feq_Equivalence.
Also it is preserved through application of functional constructors and restriction.
*)
Also it is preserved through application of functional constructors and restriction.
*)
-inline cic:/CoRN/ftc/PartFunEquality/F.var.
+inline "cic:/CoRN/ftc/PartFunEquality/F.var".
-inline cic:/CoRN/ftc/PartFunEquality/F'.var.
+inline "cic:/CoRN/ftc/PartFunEquality/F'.var".
-inline cic:/CoRN/ftc/PartFunEquality/G.var.
+inline "cic:/CoRN/ftc/PartFunEquality/G.var".
-inline cic:/CoRN/ftc/PartFunEquality/G'.var.
+inline "cic:/CoRN/ftc/PartFunEquality/G'.var".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_plus.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_inv.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_inv.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_minus.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_minus.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_mult.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_mult.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_nth.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_nth.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_recip.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_recip.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_recip'.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_recip'.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_div.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_div.con".
-inline cic:/CoRN/ftc/PartFunEquality/Feq_div'.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_div'.con".
(*#*
Notice that in the case of division we only need to require boundedness away from zero for one of the functions (as they are equal); thus the two last lemmas are stated in two different ways, as according to the context one or the other condition may be easier to prove.
(*#*
Notice that in the case of division we only need to require boundedness away from zero for one of the functions (as they are equal); thus the two last lemmas are stated in two different ways, as according to the context one or the other condition may be easier to prove.
The restriction of a function is well defined.
*)
The restriction of a function is well defined.
*)
-inline cic:/CoRN/ftc/PartFunEquality/FRestr_wd.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FRestr_wd.con".
(*#*
The image of a set is extensional.
*)
(*#*
The image of a set is extensional.
*)
-inline cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con.
+inline "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con".
(* UNEXPORTED
End Operations.
(* UNEXPORTED
End Operations.
-inline cic:/CoRN/ftc/PartFunEquality/F.var.
+inline "cic:/CoRN/ftc/PartFunEquality/F.var".
-inline cic:/CoRN/ftc/PartFunEquality/P.con.
+inline "cic:/CoRN/ftc/PartFunEquality/P.con".
-inline cic:/CoRN/ftc/PartFunEquality/Q.var.
+inline "cic:/CoRN/ftc/PartFunEquality/Q.var".
-inline cic:/CoRN/ftc/PartFunEquality/H.var.
+inline "cic:/CoRN/ftc/PartFunEquality/H.var".
-inline cic:/CoRN/ftc/PartFunEquality/Hf.var.
+inline "cic:/CoRN/ftc/PartFunEquality/Hf.var".
-inline cic:/CoRN/ftc/PartFunEquality/FNth_zero.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con".
-inline cic:/CoRN/ftc/PartFunEquality/n.var.
+inline "cic:/CoRN/ftc/PartFunEquality/n.var".
-inline cic:/CoRN/ftc/PartFunEquality/H'.var.
+inline "cic:/CoRN/ftc/PartFunEquality/H'.var".
-inline cic:/CoRN/ftc/PartFunEquality/FNth_mult.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con".
(* UNEXPORTED
End Nth_Power.
(* UNEXPORTED
End Nth_Power.
-inline cic:/CoRN/ftc/PartFunEquality/a.var.
+inline "cic:/CoRN/ftc/PartFunEquality/a.var".
-inline cic:/CoRN/ftc/PartFunEquality/b.var.
+inline "cic:/CoRN/ftc/PartFunEquality/b.var".
-inline cic:/CoRN/ftc/PartFunEquality/Hab.var.
+inline "cic:/CoRN/ftc/PartFunEquality/Hab.var".
-inline cic:/CoRN/ftc/PartFunEquality/I.con.
+inline "cic:/CoRN/ftc/PartFunEquality/I.con".
-inline cic:/CoRN/ftc/PartFunEquality/F.var.
+inline "cic:/CoRN/ftc/PartFunEquality/F.var".
-inline cic:/CoRN/ftc/PartFunEquality/incF.var.
+inline "cic:/CoRN/ftc/PartFunEquality/incF.var".
-inline cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con".
-inline cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con".
(* UNEXPORTED
End Strong_Nth_Power.
(* UNEXPORTED
End Strong_Nth_Power.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/PartInterval".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/PartInterval".
(* $Id: PartInterval.v,v 1.6 2004/04/23 10:01:00 lcf Exp $ *)
(* $Id: PartInterval.v,v 1.6 2004/04/23 10:01:00 lcf Exp $ *)
-(* INCLUDE
-IntervalFunct
-*)
+include "ftc/IntervalFunct.ma".
(* UNEXPORTED
Section Conversion.
(* UNEXPORTED
Section Conversion.
-inline cic:/CoRN/ftc/PartInterval/F.var.
+inline "cic:/CoRN/ftc/PartInterval/F.var".
-inline cic:/CoRN/ftc/PartInterval/a.var.
+inline "cic:/CoRN/ftc/PartInterval/a.var".
-inline cic:/CoRN/ftc/PartInterval/b.var.
+inline "cic:/CoRN/ftc/PartInterval/b.var".
-inline cic:/CoRN/ftc/PartInterval/Hab.var.
+inline "cic:/CoRN/ftc/PartInterval/Hab.var".
-inline cic:/CoRN/ftc/PartInterval/I.con.
+inline "cic:/CoRN/ftc/PartInterval/I.con".
-inline cic:/CoRN/ftc/PartInterval/Hf.var.
+inline "cic:/CoRN/ftc/PartInterval/Hf.var".
-inline cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con.
+inline "cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con".
-inline cic:/CoRN/ftc/PartInterval/IntPartIR.con.
+inline "cic:/CoRN/ftc/PartInterval/IntPartIR.con".
(* UNEXPORTED
End Conversion.
(* UNEXPORTED
End Conversion.
domain [[a,b]] and build the corresponding partial function.
*)
domain [[a,b]] and build the corresponding partial function.
*)
-inline cic:/CoRN/ftc/PartInterval/a.var.
+inline "cic:/CoRN/ftc/PartInterval/a.var".
-inline cic:/CoRN/ftc/PartInterval/b.var.
+inline "cic:/CoRN/ftc/PartInterval/b.var".
-inline cic:/CoRN/ftc/PartInterval/Hab.var.
+inline "cic:/CoRN/ftc/PartInterval/Hab.var".
-inline cic:/CoRN/ftc/PartInterval/I.con.
+inline "cic:/CoRN/ftc/PartInterval/I.con".
-inline cic:/CoRN/ftc/PartInterval/f.var.
+inline "cic:/CoRN/ftc/PartInterval/f.var".
-inline cic:/CoRN/ftc/PartInterval/PartInt_strext.con.
+inline "cic:/CoRN/ftc/PartInterval/PartInt_strext.con".
-inline cic:/CoRN/ftc/PartInterval/PartInt.con.
+inline "cic:/CoRN/ftc/PartInterval/PartInt.con".
(* UNEXPORTED
End AntiConversion.
(* UNEXPORTED
End AntiConversion.
In one direction these operators are inverses.
*)
In one direction these operators are inverses.
*)
-inline cic:/CoRN/ftc/PartInterval/int_part_int.con.
+inline "cic:/CoRN/ftc/PartInterval/int_part_int.con".
(* UNEXPORTED
End Inverses.
(* UNEXPORTED
End Inverses.
-inline cic:/CoRN/ftc/PartInterval/F.var.
+inline "cic:/CoRN/ftc/PartInterval/F.var".
-inline cic:/CoRN/ftc/PartInterval/G.var.
+inline "cic:/CoRN/ftc/PartInterval/G.var".
-inline cic:/CoRN/ftc/PartInterval/a.var.
+inline "cic:/CoRN/ftc/PartInterval/a.var".
-inline cic:/CoRN/ftc/PartInterval/b.var.
+inline "cic:/CoRN/ftc/PartInterval/b.var".
-inline cic:/CoRN/ftc/PartInterval/c.var.
+inline "cic:/CoRN/ftc/PartInterval/c.var".
-inline cic:/CoRN/ftc/PartInterval/Hab.var.
+inline "cic:/CoRN/ftc/PartInterval/Hab.var".
-inline cic:/CoRN/ftc/PartInterval/I.con.
+inline "cic:/CoRN/ftc/PartInterval/I.con".
-inline cic:/CoRN/ftc/PartInterval/f.var.
+inline "cic:/CoRN/ftc/PartInterval/f.var".
-inline cic:/CoRN/ftc/PartInterval/g.var.
+inline "cic:/CoRN/ftc/PartInterval/g.var".
-inline cic:/CoRN/ftc/PartInterval/Ff.var.
+inline "cic:/CoRN/ftc/PartInterval/Ff.var".
-inline cic:/CoRN/ftc/PartInterval/Gg.var.
+inline "cic:/CoRN/ftc/PartInterval/Gg.var".
-inline cic:/CoRN/ftc/PartInterval/part_int_const.con.
+inline "cic:/CoRN/ftc/PartInterval/part_int_const.con".
-inline cic:/CoRN/ftc/PartInterval/part_int_id.con.
+inline "cic:/CoRN/ftc/PartInterval/part_int_id.con".
-inline cic:/CoRN/ftc/PartInterval/part_int_plus.con.
+inline "cic:/CoRN/ftc/PartInterval/part_int_plus.con".
-inline cic:/CoRN/ftc/PartInterval/part_int_inv.con.
+inline "cic:/CoRN/ftc/PartInterval/part_int_inv.con".
-inline cic:/CoRN/ftc/PartInterval/part_int_minus.con.
+inline "cic:/CoRN/ftc/PartInterval/part_int_minus.con".
-inline cic:/CoRN/ftc/PartInterval/part_int_mult.con.
+inline "cic:/CoRN/ftc/PartInterval/part_int_mult.con".
-inline cic:/CoRN/ftc/PartInterval/part_int_nth.con.
+inline "cic:/CoRN/ftc/PartInterval/part_int_nth.con".
-inline cic:/CoRN/ftc/PartInterval/HG.var.
+inline "cic:/CoRN/ftc/PartInterval/HG.var".
-inline cic:/CoRN/ftc/PartInterval/Hg.var.
+inline "cic:/CoRN/ftc/PartInterval/Hg.var".
-inline cic:/CoRN/ftc/PartInterval/part_int_recip.con.
+inline "cic:/CoRN/ftc/PartInterval/part_int_recip.con".
-inline cic:/CoRN/ftc/PartInterval/part_int_div.con.
+inline "cic:/CoRN/ftc/PartInterval/part_int_div.con".
(* UNEXPORTED
End Equivalences.
(* UNEXPORTED
End Equivalences.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Partitions".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Partitions".
(* $Id: Partitions.v,v 1.7 2004/04/23 10:01:00 lcf Exp $ *)
(* $Id: Partitions.v,v 1.7 2004/04/23 10:01:00 lcf Exp $ *)
-(* INCLUDE
-Continuity
-*)
+include "ftc/Continuity.ma".
(*#* printing Partition_Sum %\ensuremath{\sum_P}% #∑<sub>P</sub># *)
(*#* printing Partition_Sum %\ensuremath{\sum_P}% #∑<sub>P</sub># *)
-inline cic:/CoRN/ftc/Partitions/Partition.ind.
+inline "cic:/CoRN/ftc/Partitions/Partition.ind".
+
+coercion "cic:/matita/CoRN-Decl/ftc/Partitions/Pts.con" 0 (* compounds *).
(*#* Two immediate consequences of this are that [ai [<=] aj] whenever
[i < j] and that [ai] is in [[a,b]] for all [i].
*)
(*#* Two immediate consequences of this are that [ai [<=] aj] whenever
[i < j] and that [ai] is in [[a,b]] for all [i].
*)
-inline cic:/CoRN/ftc/Partitions/Partition_mon.con.
+inline "cic:/CoRN/ftc/Partitions/Partition_mon.con".
-inline cic:/CoRN/ftc/Partitions/Partition_in_compact.con.
+inline "cic:/CoRN/ftc/Partitions/Partition_in_compact.con".
(*#*
Each partition of [[a,b]] implies a partition of the interval
(*#*
Each partition of [[a,b]] implies a partition of the interval
-inline cic:/CoRN/ftc/Partitions/part_pred_lemma.con.
+inline "cic:/CoRN/ftc/Partitions/part_pred_lemma.con".
-inline cic:/CoRN/ftc/Partitions/Partition_Dom.con.
+inline "cic:/CoRN/ftc/Partitions/Partition_Dom.con".
(*#*
The mesh of a partition is the greatest distance between two
(*#*
The mesh of a partition is the greatest distance between two
helps us in this case.
*)
helps us in this case.
*)
-inline cic:/CoRN/ftc/Partitions/Part_Mesh_List.con.
+inline "cic:/CoRN/ftc/Partitions/Part_Mesh_List.con".
-inline cic:/CoRN/ftc/Partitions/Mesh.con.
+inline "cic:/CoRN/ftc/Partitions/Mesh.con".
-inline cic:/CoRN/ftc/Partitions/AntiMesh.con.
+inline "cic:/CoRN/ftc/Partitions/AntiMesh.con".
(*#*
Even partitions (partitions where all the points are evenly spaced)
(*#*
Even partitions (partitions where all the points are evenly spaced)
presented simply to make the definition of even partition lighter.
*)
presented simply to make the definition of even partition lighter.
*)
-inline cic:/CoRN/ftc/Partitions/even_part_1.con.
+inline "cic:/CoRN/ftc/Partitions/even_part_1.con".
-inline cic:/CoRN/ftc/Partitions/even_part_2.con.
+inline "cic:/CoRN/ftc/Partitions/even_part_2.con".
-inline cic:/CoRN/ftc/Partitions/Even_Partition.con.
+inline "cic:/CoRN/ftc/Partitions/Even_Partition.con".
(* UNEXPORTED
Section Refinements.
*)
(* UNEXPORTED
Section Refinements.
*)
-inline cic:/CoRN/ftc/Partitions/a.var.
+inline "cic:/CoRN/ftc/Partitions/a.var".
-inline cic:/CoRN/ftc/Partitions/b.var.
+inline "cic:/CoRN/ftc/Partitions/b.var".
-inline cic:/CoRN/ftc/Partitions/Hab.var.
+inline "cic:/CoRN/ftc/Partitions/Hab.var".
-inline cic:/CoRN/ftc/Partitions/m.var.
+inline "cic:/CoRN/ftc/Partitions/m.var".
-inline cic:/CoRN/ftc/Partitions/n.var.
+inline "cic:/CoRN/ftc/Partitions/n.var".
-inline cic:/CoRN/ftc/Partitions/P.var.
+inline "cic:/CoRN/ftc/Partitions/P.var".
-inline cic:/CoRN/ftc/Partitions/Q.var.
+inline "cic:/CoRN/ftc/Partitions/Q.var".
(*#*
We now define what it means for a partition [Q] to be a refinement of
[P] and prove the main property of refinements.
*)
(*#*
We now define what it means for a partition [Q] to be a refinement of
[P] and prove the main property of refinements.
*)
-inline cic:/CoRN/ftc/Partitions/Refinement.con.
+inline "cic:/CoRN/ftc/Partitions/Refinement.con".
-inline cic:/CoRN/ftc/Partitions/Refinement_prop.con.
+inline "cic:/CoRN/ftc/Partitions/Refinement_prop.con".
(*#*
We will also need to consider arbitrary sums %of the form
(*#*
We will also need to consider arbitrary sums %of the form
some condition. We define the condition and the sum for a fixed [P]:
*)
some condition. We define the condition and the sum for a fixed [P]:
*)
-inline cic:/CoRN/ftc/Partitions/Points_in_Partition.con.
+inline "cic:/CoRN/ftc/Partitions/Points_in_Partition.con".
-inline cic:/CoRN/ftc/Partitions/Pts_part_lemma.con.
+inline "cic:/CoRN/ftc/Partitions/Pts_part_lemma.con".
-inline cic:/CoRN/ftc/Partitions/Partition_Sum.con.
+inline "cic:/CoRN/ftc/Partitions/Partition_Sum.con".
(* UNEXPORTED
End Refinements.
(* UNEXPORTED
End Refinements.
-inline cic:/CoRN/ftc/Partitions/a.var.
+inline "cic:/CoRN/ftc/Partitions/a.var".
-inline cic:/CoRN/ftc/Partitions/b.var.
+inline "cic:/CoRN/ftc/Partitions/b.var".
-inline cic:/CoRN/ftc/Partitions/Hab.var.
+inline "cic:/CoRN/ftc/Partitions/Hab.var".
-inline cic:/CoRN/ftc/Partitions/I.con.
+inline "cic:/CoRN/ftc/Partitions/I.con".
-inline cic:/CoRN/ftc/Partitions/m.var.
+inline "cic:/CoRN/ftc/Partitions/m.var".
-inline cic:/CoRN/ftc/Partitions/Q.var.
+inline "cic:/CoRN/ftc/Partitions/Q.var".
-inline cic:/CoRN/ftc/Partitions/Partition_imp_points.con.
+inline "cic:/CoRN/ftc/Partitions/Partition_imp_points.con".
-inline cic:/CoRN/ftc/Partitions/Partition_imp_points_1.con.
+inline "cic:/CoRN/ftc/Partitions/Partition_imp_points_1.con".
-inline cic:/CoRN/ftc/Partitions/Partition_imp_points_2.con.
+inline "cic:/CoRN/ftc/Partitions/Partition_imp_points_2.con".
(* UNEXPORTED
End Getting_Points.
(* UNEXPORTED
End Getting_Points.
As a corollary, given any continuous function [F] and a natural number we have an immediate choice of a sum of [F] in [[a,b]].
*)
As a corollary, given any continuous function [F] and a natural number we have an immediate choice of a sum of [F] in [[a,b]].
*)
-inline cic:/CoRN/ftc/Partitions/F.var.
+inline "cic:/CoRN/ftc/Partitions/F.var".
-inline cic:/CoRN/ftc/Partitions/contF.var.
+inline "cic:/CoRN/ftc/Partitions/contF.var".
-inline cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con.
+inline "cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
If a partition has more than one point then its mesh list is nonempty.
*)
If a partition has more than one point then its mesh list is nonempty.
*)
-inline cic:/CoRN/ftc/Partitions/length_Part_Mesh_List.con.
+inline "cic:/CoRN/ftc/Partitions/length_Part_Mesh_List.con".
(*#*
Any element of the auxiliary list defined to calculate the mesh of a partition has a very specific form.
*)
(*#*
Any element of the auxiliary list defined to calculate the mesh of a partition has a very specific form.
*)
-inline cic:/CoRN/ftc/Partitions/Part_Mesh_List_lemma.con.
+inline "cic:/CoRN/ftc/Partitions/Part_Mesh_List_lemma.con".
(*#*
Mesh and antimesh are always nonnegative.
*)
(*#*
Mesh and antimesh are always nonnegative.
*)
-inline cic:/CoRN/ftc/Partitions/Mesh_nonneg.con.
+inline "cic:/CoRN/ftc/Partitions/Mesh_nonneg.con".
-inline cic:/CoRN/ftc/Partitions/AntiMesh_nonneg.con.
+inline "cic:/CoRN/ftc/Partitions/AntiMesh_nonneg.con".
(*#*
Most important, [AntiMesh] and [Mesh] provide lower and upper bounds
(*#*
Most important, [AntiMesh] and [Mesh] provide lower and upper bounds
-inline cic:/CoRN/ftc/Partitions/a.var.
+inline "cic:/CoRN/ftc/Partitions/a.var".
-inline cic:/CoRN/ftc/Partitions/b.var.
+inline "cic:/CoRN/ftc/Partitions/b.var".
-inline cic:/CoRN/ftc/Partitions/I.con.
+inline "cic:/CoRN/ftc/Partitions/I.con".
-inline cic:/CoRN/ftc/Partitions/Hab.var.
+inline "cic:/CoRN/ftc/Partitions/Hab.var".
-inline cic:/CoRN/ftc/Partitions/n.var.
+inline "cic:/CoRN/ftc/Partitions/n.var".
-inline cic:/CoRN/ftc/Partitions/P.var.
+inline "cic:/CoRN/ftc/Partitions/P.var".
-inline cic:/CoRN/ftc/Partitions/Mesh_lemma.con.
+inline "cic:/CoRN/ftc/Partitions/Mesh_lemma.con".
-inline cic:/CoRN/ftc/Partitions/AntiMesh_lemma.con.
+inline "cic:/CoRN/ftc/Partitions/AntiMesh_lemma.con".
-inline cic:/CoRN/ftc/Partitions/Mesh_leEq.con.
+inline "cic:/CoRN/ftc/Partitions/Mesh_leEq.con".
(* UNEXPORTED
End Lemmas.
(* UNEXPORTED
End Lemmas.
(*#* More technical stuff. Two equal partitions have the same mesh.
*)
(*#* More technical stuff. Two equal partitions have the same mesh.
*)
-inline cic:/CoRN/ftc/Partitions/Mesh_wd.con.
+inline "cic:/CoRN/ftc/Partitions/Mesh_wd.con".
-inline cic:/CoRN/ftc/Partitions/Mesh_wd'.con.
+inline "cic:/CoRN/ftc/Partitions/Mesh_wd'.con".
(*#*
The mesh of an even partition is easily calculated.
*)
(*#*
The mesh of an even partition is easily calculated.
*)
-inline cic:/CoRN/ftc/Partitions/even_partition_Mesh.con.
+inline "cic:/CoRN/ftc/Partitions/even_partition_Mesh.con".
(*#* ** Miscellaneous
%\begin{convention}% Throughout this section, let [a,b:IR] and [I] be [[a,b]].
%\end{convention}%
*)
(*#* ** Miscellaneous
%\begin{convention}% Throughout this section, let [a,b:IR] and [I] be [[a,b]].
%\end{convention}%
*)
-inline cic:/CoRN/ftc/Partitions/a.var.
+inline "cic:/CoRN/ftc/Partitions/a.var".
-inline cic:/CoRN/ftc/Partitions/b.var.
+inline "cic:/CoRN/ftc/Partitions/b.var".
-inline cic:/CoRN/ftc/Partitions/I.con.
+inline "cic:/CoRN/ftc/Partitions/I.con".
-inline cic:/CoRN/ftc/Partitions/Hab.var.
+inline "cic:/CoRN/ftc/Partitions/Hab.var".
(*#*
An interesting property: in a partition, if [ai [<] aj] then [i < j].
*)
(*#*
An interesting property: in a partition, if [ai [<] aj] then [i < j].
*)
-inline cic:/CoRN/ftc/Partitions/Partition_Points_mon.con.
+inline "cic:/CoRN/ftc/Partitions/Partition_Points_mon.con".
-inline cic:/CoRN/ftc/Partitions/refinement_resp_mult.con.
+inline "cic:/CoRN/ftc/Partitions/refinement_resp_mult.con".
(*#*
%\begin{convention}% Assume [m,n] are positive natural numbers and
(*#*
%\begin{convention}% Assume [m,n] are positive natural numbers and
Even partitions always have a common refinement.
*)
Even partitions always have a common refinement.
*)
-inline cic:/CoRN/ftc/Partitions/m.var.
+inline "cic:/CoRN/ftc/Partitions/m.var".
-inline cic:/CoRN/ftc/Partitions/n.var.
+inline "cic:/CoRN/ftc/Partitions/n.var".
-inline cic:/CoRN/ftc/Partitions/Hm.var.
+inline "cic:/CoRN/ftc/Partitions/Hm.var".
-inline cic:/CoRN/ftc/Partitions/Hn.var.
+inline "cic:/CoRN/ftc/Partitions/Hn.var".
-inline cic:/CoRN/ftc/Partitions/P.con.
+inline "cic:/CoRN/ftc/Partitions/P.con".
-inline cic:/CoRN/ftc/Partitions/Q.con.
+inline "cic:/CoRN/ftc/Partitions/Q.con".
-inline cic:/CoRN/ftc/Partitions/even_partition_refinement.con.
+inline "cic:/CoRN/ftc/Partitions/even_partition_refinement.con".
(* UNEXPORTED
End Even_Partitions.
(* UNEXPORTED
End Even_Partitions.
Some auxiliary definitions. A partition is said to be separated if all its points are distinct.
*)
Some auxiliary definitions. A partition is said to be separated if all its points are distinct.
*)
-inline cic:/CoRN/ftc/Partitions/a.var.
+inline "cic:/CoRN/ftc/Partitions/a.var".
-inline cic:/CoRN/ftc/Partitions/b.var.
+inline "cic:/CoRN/ftc/Partitions/b.var".
-inline cic:/CoRN/ftc/Partitions/Hab.var.
+inline "cic:/CoRN/ftc/Partitions/Hab.var".
-inline cic:/CoRN/ftc/Partitions/_Separated.con.
+inline "cic:/CoRN/ftc/Partitions/_Separated.con".
(*#*
Two partitions are said to be (mutually) separated if they are both
(*#*
Two partitions are said to be (mutually) separated if they are both
-inline cic:/CoRN/ftc/Partitions/n.var.
+inline "cic:/CoRN/ftc/Partitions/n.var".
-inline cic:/CoRN/ftc/Partitions/m.var.
+inline "cic:/CoRN/ftc/Partitions/m.var".
-inline cic:/CoRN/ftc/Partitions/P.var.
+inline "cic:/CoRN/ftc/Partitions/P.var".
-inline cic:/CoRN/ftc/Partitions/Q.var.
+inline "cic:/CoRN/ftc/Partitions/Q.var".
-inline cic:/CoRN/ftc/Partitions/Separated.con.
+inline "cic:/CoRN/ftc/Partitions/Separated.con".
(* UNEXPORTED
End More_Definitions.
(* UNEXPORTED
End More_Definitions.
Section Sep_Partitions.
*)
Section Sep_Partitions.
*)
-inline cic:/CoRN/ftc/Partitions/a.var.
+inline "cic:/CoRN/ftc/Partitions/a.var".
-inline cic:/CoRN/ftc/Partitions/b.var.
+inline "cic:/CoRN/ftc/Partitions/b.var".
-inline cic:/CoRN/ftc/Partitions/I.con.
+inline "cic:/CoRN/ftc/Partitions/I.con".
-inline cic:/CoRN/ftc/Partitions/Hab.var.
+inline "cic:/CoRN/ftc/Partitions/Hab.var".
(*#*
The antimesh of a separated partition is always positive.
*)
(*#*
The antimesh of a separated partition is always positive.
*)
-inline cic:/CoRN/ftc/Partitions/pos_AntiMesh.con.
+inline "cic:/CoRN/ftc/Partitions/pos_AntiMesh.con".
(*#*
A partition can have only one point iff the endpoints of the interval
(*#*
A partition can have only one point iff the endpoints of the interval
endpoints of the interval are the same then it must have one point.
*)
endpoints of the interval are the same then it must have one point.
*)
-inline cic:/CoRN/ftc/Partitions/partition_length_zero.con.
+inline "cic:/CoRN/ftc/Partitions/partition_length_zero.con".
-inline cic:/CoRN/ftc/Partitions/_Separated_imp_length_zero.con.
+inline "cic:/CoRN/ftc/Partitions/_Separated_imp_length_zero.con".
-inline cic:/CoRN/ftc/Partitions/partition_less_imp_gt_zero.con.
+inline "cic:/CoRN/ftc/Partitions/partition_less_imp_gt_zero.con".
(* UNEXPORTED
End Sep_Partitions.
(* UNEXPORTED
End Sep_Partitions.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefLemma".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefLemma".
(* $Id: RefLemma.v,v 1.7 2004/04/23 10:01:00 lcf Exp $ *)
(* $Id: RefLemma.v,v 1.7 2004/04/23 10:01:00 lcf Exp $ *)
-(* INCLUDE
-RefSeparating
-*)
+include "ftc/RefSeparating.ma".
-(* INCLUDE
-RefSeparated
-*)
+include "ftc/RefSeparated.ma".
-(* INCLUDE
-RefSepRef
-*)
+include "ftc/RefSepRef.ma".
(* UNEXPORTED
Section Refinement_Lemma.
(* UNEXPORTED
Section Refinement_Lemma.
-inline cic:/CoRN/ftc/RefLemma/a.var.
+inline "cic:/CoRN/ftc/RefLemma/a.var".
-inline cic:/CoRN/ftc/RefLemma/b.var.
+inline "cic:/CoRN/ftc/RefLemma/b.var".
-inline cic:/CoRN/ftc/RefLemma/Hab.var.
+inline "cic:/CoRN/ftc/RefLemma/Hab.var".
-inline cic:/CoRN/ftc/RefLemma/I.con.
+inline "cic:/CoRN/ftc/RefLemma/I.con".
-inline cic:/CoRN/ftc/RefLemma/F.var.
+inline "cic:/CoRN/ftc/RefLemma/F.var".
-inline cic:/CoRN/ftc/RefLemma/contF.var.
+inline "cic:/CoRN/ftc/RefLemma/contF.var".
-inline cic:/CoRN/ftc/RefLemma/incF.var.
+inline "cic:/CoRN/ftc/RefLemma/incF.var".
-inline cic:/CoRN/ftc/RefLemma/contF'.con.
+inline "cic:/CoRN/ftc/RefLemma/contF'.con".
-inline cic:/CoRN/ftc/RefLemma/e.var.
+inline "cic:/CoRN/ftc/RefLemma/e.var".
-inline cic:/CoRN/ftc/RefLemma/He.var.
+inline "cic:/CoRN/ftc/RefLemma/He.var".
-inline cic:/CoRN/ftc/RefLemma/d.con.
+inline "cic:/CoRN/ftc/RefLemma/d.con".
-inline cic:/CoRN/ftc/RefLemma/m.var.
+inline "cic:/CoRN/ftc/RefLemma/m.var".
-inline cic:/CoRN/ftc/RefLemma/n.var.
+inline "cic:/CoRN/ftc/RefLemma/n.var".
-inline cic:/CoRN/ftc/RefLemma/P.var.
+inline "cic:/CoRN/ftc/RefLemma/P.var".
-inline cic:/CoRN/ftc/RefLemma/HMesh.var.
+inline "cic:/CoRN/ftc/RefLemma/HMesh.var".
-inline cic:/CoRN/ftc/RefLemma/Q.var.
+inline "cic:/CoRN/ftc/RefLemma/Q.var".
-inline cic:/CoRN/ftc/RefLemma/Href.var.
+inline "cic:/CoRN/ftc/RefLemma/Href.var".
-inline cic:/CoRN/ftc/RefLemma/fP.var.
+inline "cic:/CoRN/ftc/RefLemma/fP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
-inline cic:/CoRN/ftc/RefLemma/fQ.var.
+inline "cic:/CoRN/ftc/RefLemma/fQ.var".
-inline cic:/CoRN/ftc/RefLemma/HfQ.var.
+inline "cic:/CoRN/ftc/RefLemma/HfQ.var".
-inline cic:/CoRN/ftc/RefLemma/HfQ'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfQ'.var".
-inline cic:/CoRN/ftc/RefLemma/sub.con.
+inline "cic:/CoRN/ftc/RefLemma/sub.con".
-inline cic:/CoRN/ftc/RefLemma/RL_sub_0.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_sub_0.con".
-inline cic:/CoRN/ftc/RefLemma/RL_sub_n.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_sub_n.con".
-inline cic:/CoRN/ftc/RefLemma/RL_sub_mon.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_sub_mon.con".
-inline cic:/CoRN/ftc/RefLemma/RL_sub_mon'.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_sub_mon'.con".
-inline cic:/CoRN/ftc/RefLemma/RL_sub_hyp.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_sub_hyp.con".
-inline cic:/CoRN/ftc/RefLemma/RL_sub_S.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_sub_S.con".
-inline cic:/CoRN/ftc/RefLemma/H.con.
+inline "cic:/CoRN/ftc/RefLemma/H.con".
-inline cic:/CoRN/ftc/RefLemma/H'.con.
+inline "cic:/CoRN/ftc/RefLemma/H'.con".
-inline cic:/CoRN/ftc/RefLemma/H0.con.
+inline "cic:/CoRN/ftc/RefLemma/H0.con".
-inline cic:/CoRN/ftc/RefLemma/RL_sub_SS.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_sub_SS.con".
-inline cic:/CoRN/ftc/RefLemma/RL_h.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_h.con".
-inline cic:/CoRN/ftc/RefLemma/RL_g.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_g.con".
-inline cic:/CoRN/ftc/RefLemma/ref_calc1.con.
+inline "cic:/CoRN/ftc/RefLemma/ref_calc1.con".
-inline cic:/CoRN/ftc/RefLemma/ref_calc2.con.
+inline "cic:/CoRN/ftc/RefLemma/ref_calc2.con".
-inline cic:/CoRN/ftc/RefLemma/ref_calc3.con.
+inline "cic:/CoRN/ftc/RefLemma/ref_calc3.con".
-inline cic:/CoRN/ftc/RefLemma/ref_calc4.con.
+inline "cic:/CoRN/ftc/RefLemma/ref_calc4.con".
-inline cic:/CoRN/ftc/RefLemma/ref_calc5.con.
+inline "cic:/CoRN/ftc/RefLemma/ref_calc5.con".
-inline cic:/CoRN/ftc/RefLemma/ref_calc6.con.
+inline "cic:/CoRN/ftc/RefLemma/ref_calc6.con".
-inline cic:/CoRN/ftc/RefLemma/ref_calc7.con.
+inline "cic:/CoRN/ftc/RefLemma/ref_calc7.con".
-inline cic:/CoRN/ftc/RefLemma/ref_calc8.con.
+inline "cic:/CoRN/ftc/RefLemma/ref_calc8.con".
-inline cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con.
+inline "cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con".
(* UNEXPORTED
End First_Refinement_Lemma.
(* UNEXPORTED
End First_Refinement_Lemma.
-inline cic:/CoRN/ftc/RefLemma/n.var.
+inline "cic:/CoRN/ftc/RefLemma/n.var".
-inline cic:/CoRN/ftc/RefLemma/j.var.
+inline "cic:/CoRN/ftc/RefLemma/j.var".
-inline cic:/CoRN/ftc/RefLemma/k.var.
+inline "cic:/CoRN/ftc/RefLemma/k.var".
-inline cic:/CoRN/ftc/RefLemma/P.var.
+inline "cic:/CoRN/ftc/RefLemma/P.var".
-inline cic:/CoRN/ftc/RefLemma/Q.var.
+inline "cic:/CoRN/ftc/RefLemma/Q.var".
-inline cic:/CoRN/ftc/RefLemma/R.var.
+inline "cic:/CoRN/ftc/RefLemma/R.var".
-inline cic:/CoRN/ftc/RefLemma/HrefP.var.
+inline "cic:/CoRN/ftc/RefLemma/HrefP.var".
-inline cic:/CoRN/ftc/RefLemma/HrefR.var.
+inline "cic:/CoRN/ftc/RefLemma/HrefR.var".
-inline cic:/CoRN/ftc/RefLemma/e.var.
+inline "cic:/CoRN/ftc/RefLemma/e.var".
-inline cic:/CoRN/ftc/RefLemma/e'.var.
+inline "cic:/CoRN/ftc/RefLemma/e'.var".
-inline cic:/CoRN/ftc/RefLemma/He.var.
+inline "cic:/CoRN/ftc/RefLemma/He.var".
-inline cic:/CoRN/ftc/RefLemma/He'.var.
+inline "cic:/CoRN/ftc/RefLemma/He'.var".
-inline cic:/CoRN/ftc/RefLemma/d.con.
+inline "cic:/CoRN/ftc/RefLemma/d.con".
-inline cic:/CoRN/ftc/RefLemma/d'.con.
+inline "cic:/CoRN/ftc/RefLemma/d'.con".
-inline cic:/CoRN/ftc/RefLemma/HMeshP.var.
+inline "cic:/CoRN/ftc/RefLemma/HMeshP.var".
-inline cic:/CoRN/ftc/RefLemma/HMeshR.var.
+inline "cic:/CoRN/ftc/RefLemma/HMeshR.var".
-inline cic:/CoRN/ftc/RefLemma/fP.var.
+inline "cic:/CoRN/ftc/RefLemma/fP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
-inline cic:/CoRN/ftc/RefLemma/fR.var.
+inline "cic:/CoRN/ftc/RefLemma/fR.var".
-inline cic:/CoRN/ftc/RefLemma/HfR.var.
+inline "cic:/CoRN/ftc/RefLemma/HfR.var".
-inline cic:/CoRN/ftc/RefLemma/HfR'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfR'.var".
-inline cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con.
+inline "cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con".
(* UNEXPORTED
End Second_Refinement_Lemma.
(* UNEXPORTED
End Second_Refinement_Lemma.
-inline cic:/CoRN/ftc/RefLemma/n.var.
+inline "cic:/CoRN/ftc/RefLemma/n.var".
-inline cic:/CoRN/ftc/RefLemma/m.var.
+inline "cic:/CoRN/ftc/RefLemma/m.var".
-inline cic:/CoRN/ftc/RefLemma/P.var.
+inline "cic:/CoRN/ftc/RefLemma/P.var".
-inline cic:/CoRN/ftc/RefLemma/R.var.
+inline "cic:/CoRN/ftc/RefLemma/R.var".
-inline cic:/CoRN/ftc/RefLemma/e.var.
+inline "cic:/CoRN/ftc/RefLemma/e.var".
-inline cic:/CoRN/ftc/RefLemma/e'.var.
+inline "cic:/CoRN/ftc/RefLemma/e'.var".
-inline cic:/CoRN/ftc/RefLemma/He.var.
+inline "cic:/CoRN/ftc/RefLemma/He.var".
-inline cic:/CoRN/ftc/RefLemma/He'.var.
+inline "cic:/CoRN/ftc/RefLemma/He'.var".
-inline cic:/CoRN/ftc/RefLemma/d.con.
+inline "cic:/CoRN/ftc/RefLemma/d.con".
-inline cic:/CoRN/ftc/RefLemma/d'.con.
+inline "cic:/CoRN/ftc/RefLemma/d'.con".
-inline cic:/CoRN/ftc/RefLemma/HMeshP.var.
+inline "cic:/CoRN/ftc/RefLemma/HMeshP.var".
-inline cic:/CoRN/ftc/RefLemma/HMeshR.var.
+inline "cic:/CoRN/ftc/RefLemma/HMeshR.var".
-inline cic:/CoRN/ftc/RefLemma/fP.var.
+inline "cic:/CoRN/ftc/RefLemma/fP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
-inline cic:/CoRN/ftc/RefLemma/fR.var.
+inline "cic:/CoRN/ftc/RefLemma/fR.var".
-inline cic:/CoRN/ftc/RefLemma/HfR.var.
+inline "cic:/CoRN/ftc/RefLemma/HfR.var".
-inline cic:/CoRN/ftc/RefLemma/HfR'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfR'.var".
-inline cic:/CoRN/ftc/RefLemma/Hab'.var.
+inline "cic:/CoRN/ftc/RefLemma/Hab'.var".
-inline cic:/CoRN/ftc/RefLemma/beta.var.
+inline "cic:/CoRN/ftc/RefLemma/beta.var".
-inline cic:/CoRN/ftc/RefLemma/Hbeta.var.
+inline "cic:/CoRN/ftc/RefLemma/Hbeta.var".
-inline cic:/CoRN/ftc/RefLemma/alpha.con.
+inline "cic:/CoRN/ftc/RefLemma/alpha.con".
-inline cic:/CoRN/ftc/RefLemma/RL_alpha.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_alpha.con".
-inline cic:/CoRN/ftc/RefLemma/csi1.con.
+inline "cic:/CoRN/ftc/RefLemma/csi1.con".
-inline cic:/CoRN/ftc/RefLemma/RL_csi1.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_csi1.con".
-inline cic:/CoRN/ftc/RefLemma/delta1.con.
+inline "cic:/CoRN/ftc/RefLemma/delta1.con".
-inline cic:/CoRN/ftc/RefLemma/RL_delta1.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_delta1.con".
-inline cic:/CoRN/ftc/RefLemma/P'.con.
+inline "cic:/CoRN/ftc/RefLemma/P'.con".
-inline cic:/CoRN/ftc/RefLemma/RL_P'_sep.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_P'_sep.con".
-inline cic:/CoRN/ftc/RefLemma/RL_P'_Mesh.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_P'_Mesh.con".
-inline cic:/CoRN/ftc/RefLemma/fP'.con.
+inline "cic:/CoRN/ftc/RefLemma/fP'.con".
-inline cic:/CoRN/ftc/RefLemma/RL_fP'_in_P'.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_fP'_in_P'.con".
-inline cic:/CoRN/ftc/RefLemma/RL_P'_P_sum.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_P'_P_sum.con".
-inline cic:/CoRN/ftc/RefLemma/csi2.con.
+inline "cic:/CoRN/ftc/RefLemma/csi2.con".
-inline cic:/CoRN/ftc/RefLemma/RL_csi2.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_csi2.con".
-inline cic:/CoRN/ftc/RefLemma/delta2.con.
+inline "cic:/CoRN/ftc/RefLemma/delta2.con".
-inline cic:/CoRN/ftc/RefLemma/RL_delta2.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_delta2.con".
-inline cic:/CoRN/ftc/RefLemma/R'.con.
+inline "cic:/CoRN/ftc/RefLemma/R'.con".
-inline cic:/CoRN/ftc/RefLemma/RL_R'_sep.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_R'_sep.con".
-inline cic:/CoRN/ftc/RefLemma/RL_R'_Mesh.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_R'_Mesh.con".
-inline cic:/CoRN/ftc/RefLemma/fR'.con.
+inline "cic:/CoRN/ftc/RefLemma/fR'.con".
-inline cic:/CoRN/ftc/RefLemma/RL_fR'_in_R'.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_fR'_in_R'.con".
-inline cic:/CoRN/ftc/RefLemma/RL_R'_R_sum.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_R'_R_sum.con".
-inline cic:/CoRN/ftc/RefLemma/csi3.con.
+inline "cic:/CoRN/ftc/RefLemma/csi3.con".
-inline cic:/CoRN/ftc/RefLemma/RL_csi3.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_csi3.con".
-inline cic:/CoRN/ftc/RefLemma/Q.con.
+inline "cic:/CoRN/ftc/RefLemma/Q.con".
-inline cic:/CoRN/ftc/RefLemma/RL_Q_Mesh.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_Q_Mesh.con".
-inline cic:/CoRN/ftc/RefLemma/RL_Q_sep.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_Q_sep.con".
-inline cic:/CoRN/ftc/RefLemma/fQ.con.
+inline "cic:/CoRN/ftc/RefLemma/fQ.con".
-inline cic:/CoRN/ftc/RefLemma/RL_fQ_in_Q.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_fQ_in_Q.con".
-inline cic:/CoRN/ftc/RefLemma/RL_Q_P'_sum.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_Q_P'_sum.con".
-inline cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con.
+inline "cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con".
(* UNEXPORTED
End Third_Refinement_Lemma.
(* UNEXPORTED
End Third_Refinement_Lemma.
-inline cic:/CoRN/ftc/RefLemma/Fa.con.
+inline "cic:/CoRN/ftc/RefLemma/Fa.con".
-inline cic:/CoRN/ftc/RefLemma/RL_sum_lemma_aux.con.
+inline "cic:/CoRN/ftc/RefLemma/RL_sum_lemma_aux.con".
-inline cic:/CoRN/ftc/RefLemma/n.var.
+inline "cic:/CoRN/ftc/RefLemma/n.var".
-inline cic:/CoRN/ftc/RefLemma/m.var.
+inline "cic:/CoRN/ftc/RefLemma/m.var".
-inline cic:/CoRN/ftc/RefLemma/P.var.
+inline "cic:/CoRN/ftc/RefLemma/P.var".
-inline cic:/CoRN/ftc/RefLemma/R.var.
+inline "cic:/CoRN/ftc/RefLemma/R.var".
-inline cic:/CoRN/ftc/RefLemma/e.var.
+inline "cic:/CoRN/ftc/RefLemma/e.var".
-inline cic:/CoRN/ftc/RefLemma/e'.var.
+inline "cic:/CoRN/ftc/RefLemma/e'.var".
-inline cic:/CoRN/ftc/RefLemma/He.var.
+inline "cic:/CoRN/ftc/RefLemma/He.var".
-inline cic:/CoRN/ftc/RefLemma/He'.var.
+inline "cic:/CoRN/ftc/RefLemma/He'.var".
-inline cic:/CoRN/ftc/RefLemma/d.con.
+inline "cic:/CoRN/ftc/RefLemma/d.con".
-inline cic:/CoRN/ftc/RefLemma/d'.con.
+inline "cic:/CoRN/ftc/RefLemma/d'.con".
-inline cic:/CoRN/ftc/RefLemma/HMeshP.var.
+inline "cic:/CoRN/ftc/RefLemma/HMeshP.var".
-inline cic:/CoRN/ftc/RefLemma/HMeshR.var.
+inline "cic:/CoRN/ftc/RefLemma/HMeshR.var".
-inline cic:/CoRN/ftc/RefLemma/fP.var.
+inline "cic:/CoRN/ftc/RefLemma/fP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
-inline cic:/CoRN/ftc/RefLemma/fR.var.
+inline "cic:/CoRN/ftc/RefLemma/fR.var".
-inline cic:/CoRN/ftc/RefLemma/HfR.var.
+inline "cic:/CoRN/ftc/RefLemma/HfR.var".
-inline cic:/CoRN/ftc/RefLemma/HfR'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfR'.var".
-inline cic:/CoRN/ftc/RefLemma/Hab'.var.
+inline "cic:/CoRN/ftc/RefLemma/Hab'.var".
-inline cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con.
+inline "cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con".
(* UNEXPORTED
End Fourth_Refinement_Lemma.
(* UNEXPORTED
End Fourth_Refinement_Lemma.
(*#* We finish by presenting Theorem 9. *)
(*#* We finish by presenting Theorem 9. *)
-inline cic:/CoRN/ftc/RefLemma/n.var.
+inline "cic:/CoRN/ftc/RefLemma/n.var".
-inline cic:/CoRN/ftc/RefLemma/m.var.
+inline "cic:/CoRN/ftc/RefLemma/m.var".
-inline cic:/CoRN/ftc/RefLemma/P.var.
+inline "cic:/CoRN/ftc/RefLemma/P.var".
-inline cic:/CoRN/ftc/RefLemma/R.var.
+inline "cic:/CoRN/ftc/RefLemma/R.var".
-inline cic:/CoRN/ftc/RefLemma/e.var.
+inline "cic:/CoRN/ftc/RefLemma/e.var".
-inline cic:/CoRN/ftc/RefLemma/e'.var.
+inline "cic:/CoRN/ftc/RefLemma/e'.var".
-inline cic:/CoRN/ftc/RefLemma/He.var.
+inline "cic:/CoRN/ftc/RefLemma/He.var".
-inline cic:/CoRN/ftc/RefLemma/He'.var.
+inline "cic:/CoRN/ftc/RefLemma/He'.var".
-inline cic:/CoRN/ftc/RefLemma/d.con.
+inline "cic:/CoRN/ftc/RefLemma/d.con".
-inline cic:/CoRN/ftc/RefLemma/d'.con.
+inline "cic:/CoRN/ftc/RefLemma/d'.con".
-inline cic:/CoRN/ftc/RefLemma/HMeshP.var.
+inline "cic:/CoRN/ftc/RefLemma/HMeshP.var".
-inline cic:/CoRN/ftc/RefLemma/HMeshR.var.
+inline "cic:/CoRN/ftc/RefLemma/HMeshR.var".
-inline cic:/CoRN/ftc/RefLemma/fP.var.
+inline "cic:/CoRN/ftc/RefLemma/fP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP.var".
-inline cic:/CoRN/ftc/RefLemma/HfP'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
-inline cic:/CoRN/ftc/RefLemma/fR.var.
+inline "cic:/CoRN/ftc/RefLemma/fR.var".
-inline cic:/CoRN/ftc/RefLemma/HfR.var.
+inline "cic:/CoRN/ftc/RefLemma/HfR.var".
-inline cic:/CoRN/ftc/RefLemma/HfR'.var.
+inline "cic:/CoRN/ftc/RefLemma/HfR'.var".
-inline cic:/CoRN/ftc/RefLemma/refinement_lemma.con.
+inline "cic:/CoRN/ftc/RefLemma/refinement_lemma.con".
(* UNEXPORTED
End Main_Refinement_Lemma.
(* UNEXPORTED
End Main_Refinement_Lemma.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefSepRef".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefSepRef".
(* $Id: RefSepRef.v,v 1.6 2004/04/23 10:01:00 lcf Exp $ *)
(* begin hide *)
(* $Id: RefSepRef.v,v 1.6 2004/04/23 10:01:00 lcf Exp $ *)
(* begin hide *)
-(* INCLUDE
-COrdLemmas
-*)
+include "ftc/COrdLemmas.ma".
-(* INCLUDE
-Partitions
-*)
+include "ftc/Partitions.ma".
(* UNEXPORTED
Section Refining_Separated.
*)
(* UNEXPORTED
Section Refining_Separated.
*)
-inline cic:/CoRN/ftc/RefSepRef/a.var.
+inline "cic:/CoRN/ftc/RefSepRef/a.var".
-inline cic:/CoRN/ftc/RefSepRef/b.var.
+inline "cic:/CoRN/ftc/RefSepRef/b.var".
-inline cic:/CoRN/ftc/RefSepRef/Hab.var.
+inline "cic:/CoRN/ftc/RefSepRef/Hab.var".
-inline cic:/CoRN/ftc/RefSepRef/I.con.
+inline "cic:/CoRN/ftc/RefSepRef/I.con".
-inline cic:/CoRN/ftc/RefSepRef/F.var.
+inline "cic:/CoRN/ftc/RefSepRef/F.var".
-inline cic:/CoRN/ftc/RefSepRef/contF.var.
+inline "cic:/CoRN/ftc/RefSepRef/contF.var".
-inline cic:/CoRN/ftc/RefSepRef/incF.var.
+inline "cic:/CoRN/ftc/RefSepRef/incF.var".
-inline cic:/CoRN/ftc/RefSepRef/m.var.
+inline "cic:/CoRN/ftc/RefSepRef/m.var".
-inline cic:/CoRN/ftc/RefSepRef/n.var.
+inline "cic:/CoRN/ftc/RefSepRef/n.var".
-inline cic:/CoRN/ftc/RefSepRef/P.var.
+inline "cic:/CoRN/ftc/RefSepRef/P.var".
-inline cic:/CoRN/ftc/RefSepRef/R.var.
+inline "cic:/CoRN/ftc/RefSepRef/R.var".
-inline cic:/CoRN/ftc/RefSepRef/HPR.var.
+inline "cic:/CoRN/ftc/RefSepRef/HPR.var".
-inline cic:/CoRN/ftc/RefSepRef/RSR_HP.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_HP.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_HP'.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_HP'.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_HR.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_HR.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_HR'.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_HR'.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_mn0.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_mn0.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_nm0.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_nm0.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_H'.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_H'.con".
-inline cic:/CoRN/ftc/RefSepRef/f'.con.
+inline "cic:/CoRN/ftc/RefSepRef/f'.con".
-inline cic:/CoRN/ftc/RefSepRef/g'.con.
+inline "cic:/CoRN/ftc/RefSepRef/g'.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_f'_nlnf.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_f'_nlnf.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_g'_nlnf.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_g'_nlnf.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_f'_mon.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_f'_mon.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_g'_mon.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_g'_mon.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_f'_ap_g'.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_f'_ap_g'.con".
-inline cic:/CoRN/ftc/RefSepRef/h.con.
+inline "cic:/CoRN/ftc/RefSepRef/h.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_h_nlnf.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_h_nlnf.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_h_mon.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_h_mon.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_h_mon'.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_h_mon'.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_h_f'.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_h_f'.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_h_g'.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_h_g'.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_h_PropAll.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_h_PropAll.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_h_PropEx.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_h_PropEx.con".
-inline cic:/CoRN/ftc/RefSepRef/Separated_Refinement_fun.con.
+inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_fun.con".
-inline cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma1.con.
+inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma1.con".
-inline cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma3.con.
+inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma3.con".
-inline cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma4.con.
+inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma4.con".
-inline cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma2.con.
+inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma2.con".
-inline cic:/CoRN/ftc/RefSepRef/Separated_Refinement.con.
+inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxP.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxP.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxR.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxR.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma0.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma0.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_h_inj.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_h_inj.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemmai.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemmai.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemman.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemman.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma1.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma1.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma2.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma2.con".
-inline cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lft.con.
+inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lft.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma0.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma0.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmai.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmai.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmam.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmam.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma1.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma1.con".
-inline cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma2.con.
+inline "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma2.con".
-inline cic:/CoRN/ftc/RefSepRef/Separated_Refinement_rht.con.
+inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_rht.con".
(* UNEXPORTED
End Refining_Separated.
(* UNEXPORTED
End Refining_Separated.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefSeparated".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefSeparated".
(* $Id: RefSeparated.v,v 1.8 2004/04/23 10:01:00 lcf Exp $ *)
(* begin hide *)
(* $Id: RefSeparated.v,v 1.8 2004/04/23 10:01:00 lcf Exp $ *)
(* begin hide *)
-(* INCLUDE
-COrdLemmas
-*)
+include "ftc/COrdLemmas.ma".
-(* INCLUDE
-Partitions
-*)
+include "ftc/Partitions.ma".
(* UNEXPORTED
Section Separating__Separated.
*)
(* UNEXPORTED
Section Separating__Separated.
*)
-inline cic:/CoRN/ftc/RefSeparated/a.var.
+inline "cic:/CoRN/ftc/RefSeparated/a.var".
-inline cic:/CoRN/ftc/RefSeparated/b.var.
+inline "cic:/CoRN/ftc/RefSeparated/b.var".
-inline cic:/CoRN/ftc/RefSeparated/Hab.var.
+inline "cic:/CoRN/ftc/RefSeparated/Hab.var".
-inline cic:/CoRN/ftc/RefSeparated/I.con.
+inline "cic:/CoRN/ftc/RefSeparated/I.con".
-inline cic:/CoRN/ftc/RefSeparated/F.var.
+inline "cic:/CoRN/ftc/RefSeparated/F.var".
-inline cic:/CoRN/ftc/RefSeparated/contF.var.
+inline "cic:/CoRN/ftc/RefSeparated/contF.var".
-inline cic:/CoRN/ftc/RefSeparated/incF.var.
+inline "cic:/CoRN/ftc/RefSeparated/incF.var".
-inline cic:/CoRN/ftc/RefSeparated/Hab'.var.
+inline "cic:/CoRN/ftc/RefSeparated/Hab'.var".
-inline cic:/CoRN/ftc/RefSeparated/m.var.
+inline "cic:/CoRN/ftc/RefSeparated/m.var".
-inline cic:/CoRN/ftc/RefSeparated/n.var.
+inline "cic:/CoRN/ftc/RefSeparated/n.var".
-inline cic:/CoRN/ftc/RefSeparated/P.var.
+inline "cic:/CoRN/ftc/RefSeparated/P.var".
-inline cic:/CoRN/ftc/RefSeparated/R.var.
+inline "cic:/CoRN/ftc/RefSeparated/R.var".
-inline cic:/CoRN/ftc/RefSeparated/HP.var.
+inline "cic:/CoRN/ftc/RefSeparated/HP.var".
-inline cic:/CoRN/ftc/RefSeparated/HR.var.
+inline "cic:/CoRN/ftc/RefSeparated/HR.var".
-inline cic:/CoRN/ftc/RefSeparated/RS_pos_n.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_pos_n.con".
-inline cic:/CoRN/ftc/RefSeparated/RS_pos_m.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_pos_m.con".
-inline cic:/CoRN/ftc/RefSeparated/alpha.var.
+inline "cic:/CoRN/ftc/RefSeparated/alpha.var".
-inline cic:/CoRN/ftc/RefSeparated/Halpha.var.
+inline "cic:/CoRN/ftc/RefSeparated/Halpha.var".
-inline cic:/CoRN/ftc/RefSeparated/e.con.
+inline "cic:/CoRN/ftc/RefSeparated/e.con".
-inline cic:/CoRN/ftc/RefSeparated/RS_He.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_He.con".
-inline cic:/CoRN/ftc/RefSeparated/contF'.con.
+inline "cic:/CoRN/ftc/RefSeparated/contF'.con".
-inline cic:/CoRN/ftc/RefSeparated/d.con.
+inline "cic:/CoRN/ftc/RefSeparated/d.con".
-inline cic:/CoRN/ftc/RefSeparated/RS_Hd.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_Hd.con".
-inline cic:/CoRN/ftc/RefSeparated/RS_Hd'.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_Hd'.con".
-inline cic:/CoRN/ftc/RefSeparated/csi.var.
+inline "cic:/CoRN/ftc/RefSeparated/csi.var".
-inline cic:/CoRN/ftc/RefSeparated/Hcsi.var.
+inline "cic:/CoRN/ftc/RefSeparated/Hcsi.var".
-inline cic:/CoRN/ftc/RefSeparated/M.con.
+inline "cic:/CoRN/ftc/RefSeparated/M.con".
-inline cic:/CoRN/ftc/RefSeparated/deltaP.con.
+inline "cic:/CoRN/ftc/RefSeparated/deltaP.con".
-inline cic:/CoRN/ftc/RefSeparated/deltaR.con.
+inline "cic:/CoRN/ftc/RefSeparated/deltaR.con".
-inline cic:/CoRN/ftc/RefSeparated/delta.con.
+inline "cic:/CoRN/ftc/RefSeparated/delta.con".
-inline cic:/CoRN/ftc/RefSeparated/RS_delta_deltaP.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaP.con".
-inline cic:/CoRN/ftc/RefSeparated/RS_delta_deltaR.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaR.con".
-inline cic:/CoRN/ftc/RefSeparated/RS_delta_csi.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_delta_csi.con".
-inline cic:/CoRN/ftc/RefSeparated/RS_delta_d.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_delta_d.con".
-inline cic:/CoRN/ftc/RefSeparated/RS_delta_pos.con.
+inline "cic:/CoRN/ftc/RefSeparated/RS_delta_pos.con".
(* UNEXPORTED
Section Defining_ai'.
*)
(* UNEXPORTED
Section Defining_ai'.
*)
-inline cic:/CoRN/ftc/RefSeparated/i.var.
+inline "cic:/CoRN/ftc/RefSeparated/i.var".
-inline cic:/CoRN/ftc/RefSeparated/Hi.var.
+inline "cic:/CoRN/ftc/RefSeparated/Hi.var".
-inline cic:/CoRN/ftc/RefSeparated/separation_conseq.con.
+inline "cic:/CoRN/ftc/RefSeparated/separation_conseq.con".
-inline cic:/CoRN/ftc/RefSeparated/pred1.con.
+inline "cic:/CoRN/ftc/RefSeparated/pred1.con".
-inline cic:/CoRN/ftc/RefSeparated/pred2.con.
+inline "cic:/CoRN/ftc/RefSeparated/pred2.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_aux_lemma.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_aux_lemma.con".
-inline cic:/CoRN/ftc/RefSeparated/Hi0.var.
+inline "cic:/CoRN/ftc/RefSeparated/Hi0.var".
-inline cic:/CoRN/ftc/RefSeparated/Hin.var.
+inline "cic:/CoRN/ftc/RefSeparated/Hin.var".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_leEq.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_leEq.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_less.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_less.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_ap.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_ap.con".
(* UNEXPORTED
End Defining_ai'.
*)
(* UNEXPORTED
End Defining_ai'.
*)
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_fun.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_delta.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_delta.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_fun_delta.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_delta.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_mon_i.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_mon_i.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_mon.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_mon.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_wd.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_wd.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_fun_wd.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_wd.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_part.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_part.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con".
-inline cic:/CoRN/ftc/RefSeparated/g.var.
+inline "cic:/CoRN/ftc/RefSeparated/g.var".
-inline cic:/CoRN/ftc/RefSeparated/gP.var.
+inline "cic:/CoRN/ftc/RefSeparated/gP.var".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_points.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_points.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_points_lemma.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_points_lemma.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_aux.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_aux.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_Sum.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_Sum.con".
-inline cic:/CoRN/ftc/RefSeparated/sep__sep_Mesh.con.
+inline "cic:/CoRN/ftc/RefSeparated/sep__sep_Mesh.con".
(* UNEXPORTED
End Separating__Separated.
(* UNEXPORTED
End Separating__Separated.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefSeparating".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefSeparating".
(* $Id: RefSeparating.v,v 1.7 2004/04/23 10:01:01 lcf Exp $ *)
(* begin hide *)
(* $Id: RefSeparating.v,v 1.7 2004/04/23 10:01:01 lcf Exp $ *)
(* begin hide *)
-(* INCLUDE
-COrdLemmas
-*)
+include "ftc/COrdLemmas.ma".
-(* INCLUDE
-Partitions
-*)
+include "ftc/Partitions.ma".
(* UNEXPORTED
Section Separating_Partition.
*)
(* UNEXPORTED
Section Separating_Partition.
*)
-inline cic:/CoRN/ftc/RefSeparating/a.var.
+inline "cic:/CoRN/ftc/RefSeparating/a.var".
-inline cic:/CoRN/ftc/RefSeparating/b.var.
+inline "cic:/CoRN/ftc/RefSeparating/b.var".
-inline cic:/CoRN/ftc/RefSeparating/Hab.var.
+inline "cic:/CoRN/ftc/RefSeparating/Hab.var".
-inline cic:/CoRN/ftc/RefSeparating/I.con.
+inline "cic:/CoRN/ftc/RefSeparating/I.con".
-inline cic:/CoRN/ftc/RefSeparating/F.var.
+inline "cic:/CoRN/ftc/RefSeparating/F.var".
-inline cic:/CoRN/ftc/RefSeparating/contF.var.
+inline "cic:/CoRN/ftc/RefSeparating/contF.var".
-inline cic:/CoRN/ftc/RefSeparating/incF.var.
+inline "cic:/CoRN/ftc/RefSeparating/incF.var".
-inline cic:/CoRN/ftc/RefSeparating/Hab'.var.
+inline "cic:/CoRN/ftc/RefSeparating/Hab'.var".
-inline cic:/CoRN/ftc/RefSeparating/n.var.
+inline "cic:/CoRN/ftc/RefSeparating/n.var".
-inline cic:/CoRN/ftc/RefSeparating/P.var.
+inline "cic:/CoRN/ftc/RefSeparating/P.var".
-inline cic:/CoRN/ftc/RefSeparating/alpha.var.
+inline "cic:/CoRN/ftc/RefSeparating/alpha.var".
-inline cic:/CoRN/ftc/RefSeparating/Halpha.var.
+inline "cic:/CoRN/ftc/RefSeparating/Halpha.var".
-inline cic:/CoRN/ftc/RefSeparating/csi.var.
+inline "cic:/CoRN/ftc/RefSeparating/csi.var".
-inline cic:/CoRN/ftc/RefSeparating/Hcsi.var.
+inline "cic:/CoRN/ftc/RefSeparating/Hcsi.var".
-inline cic:/CoRN/ftc/RefSeparating/M.con.
+inline "cic:/CoRN/ftc/RefSeparating/M.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_pos_n.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_pos_n.con".
-inline cic:/CoRN/ftc/RefSeparating/SPap_n.con.
+inline "cic:/CoRN/ftc/RefSeparating/SPap_n.con".
-inline cic:/CoRN/ftc/RefSeparating/delta.con.
+inline "cic:/CoRN/ftc/RefSeparating/delta.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_delta_pos.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_delta_pos.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con".
-inline cic:/CoRN/ftc/RefSeparating/Hab''.var.
+inline "cic:/CoRN/ftc/RefSeparating/Hab''.var".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_h.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_h.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_h_bnd.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_h_bnd.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_1.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_1.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_2.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_2.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_3.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_3.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_app_n.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_app_n.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma2.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma2.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma3.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma3.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_delta2_delta4.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_delta2_delta4.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_m1.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_m1.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_m.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_m.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_length.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_length.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_m_m1.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_m_m1.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_pos_m.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_pos_m.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun_0.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun_0.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun_i.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun_m.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun_m.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun_i'.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i'.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd'.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd'.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun_wd.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun_wd.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon_pts.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon_pts.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_mon.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_mon.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con".
-inline cic:/CoRN/ftc/RefSeparating/g.var.
+inline "cic:/CoRN/ftc/RefSeparating/g.var".
-inline cic:/CoRN/ftc/RefSeparating/gP.var.
+inline "cic:/CoRN/ftc/RefSeparating/gP.var".
-inline cic:/CoRN/ftc/RefSeparating/gP'.var.
+inline "cic:/CoRN/ftc/RefSeparating/gP'.var".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_pts.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_pts.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_pts_lemma.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_pts_lemma.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_pts_in_Partition.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_pts_in_Partition.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_Hsep_S.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_Hsep_S.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_Hsep.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_Hsep.con".
-inline cic:/CoRN/ftc/RefSeparating/RS'_h.con.
+inline "cic:/CoRN/ftc/RefSeparating/RS'_h.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_suRS'_m1.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_suRS'_m1.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_Sum2.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_Sum2.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_Sum3.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_Sum3.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_Sum4.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_Sum4.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_aux.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_aux.con".
-inline cic:/CoRN/ftc/RefSeparating/sep__part_Sum.con.
+inline "cic:/CoRN/ftc/RefSeparating/sep__part_Sum.con".
(* UNEXPORTED
End Separating_Partition.
(* UNEXPORTED
End Separating_Partition.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Rolle".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Rolle".
(* $Id: Rolle.v,v 1.6 2004/04/23 10:01:01 lcf Exp $ *)
(* $Id: Rolle.v,v 1.6 2004/04/23 10:01:01 lcf Exp $ *)
-(* INCLUDE
-DiffTactics2
-*)
+include "tactics/DiffTactics2.ma".
-(* INCLUDE
-MoreFunctions
-*)
+include "ftc/MoreFunctions.ma".
(* UNEXPORTED
Section Rolle.
(* UNEXPORTED
Section Rolle.
-inline cic:/CoRN/ftc/Rolle/a.var.
+inline "cic:/CoRN/ftc/Rolle/a.var".
-inline cic:/CoRN/ftc/Rolle/b.var.
+inline "cic:/CoRN/ftc/Rolle/b.var".
-inline cic:/CoRN/ftc/Rolle/Hab'.var.
+inline "cic:/CoRN/ftc/Rolle/Hab'.var".
-inline cic:/CoRN/ftc/Rolle/Hab.con.
+inline "cic:/CoRN/ftc/Rolle/Hab.con".
-inline cic:/CoRN/ftc/Rolle/I.con.
+inline "cic:/CoRN/ftc/Rolle/I.con".
-inline cic:/CoRN/ftc/Rolle/F.var.
+inline "cic:/CoRN/ftc/Rolle/F.var".
-inline cic:/CoRN/ftc/Rolle/F'.var.
+inline "cic:/CoRN/ftc/Rolle/F'.var".
-inline cic:/CoRN/ftc/Rolle/derF.var.
+inline "cic:/CoRN/ftc/Rolle/derF.var".
-inline cic:/CoRN/ftc/Rolle/Ha.var.
+inline "cic:/CoRN/ftc/Rolle/Ha.var".
-inline cic:/CoRN/ftc/Rolle/Hb.var.
+inline "cic:/CoRN/ftc/Rolle/Hb.var".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/Rolle/Fab.var.
+inline "cic:/CoRN/ftc/Rolle/Fab.var".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/Rolle/e.var.
+inline "cic:/CoRN/ftc/Rolle/e.var".
-inline cic:/CoRN/ftc/Rolle/He.var.
+inline "cic:/CoRN/ftc/Rolle/He.var".
-inline cic:/CoRN/ftc/Rolle/contF'.con.
+inline "cic:/CoRN/ftc/Rolle/contF'.con".
-inline cic:/CoRN/ftc/Rolle/derivF.con.
+inline "cic:/CoRN/ftc/Rolle/derivF.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma2.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma2.con".
-inline cic:/CoRN/ftc/Rolle/df.con.
+inline "cic:/CoRN/ftc/Rolle/df.con".
-inline cic:/CoRN/ftc/Rolle/Hdf.con.
+inline "cic:/CoRN/ftc/Rolle/Hdf.con".
-inline cic:/CoRN/ftc/Rolle/Hf.con.
+inline "cic:/CoRN/ftc/Rolle/Hf.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma3.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma3.con".
-inline cic:/CoRN/ftc/Rolle/df'.con.
+inline "cic:/CoRN/ftc/Rolle/df'.con".
-inline cic:/CoRN/ftc/Rolle/Hdf'.con.
+inline "cic:/CoRN/ftc/Rolle/Hdf'.con".
-inline cic:/CoRN/ftc/Rolle/Hf'.con.
+inline "cic:/CoRN/ftc/Rolle/Hf'.con".
-inline cic:/CoRN/ftc/Rolle/d.con.
+inline "cic:/CoRN/ftc/Rolle/d.con".
-inline cic:/CoRN/ftc/Rolle/Hd.con.
+inline "cic:/CoRN/ftc/Rolle/Hd.con".
-inline cic:/CoRN/ftc/Rolle/incF.con.
+inline "cic:/CoRN/ftc/Rolle/incF.con".
-inline cic:/CoRN/ftc/Rolle/n.con.
+inline "cic:/CoRN/ftc/Rolle/n.con".
-inline cic:/CoRN/ftc/Rolle/fcp.con.
+inline "cic:/CoRN/ftc/Rolle/fcp.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma1.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma1.con".
-inline cic:/CoRN/ftc/Rolle/incF'.con.
+inline "cic:/CoRN/ftc/Rolle/incF'.con".
-inline cic:/CoRN/ftc/Rolle/fcp'.con.
+inline "cic:/CoRN/ftc/Rolle/fcp'.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma4.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma4.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma5.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma5.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma6.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma6.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma7.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma7.con".
-inline cic:/CoRN/ftc/Rolle/j.con.
+inline "cic:/CoRN/ftc/Rolle/j.con".
-inline cic:/CoRN/ftc/Rolle/Hj.con.
+inline "cic:/CoRN/ftc/Rolle/Hj.con".
-inline cic:/CoRN/ftc/Rolle/Hj'.con.
+inline "cic:/CoRN/ftc/Rolle/Hj'.con".
-inline cic:/CoRN/ftc/Rolle/k.con.
+inline "cic:/CoRN/ftc/Rolle/k.con".
-inline cic:/CoRN/ftc/Rolle/Hk.con.
+inline "cic:/CoRN/ftc/Rolle/Hk.con".
-inline cic:/CoRN/ftc/Rolle/Hk'.con.
+inline "cic:/CoRN/ftc/Rolle/Hk'.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma8.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma8.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma9.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma9.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma10.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma10.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma11.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma11.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma12.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma12.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma13.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma13.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma15.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma15.con".
-inline cic:/CoRN/ftc/Rolle/Rolle.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle.con".
The following is a simple corollary:
*)
The following is a simple corollary:
*)
-inline cic:/CoRN/ftc/Rolle/a.var.
+inline "cic:/CoRN/ftc/Rolle/a.var".
-inline cic:/CoRN/ftc/Rolle/b.var.
+inline "cic:/CoRN/ftc/Rolle/b.var".
-inline cic:/CoRN/ftc/Rolle/Hab'.var.
+inline "cic:/CoRN/ftc/Rolle/Hab'.var".
-inline cic:/CoRN/ftc/Rolle/Hab.con.
+inline "cic:/CoRN/ftc/Rolle/Hab.con".
-inline cic:/CoRN/ftc/Rolle/I.con.
+inline "cic:/CoRN/ftc/Rolle/I.con".
-inline cic:/CoRN/ftc/Rolle/F.var.
+inline "cic:/CoRN/ftc/Rolle/F.var".
-inline cic:/CoRN/ftc/Rolle/F'.var.
+inline "cic:/CoRN/ftc/Rolle/F'.var".
-inline cic:/CoRN/ftc/Rolle/HF.var.
+inline "cic:/CoRN/ftc/Rolle/HF.var".
-inline cic:/CoRN/ftc/Rolle/HA.var.
+inline "cic:/CoRN/ftc/Rolle/HA.var".
-inline cic:/CoRN/ftc/Rolle/HB.var.
+inline "cic:/CoRN/ftc/Rolle/HB.var".
-inline cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con.
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con".
(* UNEXPORTED
End Law_of_the_Mean.
(* UNEXPORTED
End Law_of_the_Mean.
We can also state these theorems without expliciting the derivative of [F].
*)
We can also state these theorems without expliciting the derivative of [F].
*)
-inline cic:/CoRN/ftc/Rolle/a.var.
+inline "cic:/CoRN/ftc/Rolle/a.var".
-inline cic:/CoRN/ftc/Rolle/b.var.
+inline "cic:/CoRN/ftc/Rolle/b.var".
-inline cic:/CoRN/ftc/Rolle/Hab'.var.
+inline "cic:/CoRN/ftc/Rolle/Hab'.var".
-inline cic:/CoRN/ftc/Rolle/Hab.con.
+inline "cic:/CoRN/ftc/Rolle/Hab.con".
-inline cic:/CoRN/ftc/Rolle/F.var.
+inline "cic:/CoRN/ftc/Rolle/F.var".
-inline cic:/CoRN/ftc/Rolle/HF.var.
+inline "cic:/CoRN/ftc/Rolle/HF.var".
-inline cic:/CoRN/ftc/Rolle/Rolle'.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle'.con".
-inline cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con.
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con".
(* UNEXPORTED
End Corollaries.
(* UNEXPORTED
End Corollaries.
-inline cic:/CoRN/ftc/Rolle/I.var.
+inline "cic:/CoRN/ftc/Rolle/I.var".
-inline cic:/CoRN/ftc/Rolle/pI.var.
+inline "cic:/CoRN/ftc/Rolle/pI.var".
-inline cic:/CoRN/ftc/Rolle/F.var.
+inline "cic:/CoRN/ftc/Rolle/F.var".
-inline cic:/CoRN/ftc/Rolle/F'.var.
+inline "cic:/CoRN/ftc/Rolle/F'.var".
-inline cic:/CoRN/ftc/Rolle/derF.var.
+inline "cic:/CoRN/ftc/Rolle/derF.var".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/Rolle/incF.con.
+inline "cic:/CoRN/ftc/Rolle/incF.con".
-inline cic:/CoRN/ftc/Rolle/incF'.con.
+inline "cic:/CoRN/ftc/Rolle/incF'.con".
-inline cic:/CoRN/ftc/Rolle/Law_of_the_Mean.con.
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean.con".
(*#*
We further generalize the mean law by writing as an explicit bound.
*)
(*#*
We further generalize the mean law by writing as an explicit bound.
*)
-inline cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con.
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con".
(* UNEXPORTED
End Generalizations.
(* UNEXPORTED
End Generalizations.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/StrongIVT".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/StrongIVT".
(* $Id: StrongIVT.v,v 1.5 2004/04/23 10:01:01 lcf Exp $ *)
(* $Id: StrongIVT.v,v 1.5 2004/04/23 10:01:01 lcf Exp $ *)
+include "ftc/WeakIVT.ma".
-(* INCLUDE
-CalculusTheorems
-*)
+include "ftc/CalculusTheorems.ma".
(* UNEXPORTED
Section IVT'.
(* UNEXPORTED
Section IVT'.
The same notations and conventions apply as before.
*)
The same notations and conventions apply as before.
*)
-inline cic:/CoRN/ftc/StrongIVT/a.var.
+inline "cic:/CoRN/ftc/StrongIVT/a.var".
-inline cic:/CoRN/ftc/StrongIVT/b.var.
+inline "cic:/CoRN/ftc/StrongIVT/b.var".
-inline cic:/CoRN/ftc/StrongIVT/Hab'.var.
+inline "cic:/CoRN/ftc/StrongIVT/Hab'.var".
-inline cic:/CoRN/ftc/StrongIVT/Hab.var.
+inline "cic:/CoRN/ftc/StrongIVT/Hab.var".
-inline cic:/CoRN/ftc/StrongIVT/I.con.
+inline "cic:/CoRN/ftc/StrongIVT/I.con".
-inline cic:/CoRN/ftc/StrongIVT/I'.con.
+inline "cic:/CoRN/ftc/StrongIVT/I'.con".
-inline cic:/CoRN/ftc/StrongIVT/F.var.
+inline "cic:/CoRN/ftc/StrongIVT/F.var".
-inline cic:/CoRN/ftc/StrongIVT/contF.var.
+inline "cic:/CoRN/ftc/StrongIVT/contF.var".
-inline cic:/CoRN/ftc/StrongIVT/incF.con.
+inline "cic:/CoRN/ftc/StrongIVT/incF.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/StrongIVT/incrF.var.
+inline "cic:/CoRN/ftc/StrongIVT/incrF.var".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/StrongIVT/Ha.con.
+inline "cic:/CoRN/ftc/StrongIVT/Ha.con".
-inline cic:/CoRN/ftc/StrongIVT/Hb.con.
+inline "cic:/CoRN/ftc/StrongIVT/Hb.con".
-inline cic:/CoRN/ftc/StrongIVT/HFab'.con.
+inline "cic:/CoRN/ftc/StrongIVT/HFab'.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/StrongIVT/z.var.
+inline "cic:/CoRN/ftc/StrongIVT/z.var".
-inline cic:/CoRN/ftc/StrongIVT/Haz.var.
+inline "cic:/CoRN/ftc/StrongIVT/Haz.var".
-inline cic:/CoRN/ftc/StrongIVT/Hzb.var.
+inline "cic:/CoRN/ftc/StrongIVT/Hzb.var".
-inline cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con.
+inline "cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con".
-inline cic:/CoRN/ftc/StrongIVT/IVT'_aux_seq_type.ind.
+inline "cic:/CoRN/ftc/StrongIVT/IVT'_aux_seq_type.ind".
-inline cic:/CoRN/ftc/StrongIVT/IVT'_iter.con.
+inline "cic:/CoRN/ftc/StrongIVT/IVT'_iter.con".
-inline cic:/CoRN/ftc/StrongIVT/IVT'_seq.con.
+inline "cic:/CoRN/ftc/StrongIVT/IVT'_seq.con".
-inline cic:/CoRN/ftc/StrongIVT/a'_seq.con.
+inline "cic:/CoRN/ftc/StrongIVT/a'_seq.con".
-inline cic:/CoRN/ftc/StrongIVT/b'_seq.con.
+inline "cic:/CoRN/ftc/StrongIVT/b'_seq.con".
-inline cic:/CoRN/ftc/StrongIVT/a'_seq_I.con.
+inline "cic:/CoRN/ftc/StrongIVT/a'_seq_I.con".
-inline cic:/CoRN/ftc/StrongIVT/b'_seq_I.con.
+inline "cic:/CoRN/ftc/StrongIVT/b'_seq_I.con".
-inline cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con.
+inline "cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con".
-inline cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con.
+inline "cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con".
-inline cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con.
+inline "cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con".
-inline cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con.
+inline "cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con".
-inline cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con.
+inline "cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con".
-inline cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con.
+inline "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con".
-inline cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con.
+inline "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con".
-inline cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con.
+inline "cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con".
-inline cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con.
+inline "cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con".
-inline cic:/CoRN/ftc/StrongIVT/xa.con.
+inline "cic:/CoRN/ftc/StrongIVT/xa.con".
-inline cic:/CoRN/ftc/StrongIVT/xb.con.
+inline "cic:/CoRN/ftc/StrongIVT/xb.con".
-inline cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con.
+inline "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con".
-inline cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con.
+inline "cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con".
-inline cic:/CoRN/ftc/StrongIVT/IVT'_I.con.
+inline "cic:/CoRN/ftc/StrongIVT/IVT'_I.con".
theorem to more widely applicable forms.
*)
theorem to more widely applicable forms.
*)
-inline cic:/CoRN/ftc/StrongIVT/Weak_IVT.con.
+inline "cic:/CoRN/ftc/StrongIVT/Weak_IVT.con".
-inline cic:/CoRN/ftc/StrongIVT/IVT_inc.con.
+inline "cic:/CoRN/ftc/StrongIVT/IVT_inc.con".
(* UNEXPORTED
Transparent Min.
*)
(* UNEXPORTED
Transparent Min.
*)
-inline cic:/CoRN/ftc/StrongIVT/IVT_dec.con.
+inline "cic:/CoRN/ftc/StrongIVT/IVT_dec.con".
-inline cic:/CoRN/ftc/StrongIVT/IVT'_inc.con.
+inline "cic:/CoRN/ftc/StrongIVT/IVT'_inc.con".
(* UNEXPORTED
Transparent Min.
*)
(* UNEXPORTED
Transparent Min.
*)
-inline cic:/CoRN/ftc/StrongIVT/IVT'_dec.con.
+inline "cic:/CoRN/ftc/StrongIVT/IVT'_dec.con".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Taylor".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/Taylor".
(* $Id: Taylor.v,v 1.10 2004/04/23 10:01:01 lcf Exp $ *)
(* $Id: Taylor.v,v 1.10 2004/04/23 10:01:01 lcf Exp $ *)
-(* INCLUDE
-TaylorLemma
-*)
+include "ftc/TaylorLemma.ma".
(* UNEXPORTED
Opaque Min Max N_Deriv.
(* UNEXPORTED
Opaque Min Max N_Deriv.
-inline cic:/CoRN/ftc/Taylor/I.var.
+inline "cic:/CoRN/ftc/Taylor/I.var".
-inline cic:/CoRN/ftc/Taylor/pI.var.
+inline "cic:/CoRN/ftc/Taylor/pI.var".
-inline cic:/CoRN/ftc/Taylor/F.var.
+inline "cic:/CoRN/ftc/Taylor/F.var".
-inline cic:/CoRN/ftc/Taylor/deriv_Sn.con.
+inline "cic:/CoRN/ftc/Taylor/deriv_Sn.con".
-inline cic:/CoRN/ftc/Taylor/a.var.
+inline "cic:/CoRN/ftc/Taylor/a.var".
-inline cic:/CoRN/ftc/Taylor/b.var.
+inline "cic:/CoRN/ftc/Taylor/b.var".
-inline cic:/CoRN/ftc/Taylor/Ha.var.
+inline "cic:/CoRN/ftc/Taylor/Ha.var".
-inline cic:/CoRN/ftc/Taylor/Hb.var.
+inline "cic:/CoRN/ftc/Taylor/Hb.var".
-inline cic:/CoRN/ftc/Taylor/fi.con.
+inline "cic:/CoRN/ftc/Taylor/fi.con".
-inline cic:/CoRN/ftc/Taylor/funct_i.con.
+inline "cic:/CoRN/ftc/Taylor/funct_i.con".
-inline cic:/CoRN/ftc/Taylor/Taylor_Seq'.con.
+inline "cic:/CoRN/ftc/Taylor/Taylor_Seq'.con".
-inline cic:/CoRN/ftc/Taylor/TaylorB.con.
+inline "cic:/CoRN/ftc/Taylor/TaylorB.con".
-inline cic:/CoRN/ftc/Taylor/Taylor_Rem.con.
+inline "cic:/CoRN/ftc/Taylor/Taylor_Rem.con".
-inline cic:/CoRN/ftc/Taylor/Taylor_Sumx_lemma.con.
+inline "cic:/CoRN/ftc/Taylor/Taylor_Sumx_lemma.con".
-inline cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con.
+inline "cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con".
-inline cic:/CoRN/ftc/Taylor/Taylor'.con.
+inline "cic:/CoRN/ftc/Taylor/Taylor'.con".
(* UNEXPORTED
End More_Taylor_Defs.
(* UNEXPORTED
End More_Taylor_Defs.
-inline cic:/CoRN/ftc/Taylor/I.var.
+inline "cic:/CoRN/ftc/Taylor/I.var".
-inline cic:/CoRN/ftc/Taylor/pI.var.
+inline "cic:/CoRN/ftc/Taylor/pI.var".
-inline cic:/CoRN/ftc/Taylor/F.var.
+inline "cic:/CoRN/ftc/Taylor/F.var".
-inline cic:/CoRN/ftc/Taylor/n.var.
+inline "cic:/CoRN/ftc/Taylor/n.var".
-inline cic:/CoRN/ftc/Taylor/f.var.
+inline "cic:/CoRN/ftc/Taylor/f.var".
-inline cic:/CoRN/ftc/Taylor/goodF.var.
+inline "cic:/CoRN/ftc/Taylor/goodF.var".
-inline cic:/CoRN/ftc/Taylor/goodF'.var.
+inline "cic:/CoRN/ftc/Taylor/goodF'.var".
-inline cic:/CoRN/ftc/Taylor/derF.var.
+inline "cic:/CoRN/ftc/Taylor/derF.var".
-inline cic:/CoRN/ftc/Taylor/F'.var.
+inline "cic:/CoRN/ftc/Taylor/F'.var".
-inline cic:/CoRN/ftc/Taylor/derF'.var.
+inline "cic:/CoRN/ftc/Taylor/derF'.var".
-inline cic:/CoRN/ftc/Taylor/a.var.
+inline "cic:/CoRN/ftc/Taylor/a.var".
-inline cic:/CoRN/ftc/Taylor/b.var.
+inline "cic:/CoRN/ftc/Taylor/b.var".
-inline cic:/CoRN/ftc/Taylor/Ha.var.
+inline "cic:/CoRN/ftc/Taylor/Ha.var".
-inline cic:/CoRN/ftc/Taylor/Hb.var.
+inline "cic:/CoRN/ftc/Taylor/Hb.var".
-inline cic:/CoRN/ftc/Taylor/funct_i.con.
+inline "cic:/CoRN/ftc/Taylor/funct_i.con".
-inline cic:/CoRN/ftc/Taylor/Taylor_Seq.con.
+inline "cic:/CoRN/ftc/Taylor/Taylor_Seq.con".
-inline cic:/CoRN/ftc/Taylor/deriv_Sn.con.
+inline "cic:/CoRN/ftc/Taylor/deriv_Sn.con".
-inline cic:/CoRN/ftc/Taylor/Taylor_aux.con.
+inline "cic:/CoRN/ftc/Taylor/Taylor_aux.con".
(* UNEXPORTED
Transparent N_Deriv.
*)
(* UNEXPORTED
Transparent N_Deriv.
*)
-inline cic:/CoRN/ftc/Taylor/Taylor.con.
+inline "cic:/CoRN/ftc/Taylor/Taylor.con".
(* UNEXPORTED
End Taylor_Theorem.
(* UNEXPORTED
End Taylor_Theorem.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/TaylorLemma".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/TaylorLemma".
(* $Id: TaylorLemma.v,v 1.8 2004/04/23 10:01:01 lcf Exp $ *)
(* $Id: TaylorLemma.v,v 1.8 2004/04/23 10:01:01 lcf Exp $ *)
(* UNEXPORTED
Opaque Min.
(* UNEXPORTED
Opaque Min.
[[Min(a,b),Max(a,b)]].
*)
[[Min(a,b),Max(a,b)]].
*)
-inline cic:/CoRN/ftc/TaylorLemma/a.var.
+inline "cic:/CoRN/ftc/TaylorLemma/a.var".
-inline cic:/CoRN/ftc/TaylorLemma/b.var.
+inline "cic:/CoRN/ftc/TaylorLemma/b.var".
-inline cic:/CoRN/ftc/TaylorLemma/Hap.var.
+inline "cic:/CoRN/ftc/TaylorLemma/Hap.var".
-inline cic:/CoRN/ftc/TaylorLemma/Hab'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Hab'.con".
-inline cic:/CoRN/ftc/TaylorLemma/Hab.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Hab.con".
-inline cic:/CoRN/ftc/TaylorLemma/I.con.
+inline "cic:/CoRN/ftc/TaylorLemma/I.con".
-inline cic:/CoRN/ftc/TaylorLemma/F.var.
+inline "cic:/CoRN/ftc/TaylorLemma/F.var".
-inline cic:/CoRN/ftc/TaylorLemma/Ha.var.
+inline "cic:/CoRN/ftc/TaylorLemma/Ha.var".
-inline cic:/CoRN/ftc/TaylorLemma/Hb.var.
+inline "cic:/CoRN/ftc/TaylorLemma/Hb.var".
-inline cic:/CoRN/ftc/TaylorLemma/fi.con.
+inline "cic:/CoRN/ftc/TaylorLemma/fi.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_compact_a.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_compact_a.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_compact_b.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_compact_b.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/TaylorLemma/funct_i.con.
+inline "cic:/CoRN/ftc/TaylorLemma/funct_i.con".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/funct_i'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/funct_i'.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_a_i.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_a_i.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_b_i.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_b_i.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_x_i.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_x_i.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con".
Taylor sum of order [n].
*)
Taylor sum of order [n].
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_seq'_aux.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'_aux.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con".
It is easy to show that [b] is in the domain of this series, which allows us to write down the Taylor remainder around [b].
*)
It is easy to show that [b] is in the domain of this series, which allows us to write down the Taylor remainder around [b].
*)
-inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con".
-inline cic:/CoRN/ftc/TaylorLemma/g.con.
+inline "cic:/CoRN/ftc/TaylorLemma/g.con".
(* UNEXPORTED
Opaque Taylor_seq'_aux Taylor_rem.
(* UNEXPORTED
Opaque Taylor_seq'_aux Taylor_rem.
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con".
(* UNEXPORTED
Transparent funct_i funct_i'.
(* UNEXPORTED
Transparent funct_i funct_i'.
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con".
(* UNEXPORTED
Transparent funct_i' FSumx.
*)
(* UNEXPORTED
Transparent funct_i' FSumx.
*)
-inline cic:/CoRN/ftc/TaylorLemma/funct_aux.con.
+inline "cic:/CoRN/ftc/TaylorLemma/funct_aux.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con".
(* UNEXPORTED
Ltac Lazy_Included :=
(* UNEXPORTED
Ltac Lazy_Included :=
| apply csf_wd_unfolded ]; Algebra.
*)
| apply csf_wd_unfolded ]; Algebra.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con".
(* UNEXPORTED
Opaque funct_aux.
(* UNEXPORTED
Opaque funct_aux.
Transparent funct_aux.
*)
Transparent funct_aux.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con".
-inline cic:/CoRN/ftc/TaylorLemma/g'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/g'.con".
(* UNEXPORTED
Opaque Taylor_rem funct_aux.
*)
(* UNEXPORTED
Opaque Taylor_rem funct_aux.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con".
(* UNEXPORTED
Transparent Taylor_rem funct_aux.
(* UNEXPORTED
Transparent Taylor_rem funct_aux.
-inline cic:/CoRN/ftc/TaylorLemma/e.var.
+inline "cic:/CoRN/ftc/TaylorLemma/e.var".
-inline cic:/CoRN/ftc/TaylorLemma/He.var.
+inline "cic:/CoRN/ftc/TaylorLemma/He.var".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/TaylorLemma/deriv_Sn'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/deriv_Sn'.con".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/TLH.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TLH.con".
Transparent Taylor_rem funct_aux.
*)
Transparent Taylor_rem funct_aux.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con".
(* UNEXPORTED
End Taylor_Defs.
(* UNEXPORTED
End Taylor_Defs.
set "baseuri" "cic:/matita/CoRN-Decl/ftc/WeakIVT".
set "baseuri" "cic:/matita/CoRN-Decl/ftc/WeakIVT".
(* $Id: WeakIVT.v,v 1.9 2004/04/23 10:01:01 lcf Exp $ *)
(*#* printing ** %\ensuremath\times% #×# *)
(* $Id: WeakIVT.v,v 1.9 2004/04/23 10:01:01 lcf Exp $ *)
(*#* printing ** %\ensuremath\times% #×# *)
-(* INCLUDE
-Continuity
-*)
+include "ftc/Continuity.ma".
(*#* *IVT for Partial Functions
(*#* *IVT for Partial Functions
-inline cic:/CoRN/ftc/WeakIVT/a.var.
+inline "cic:/CoRN/ftc/WeakIVT/a.var".
-inline cic:/CoRN/ftc/WeakIVT/b.var.
+inline "cic:/CoRN/ftc/WeakIVT/b.var".
-inline cic:/CoRN/ftc/WeakIVT/Hab.var.
+inline "cic:/CoRN/ftc/WeakIVT/Hab.var".
-inline cic:/CoRN/ftc/WeakIVT/I.con.
+inline "cic:/CoRN/ftc/WeakIVT/I.con".
-inline cic:/CoRN/ftc/WeakIVT/F.var.
+inline "cic:/CoRN/ftc/WeakIVT/F.var".
-inline cic:/CoRN/ftc/WeakIVT/contF.var.
+inline "cic:/CoRN/ftc/WeakIVT/contF.var".
-inline cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con.
+inline "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con".
(* UNEXPORTED
End Lemma1.
(* UNEXPORTED
End Lemma1.
-inline cic:/CoRN/ftc/WeakIVT/a.var.
+inline "cic:/CoRN/ftc/WeakIVT/a.var".
-inline cic:/CoRN/ftc/WeakIVT/b.var.
+inline "cic:/CoRN/ftc/WeakIVT/b.var".
-inline cic:/CoRN/ftc/WeakIVT/Hab.var.
+inline "cic:/CoRN/ftc/WeakIVT/Hab.var".
-inline cic:/CoRN/ftc/WeakIVT/I.con.
+inline "cic:/CoRN/ftc/WeakIVT/I.con".
-inline cic:/CoRN/ftc/WeakIVT/F.var.
+inline "cic:/CoRN/ftc/WeakIVT/F.var".
-inline cic:/CoRN/ftc/WeakIVT/contF.var.
+inline "cic:/CoRN/ftc/WeakIVT/contF.var".
(*#*
If [f(b) [<] f(a)], a similar result holds:
*)
(*#*
If [f(b) [<] f(a)], a similar result holds:
*)
-inline cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con.
+inline "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con".
(* UNEXPORTED
End Lemma2.
(* UNEXPORTED
End Lemma2.
converge to [x0] such that [f(x0) [=] z].
*)
converge to [x0] such that [f(x0) [=] z].
*)
-inline cic:/CoRN/ftc/WeakIVT/a.var.
+inline "cic:/CoRN/ftc/WeakIVT/a.var".
-inline cic:/CoRN/ftc/WeakIVT/b.var.
+inline "cic:/CoRN/ftc/WeakIVT/b.var".
-inline cic:/CoRN/ftc/WeakIVT/Hab'.var.
+inline "cic:/CoRN/ftc/WeakIVT/Hab'.var".
-inline cic:/CoRN/ftc/WeakIVT/Hab.var.
+inline "cic:/CoRN/ftc/WeakIVT/Hab.var".
-inline cic:/CoRN/ftc/WeakIVT/I.con.
+inline "cic:/CoRN/ftc/WeakIVT/I.con".
-inline cic:/CoRN/ftc/WeakIVT/F.var.
+inline "cic:/CoRN/ftc/WeakIVT/F.var".
-inline cic:/CoRN/ftc/WeakIVT/contF.var.
+inline "cic:/CoRN/ftc/WeakIVT/contF.var".
-inline cic:/CoRN/ftc/WeakIVT/incF.con.
+inline "cic:/CoRN/ftc/WeakIVT/incF.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/WeakIVT/incrF.var.
+inline "cic:/CoRN/ftc/WeakIVT/incrF.var".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/WeakIVT/Ha.con.
+inline "cic:/CoRN/ftc/WeakIVT/Ha.con".
-inline cic:/CoRN/ftc/WeakIVT/Hb.con.
+inline "cic:/CoRN/ftc/WeakIVT/Hb.con".
-inline cic:/CoRN/ftc/WeakIVT/HFab'.con.
+inline "cic:/CoRN/ftc/WeakIVT/HFab'.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/WeakIVT/z.var.
+inline "cic:/CoRN/ftc/WeakIVT/z.var".
-inline cic:/CoRN/ftc/WeakIVT/Haz.var.
+inline "cic:/CoRN/ftc/WeakIVT/Haz.var".
-inline cic:/CoRN/ftc/WeakIVT/Hzb.var.
+inline "cic:/CoRN/ftc/WeakIVT/Hzb.var".
and [x' [<=] z [<=] y'].
*)
and [x' [<=] z [<=] y'].
*)
-inline cic:/CoRN/ftc/WeakIVT/IVT_seq_lemma.con.
+inline "cic:/CoRN/ftc/WeakIVT/IVT_seq_lemma.con".
We now iterate this construction.
*)
We now iterate this construction.
*)
-inline cic:/CoRN/ftc/WeakIVT/IVT_aux_seq_type.ind.
+inline "cic:/CoRN/ftc/WeakIVT/IVT_aux_seq_type.ind".
-inline cic:/CoRN/ftc/WeakIVT/IVT_iter.con.
+inline "cic:/CoRN/ftc/WeakIVT/IVT_iter.con".
-inline cic:/CoRN/ftc/WeakIVT/IVT_seq.con.
+inline "cic:/CoRN/ftc/WeakIVT/IVT_seq.con".
(*#*
We now define the sequences built from this iteration, starting with [a] and [b].
*)
(*#*
We now define the sequences built from this iteration, starting with [a] and [b].
*)
-inline cic:/CoRN/ftc/WeakIVT/a_seq.con.
+inline "cic:/CoRN/ftc/WeakIVT/a_seq.con".
-inline cic:/CoRN/ftc/WeakIVT/b_seq.con.
+inline "cic:/CoRN/ftc/WeakIVT/b_seq.con".
-inline cic:/CoRN/ftc/WeakIVT/a_seq_I.con.
+inline "cic:/CoRN/ftc/WeakIVT/a_seq_I.con".
-inline cic:/CoRN/ftc/WeakIVT/b_seq_I.con.
+inline "cic:/CoRN/ftc/WeakIVT/b_seq_I.con".
-inline cic:/CoRN/ftc/WeakIVT/a_seq_less_b_seq.con.
+inline "cic:/CoRN/ftc/WeakIVT/a_seq_less_b_seq.con".
-inline cic:/CoRN/ftc/WeakIVT/a_seq_leEq_z.con.
+inline "cic:/CoRN/ftc/WeakIVT/a_seq_leEq_z.con".
-inline cic:/CoRN/ftc/WeakIVT/z_leEq_b_seq.con.
+inline "cic:/CoRN/ftc/WeakIVT/z_leEq_b_seq.con".
-inline cic:/CoRN/ftc/WeakIVT/a_seq_mon.con.
+inline "cic:/CoRN/ftc/WeakIVT/a_seq_mon.con".
-inline cic:/CoRN/ftc/WeakIVT/b_seq_mon.con.
+inline "cic:/CoRN/ftc/WeakIVT/b_seq_mon.con".
-inline cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist_n.con.
+inline "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist_n.con".
-inline cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist.con.
+inline "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist.con".
-inline cic:/CoRN/ftc/WeakIVT/a_seq_Cauchy.con.
+inline "cic:/CoRN/ftc/WeakIVT/a_seq_Cauchy.con".
-inline cic:/CoRN/ftc/WeakIVT/b_seq_Cauchy.con.
+inline "cic:/CoRN/ftc/WeakIVT/b_seq_Cauchy.con".
-inline cic:/CoRN/ftc/WeakIVT/xa.con.
+inline "cic:/CoRN/ftc/WeakIVT/xa.con".
-inline cic:/CoRN/ftc/WeakIVT/xb.con.
+inline "cic:/CoRN/ftc/WeakIVT/xb.con".
-inline cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_lim.con.
+inline "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_lim.con".
-inline cic:/CoRN/ftc/WeakIVT/xa_in_interval.con.
+inline "cic:/CoRN/ftc/WeakIVT/xa_in_interval.con".
-inline cic:/CoRN/ftc/WeakIVT/IVT_I.con.
+inline "cic:/CoRN/ftc/WeakIVT/IVT_I.con".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/CMetricSpaces".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/CMetricSpaces".
(* $Id: CMetricSpaces.v,v 1.4 2004/04/23 10:01:01 lcf Exp $ *)
(* $Id: CMetricSpaces.v,v 1.4 2004/04/23 10:01:01 lcf Exp $ *)
-(* INCLUDE
-Prod_Sub
-*)
+include "metrics/Prod_Sub.ma".
+include "metrics/Equiv.ma".
(* UNEXPORTED
Section Definition_MS.
(* UNEXPORTED
Section Definition_MS.
(*#* **Definition of Metric Space
*)
(*#* **Definition of Metric Space
*)
-inline cic:/CoRN/metrics/CMetricSpaces/CMetricSpace.ind.
+inline "cic:/CoRN/metrics/CMetricSpaces/CMetricSpace.ind".
+
+coercion "cic:/matita/CoRN-Decl/metrics/CMetricSpaces/scms_crr.con" 0 (* compounds *).
(* UNEXPORTED
End Definition_MS.
(* UNEXPORTED
End Definition_MS.
(*#* **Metric Space basics
*)
(*#* **Metric Space basics
*)
-inline cic:/CoRN/metrics/CMetricSpaces/d_CMetricSpace_apdiag_imp_grzero.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/d_CMetricSpace_apdiag_imp_grzero.con".
-inline cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con".
-inline cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con".
(* UNEXPORTED
End MS_basics.
(* UNEXPORTED
End MS_basics.
The product of two metric spaces is again a metric space.
*)
The product of two metric spaces is again a metric space.
*)
-inline cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpaces_apdiag_grzero.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpaces_apdiag_grzero.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpace.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpace.con".
(*#*
A subspace of a metric space is again a metric space.
(*#*
A subspace of a metric space is again a metric space.
Implicit Arguments SubPsMetricSpace [X].
*)
Implicit Arguments SubPsMetricSpace [X].
*)
-inline cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace_apdiag_grzero.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace_apdiag_grzero.con".
-inline cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace.con".
(* UNEXPORTED
Implicit Arguments SubMetricSpace [X].
(* UNEXPORTED
Implicit Arguments SubMetricSpace [X].
Not all pseudo metric spaces are a metric space:
*)
Not all pseudo metric spaces are a metric space:
*)
-inline cic:/CoRN/metrics/CMetricSpaces/zf_nis_CMetricSpace.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/zf_nis_CMetricSpace.con".
(*#*
But a pseudo metric space induces a metric space:
*)
(*#*
But a pseudo metric space induces a metric space:
*)
-inline cic:/CoRN/metrics/CMetricSpaces/metric_ap.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap.con".
-inline cic:/CoRN/metrics/CMetricSpaces/metric_eq.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/metric_eq.con".
-inline cic:/CoRN/metrics/CMetricSpaces/metric_ap_irreflexive.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap_irreflexive.con".
-inline cic:/CoRN/metrics/CMetricSpaces/metric_ap_symmetric.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap_symmetric.con".
-inline cic:/CoRN/metrics/CMetricSpaces/metric_ap_cotransitive.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap_cotransitive.con".
-inline cic:/CoRN/metrics/CMetricSpaces/metric_ap_tight.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/metric_ap_tight.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Metric_CSet_is_CSetoid.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Metric_CSet_is_CSetoid.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Metric_CSetoid.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Metric_CSetoid.con".
-inline cic:/CoRN/metrics/CMetricSpaces/metric_d.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/metric_d.con".
-inline cic:/CoRN/metrics/CMetricSpaces/metric_d_strext.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/metric_d_strext.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Metric_d.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Metric_d_com.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_com.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Metric_d_nneg.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_nneg.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Metric_d_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_pos_imp_ap.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Metric_d_tri_ineq.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_tri_ineq.con".
-inline cic:/CoRN/metrics/CMetricSpaces/QuotientCSetoid_is_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/QuotientCSetoid_is_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/CMetricSpaces/QuotientCPsMetricSpace.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/QuotientCPsMetricSpace.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Metric_d_apdiag_grzero.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Metric_d_apdiag_grzero.con".
-inline cic:/CoRN/metrics/CMetricSpaces/QuotientCMetricSpace.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/QuotientCMetricSpace.con".
(*#*
Some pseudo metric spaces already are a metric space:
*)
(*#*
Some pseudo metric spaces already are a metric space:
*)
-inline cic:/CoRN/metrics/CMetricSpaces/dIR_apdiag_grzero.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/dIR_apdiag_grzero.con".
-inline cic:/CoRN/metrics/CMetricSpaces/IR_as_CMetricSpace.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/IR_as_CMetricSpace.con".
(*#*
In that case the induced metric space is equivalent to the original one:
*)
(*#*
In that case the induced metric space is equivalent to the original one:
*)
-inline cic:/CoRN/metrics/CMetricSpaces/emb.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/emb.con".
-inline cic:/CoRN/metrics/CMetricSpaces/emb_strext.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/emb_strext.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Emb.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Emb.con".
-inline cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con".
(* UNEXPORTED
End Zeroff.
(* UNEXPORTED
End Zeroff.
-inline cic:/CoRN/metrics/CMetricSpaces/nz.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/nz.con".
(* end hide *)
(* begin hide *)
(* end hide *)
(* begin hide *)
-inline cic:/CoRN/metrics/CMetricSpaces/d_wd.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/d_wd.con".
-inline cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con.
+inline "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con".
(* UNEXPORTED
End Limitt.
(* UNEXPORTED
End Limitt.
set "baseuri" "cic:/matita/CoRN-Decl/metrics/CPMSTheory".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/CPMSTheory".
(* $Id: CPMSTheory.v,v 1.6 2004/04/23 10:01:02 lcf Exp $ *)
(* $Id: CPMSTheory.v,v 1.6 2004/04/23 10:01:02 lcf Exp $ *)
-(* INCLUDE
-Prod_Sub
-*)
+include "metrics/Prod_Sub.ma".
(* UNEXPORTED
Section lists.
(* UNEXPORTED
Section lists.
the proofs a bit easier.
*)
the proofs a bit easier.
*)
-inline cic:/CoRN/metrics/CPMSTheory/MSmember.con.
+inline "cic:/CoRN/metrics/CPMSTheory/MSmember.con".
(* UNEXPORTED
Implicit Arguments MSmember [X].
*)
(* UNEXPORTED
Implicit Arguments MSmember [X].
*)
-inline cic:/CoRN/metrics/CPMSTheory/to_IR.con.
+inline "cic:/CoRN/metrics/CPMSTheory/to_IR.con".
-inline cic:/CoRN/metrics/CPMSTheory/from_IR.con.
+inline "cic:/CoRN/metrics/CPMSTheory/from_IR.con".
-inline cic:/CoRN/metrics/CPMSTheory/list_IR.con.
+inline "cic:/CoRN/metrics/CPMSTheory/list_IR.con".
-inline cic:/CoRN/metrics/CPMSTheory/is_P.con.
+inline "cic:/CoRN/metrics/CPMSTheory/is_P.con".
(*#*
If a real number is element of a list in the above defined sense,
(*#*
If a real number is element of a list in the above defined sense,
that uses the setoid equality.
*)
that uses the setoid equality.
*)
-inline cic:/CoRN/metrics/CPMSTheory/member1.con.
+inline "cic:/CoRN/metrics/CPMSTheory/member1.con".
(*#*
The image under a certain mapping of an element of a list $l$ #<I>l</I># is member
of the list of images of elements of $l$ #<I>l</I>#.
*)
(*#*
The image under a certain mapping of an element of a list $l$ #<I>l</I># is member
of the list of images of elements of $l$ #<I>l</I>#.
*)
-inline cic:/CoRN/metrics/CPMSTheory/map_member.con.
+inline "cic:/CoRN/metrics/CPMSTheory/map_member.con".
(*#* **Pseudo Metric Space theory
*)
(*#* **Pseudo Metric Space theory
*)
-inline cic:/CoRN/metrics/CPMSTheory/Re_co_do.con.
+inline "cic:/CoRN/metrics/CPMSTheory/Re_co_do.con".
-inline cic:/CoRN/metrics/CPMSTheory/Re_co_do_strext.con.
+inline "cic:/CoRN/metrics/CPMSTheory/Re_co_do_strext.con".
-inline cic:/CoRN/metrics/CPMSTheory/re_co_do.con.
+inline "cic:/CoRN/metrics/CPMSTheory/re_co_do.con".
-inline cic:/CoRN/metrics/CPMSTheory/re_co_do_well_def.con.
+inline "cic:/CoRN/metrics/CPMSTheory/re_co_do_well_def.con".
(* UNEXPORTED
Implicit Arguments MSmember [X].
(* UNEXPORTED
Implicit Arguments MSmember [X].
#<I>l</I># is member of the list of images of elements of $l$ #<I>l</I>#.
*)
#<I>l</I># is member of the list of images of elements of $l$ #<I>l</I>#.
*)
-inline cic:/CoRN/metrics/CPMSTheory/map_member'.con.
+inline "cic:/CoRN/metrics/CPMSTheory/map_member'.con".
-inline cic:/CoRN/metrics/CPMSTheory/bounded.con.
+inline "cic:/CoRN/metrics/CPMSTheory/bounded.con".
-inline cic:/CoRN/metrics/CPMSTheory/MStotally_bounded.con.
+inline "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded.con".
(*#*
Total boundedness is preserved under uniformly continuous mappings.
(*#*
Total boundedness is preserved under uniformly continuous mappings.
Implicit Arguments SubPsMetricSpace [X].
*)
Implicit Arguments SubPsMetricSpace [X].
*)
-inline cic:/CoRN/metrics/CPMSTheory/unicon_resp_totallybounded.con.
+inline "cic:/CoRN/metrics/CPMSTheory/unicon_resp_totallybounded.con".
-inline cic:/CoRN/metrics/CPMSTheory/MStotallybounded_totallybounded.con.
+inline "cic:/CoRN/metrics/CPMSTheory/MStotallybounded_totallybounded.con".
(*#*
Every image under an uniformly continuous function of an totally bounded
pseudo metric space has an infimum and a supremum.
*)
(*#*
Every image under an uniformly continuous function of an totally bounded
pseudo metric space has an infimum and a supremum.
*)
-inline cic:/CoRN/metrics/CPMSTheory/infimum_exists.con.
+inline "cic:/CoRN/metrics/CPMSTheory/infimum_exists.con".
-inline cic:/CoRN/metrics/CPMSTheory/supremum_exists.con.
+inline "cic:/CoRN/metrics/CPMSTheory/supremum_exists.con".
(*#*
A subspace $P$#<I>P</I># of a pseudo metric space $X$#<I>X</I># is said to be located if for all
(*#*
A subspace $P$#<I>P</I># of a pseudo metric space $X$#<I>X</I># is said to be located if for all
Implicit Arguments dsub'_as_cs_fun [X].
*)
Implicit Arguments dsub'_as_cs_fun [X].
*)
-inline cic:/CoRN/metrics/CPMSTheory/located.con.
+inline "cic:/CoRN/metrics/CPMSTheory/located.con".
(* UNEXPORTED
Implicit Arguments located [X].
*)
(* UNEXPORTED
Implicit Arguments located [X].
*)
-inline cic:/CoRN/metrics/CPMSTheory/located'.con.
+inline "cic:/CoRN/metrics/CPMSTheory/located'.con".
(* UNEXPORTED
Implicit Arguments located' [X].
*)
(* UNEXPORTED
Implicit Arguments located' [X].
*)
-inline cic:/CoRN/metrics/CPMSTheory/located_imp_located'.con.
+inline "cic:/CoRN/metrics/CPMSTheory/located_imp_located'.con".
(*#*
Every totally bounded pseudo metric space is located.
*)
(*#*
Every totally bounded pseudo metric space is located.
*)
-inline cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con.
+inline "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con".
(*#*
For all $x$#<I>x</I># in a pseudo metric space $X$#<I>X</I>#, for all located subspaces $P$#<I>P</I># of $X$#<I>X</I>#,
(*#*
For all $x$#<I>x</I># in a pseudo metric space $X$#<I>X</I>#, for all located subspaces $P$#<I>P</I># of $X$#<I>X</I>#,
one to use the latter as an argument of [map].
*)
one to use the latter as an argument of [map].
*)
-inline cic:/CoRN/metrics/CPMSTheory/Floc.con.
+inline "cic:/CoRN/metrics/CPMSTheory/Floc.con".
-inline cic:/CoRN/metrics/CPMSTheory/Flocfun.con.
+inline "cic:/CoRN/metrics/CPMSTheory/Flocfun.con".
(*#*
A located subset $P$#<I>P</I># of a totally bounded pseudo metric space $X$
(*#*
A located subset $P$#<I>P</I># of a totally bounded pseudo metric space $X$
-inline cic:/CoRN/metrics/CPMSTheory/locatedsub_totallybounded_imp_totallyboundedsub.con.
+inline "cic:/CoRN/metrics/CPMSTheory/locatedsub_totallybounded_imp_totallyboundedsub.con".
(*#*
Here are some definitions that could come in handy:
*)
(*#*
Here are some definitions that could come in handy:
*)
-inline cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con.
+inline "cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con".
(* UNEXPORTED
Implicit Arguments MSseqLimit' [X].
*)
(* UNEXPORTED
Implicit Arguments MSseqLimit' [X].
*)
-inline cic:/CoRN/metrics/CPMSTheory/MSComplete.con.
+inline "cic:/CoRN/metrics/CPMSTheory/MSComplete.con".
(*#*
A compact pseudo metric space is a pseudo metric space which is complete and
totally bounded.
*)
(*#*
A compact pseudo metric space is a pseudo metric space which is complete and
totally bounded.
*)
-inline cic:/CoRN/metrics/CPMSTheory/MSCompact.con.
+inline "cic:/CoRN/metrics/CPMSTheory/MSCompact.con".
(*#*
A subset $P$#<I>P</I># is %\emph{open}%#<I>open</I># if for all $x$#<I>x</I># in $P$#<I>P</I># there exists an open sphere
with centre $x$#<I>x</I># that is contained in $P$#<I>P</I>#.
*)
(*#*
A subset $P$#<I>P</I># is %\emph{open}%#<I>open</I># if for all $x$#<I>x</I># in $P$#<I>P</I># there exists an open sphere
with centre $x$#<I>x</I># that is contained in $P$#<I>P</I>#.
*)
-inline cic:/CoRN/metrics/CPMSTheory/open.con.
+inline "cic:/CoRN/metrics/CPMSTheory/open.con".
(* UNEXPORTED
Implicit Arguments open [X].
(* UNEXPORTED
Implicit Arguments open [X].
subspace $P$#<I>P</I># of $X$#<I>X</I>#.
*)
subspace $P$#<I>P</I># of $X$#<I>X</I>#.
*)
-inline cic:/CoRN/metrics/CPMSTheory/infima.con.
+inline "cic:/CoRN/metrics/CPMSTheory/infima.con".
(* UNEXPORTED
Implicit Arguments infima [X].
(* UNEXPORTED
Implicit Arguments infima [X].
all points that are in some sense close to $P$#<I>P</I>#.
*)
all points that are in some sense close to $P$#<I>P</I>#.
*)
-inline cic:/CoRN/metrics/CPMSTheory/well_contained.con.
+inline "cic:/CoRN/metrics/CPMSTheory/well_contained.con".
(* UNEXPORTED
End loc_and_bound.
(* UNEXPORTED
End loc_and_bound.
set "baseuri" "cic:/matita/CoRN-Decl/metrics/CPseudoMSpaces".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/CPseudoMSpaces".
(* $Id: CPseudoMSpaces.v,v 1.3 2004/04/23 10:01:02 lcf Exp $ *)
(* $Id: CPseudoMSpaces.v,v 1.3 2004/04/23 10:01:02 lcf Exp $ *)
-(* INCLUDE
-Intervals
-*)
+include "reals/Intervals.ma".
-inline cic:/CoRN/metrics/CPseudoMSpaces/A.var.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/A.var".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d.var.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/d.var".
(* UNEXPORTED
Set Implicit Arguments.
(* UNEXPORTED
Set Implicit Arguments.
Unset Strict Implicit.
*)
Unset Strict Implicit.
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/com.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/com.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/nneg.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/nneg.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/tri_ineq.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/tri_ineq.con".
(* UNEXPORTED
Set Strict Implicit.
(* UNEXPORTED
Set Strict Implicit.
Unset Implicit Arguments.
*)
Unset Implicit Arguments.
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/diag_zero.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con".
(* UNEXPORTED
End Relations.
(* UNEXPORTED
End Relations.
%''distance''% #"distance"#, a binairy function that fulfils certain properties.
*)
%''distance''% #"distance"#, a binairy function that fulfils certain properties.
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace.ind.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace.ind".
+
+inline "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace.ind".
-inline cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace.ind.
+coercion "cic:/matita/CoRN-Decl/metrics/CPseudoMSpaces/cms_crr.con" 0 (* compounds *).
(* UNEXPORTED
End Definition_PsMS0.
(* UNEXPORTED
End Definition_PsMS0.
-inline cic:/CoRN/metrics/CPseudoMSpaces/A.var.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/A.var".
-inline cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d_com.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/d_com.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d_nneg.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/d_nneg.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/d_pos_imp_ap.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con".
(* UNEXPORTED
End PsMS_axioms.
(* UNEXPORTED
End PsMS_axioms.
-inline cic:/CoRN/metrics/CPseudoMSpaces/Y.var.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/Y.var".
-inline cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con".
(*#*
Instead of taking [pos_imp_ap] as axiom,
we could as well have taken [diag_zero].
*)
(*#*
Instead of taking [pos_imp_ap] as axiom,
we could as well have taken [diag_zero].
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/diag_zero_imp_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero_imp_pos_imp_ap.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap_imp_diag_zero.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap_imp_diag_zero.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con".
(* UNEXPORTED
End PsMS_basics.
(* UNEXPORTED
End PsMS_basics.
a pseudo metric space.
*)
a pseudo metric space.
*)
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_strext.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_strext.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/Zero_fun.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/Zero_fun.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_com.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_com.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_nneg.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_nneg.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_pos_imp_ap.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_tri_ineq.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_tri_ineq.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zf_is_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zf_is_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/ContFunctions".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/ContFunctions".
(* $Id: ContFunctions.v,v 1.3 2004/04/23 10:01:02 lcf Exp $ *)
(* $Id: ContFunctions.v,v 1.3 2004/04/23 10:01:02 lcf Exp $ *)
-(* INCLUDE
-CPseudoMSpaces
-*)
+include "metrics/CPseudoMSpaces.ma".
(* UNEXPORTED
Section Continuous_functions.
(* UNEXPORTED
Section Continuous_functions.
-inline cic:/CoRN/metrics/ContFunctions/A.var.
+inline "cic:/CoRN/metrics/ContFunctions/A.var".
-inline cic:/CoRN/metrics/ContFunctions/B.var.
+inline "cic:/CoRN/metrics/ContFunctions/B.var".
(*#*
We will look at some notions of continuous functions.
*)
(*#*
We will look at some notions of continuous functions.
*)
-inline cic:/CoRN/metrics/ContFunctions/continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/continuous.con".
-inline cic:/CoRN/metrics/ContFunctions/continuous'.con.
+inline "cic:/CoRN/metrics/ContFunctions/continuous'.con".
-inline cic:/CoRN/metrics/ContFunctions/uni_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/uni_continuous.con".
-inline cic:/CoRN/metrics/ContFunctions/uni_continuous'.con.
+inline "cic:/CoRN/metrics/ContFunctions/uni_continuous'.con".
-inline cic:/CoRN/metrics/ContFunctions/uni_continuous''.con.
+inline "cic:/CoRN/metrics/ContFunctions/uni_continuous''.con".
-inline cic:/CoRN/metrics/ContFunctions/lipschitz.con.
+inline "cic:/CoRN/metrics/ContFunctions/lipschitz.con".
-inline cic:/CoRN/metrics/ContFunctions/lipschitz'.con.
+inline "cic:/CoRN/metrics/ContFunctions/lipschitz'.con".
(* UNEXPORTED
End Continuous_functions.
(* UNEXPORTED
End Continuous_functions.
-inline cic:/CoRN/metrics/ContFunctions/nexp_power.con.
+inline "cic:/CoRN/metrics/ContFunctions/nexp_power.con".
-inline cic:/CoRN/metrics/ContFunctions/continuous_imp_continuous'.con.
+inline "cic:/CoRN/metrics/ContFunctions/continuous_imp_continuous'.con".
-inline cic:/CoRN/metrics/ContFunctions/continuous'_imp_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/continuous'_imp_continuous.con".
-inline cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_uni_continuous'.con.
+inline "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_uni_continuous'.con".
-inline cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous.con".
-inline cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous''.con.
+inline "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous''.con".
-inline cic:/CoRN/metrics/ContFunctions/lipschitz_imp_lipschitz'.con.
+inline "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_lipschitz'.con".
-inline cic:/CoRN/metrics/ContFunctions/lipschitz'_imp_lipschitz.con.
+inline "cic:/CoRN/metrics/ContFunctions/lipschitz'_imp_lipschitz.con".
(*#*
Every uniformly continuous function is continuous and
every Lipschitz function is uniformly continuous.
*)
(*#*
Every uniformly continuous function is continuous and
every Lipschitz function is uniformly continuous.
*)
-inline cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_continuous.con".
-inline cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con".
(* UNEXPORTED
End Lemmas.
(* UNEXPORTED
End Lemmas.
Hence it is uniformly continuous and continuous.
*)
Hence it is uniformly continuous and continuous.
*)
-inline cic:/CoRN/metrics/ContFunctions/id_is_lipschitz.con.
+inline "cic:/CoRN/metrics/ContFunctions/id_is_lipschitz.con".
-inline cic:/CoRN/metrics/ContFunctions/id_is_uni_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/id_is_uni_continuous.con".
-inline cic:/CoRN/metrics/ContFunctions/id_is_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/id_is_continuous.con".
(* UNEXPORTED
End Identity.
(* UNEXPORTED
End Identity.
Hence it is uniformly continuous and continuous.
*)
Hence it is uniformly continuous and continuous.
*)
-inline cic:/CoRN/metrics/ContFunctions/B.var.
+inline "cic:/CoRN/metrics/ContFunctions/B.var".
-inline cic:/CoRN/metrics/ContFunctions/X.var.
+inline "cic:/CoRN/metrics/ContFunctions/X.var".
-inline cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con.
+inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con".
-inline cic:/CoRN/metrics/ContFunctions/const_fun_is_uni_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_uni_continuous.con".
-inline cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con".
(* UNEXPORTED
End Constant.
(* UNEXPORTED
End Constant.
again Lipschitz/uniformly continuous/continuous.
*)
again Lipschitz/uniformly continuous/continuous.
*)
-inline cic:/CoRN/metrics/ContFunctions/X.var.
+inline "cic:/CoRN/metrics/ContFunctions/X.var".
-inline cic:/CoRN/metrics/ContFunctions/B.var.
+inline "cic:/CoRN/metrics/ContFunctions/B.var".
-inline cic:/CoRN/metrics/ContFunctions/f.var.
+inline "cic:/CoRN/metrics/ContFunctions/f.var".
-inline cic:/CoRN/metrics/ContFunctions/C.var.
+inline "cic:/CoRN/metrics/ContFunctions/C.var".
-inline cic:/CoRN/metrics/ContFunctions/g.var.
+inline "cic:/CoRN/metrics/ContFunctions/g.var".
-inline cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con.
+inline "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con".
-inline cic:/CoRN/metrics/ContFunctions/comp_resp_uni_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/comp_resp_uni_continuous.con".
-inline cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con.
+inline "cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con".
(* UNEXPORTED
End Composition.
(* UNEXPORTED
End Composition.
-inline cic:/CoRN/metrics/ContFunctions/MSseqLimit.con.
+inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit.con".
(* UNEXPORTED
Implicit Arguments MSseqLimit [X].
*)
(* UNEXPORTED
Implicit Arguments MSseqLimit [X].
*)
-inline cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con.
+inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con".
(* UNEXPORTED
Implicit Arguments MSseqLimit' [X].
*)
(* UNEXPORTED
Implicit Arguments MSseqLimit' [X].
*)
-inline cic:/CoRN/metrics/ContFunctions/MSseqLimit_imp_MSseqLimit'.con.
+inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit_imp_MSseqLimit'.con".
-inline cic:/CoRN/metrics/ContFunctions/MSseqLimit'_imp_MSseqLimit.con.
+inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit'_imp_MSseqLimit.con".
-inline cic:/CoRN/metrics/ContFunctions/seqcontinuous'.con.
+inline "cic:/CoRN/metrics/ContFunctions/seqcontinuous'.con".
(* UNEXPORTED
Implicit Arguments seqcontinuous' [A B].
*)
(* UNEXPORTED
Implicit Arguments seqcontinuous' [A B].
*)
-inline cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con.
+inline "cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/Equiv".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/Equiv".
(* $Id: Equiv.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
(* $Id: Equiv.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
-(* INCLUDE
-IR_CPMSpace
-*)
+include "metrics/IR_CPMSpace.ma".
(* UNEXPORTED
Section equivalent.
(* UNEXPORTED
Section equivalent.
bijective, structure-preserving function between them.
*)
bijective, structure-preserving function between them.
*)
-inline cic:/CoRN/metrics/Equiv/equivalent_psmetric.con.
+inline "cic:/CoRN/metrics/Equiv/equivalent_psmetric.con".
-inline cic:/CoRN/metrics/Equiv/isopsmetry.con.
+inline "cic:/CoRN/metrics/Equiv/isopsmetry.con".
(* UNEXPORTED
Implicit Arguments isopsmetry [X Y].
*)
(* UNEXPORTED
Implicit Arguments isopsmetry [X Y].
*)
-inline cic:/CoRN/metrics/Equiv/isopsmetry_imp_bij.con.
+inline "cic:/CoRN/metrics/Equiv/isopsmetry_imp_bij.con".
-inline cic:/CoRN/metrics/Equiv/isopsmetry_imp_lipschitz.con.
+inline "cic:/CoRN/metrics/Equiv/isopsmetry_imp_lipschitz.con".
-inline cic:/CoRN/metrics/Equiv/id_is_isopsmetry.con.
+inline "cic:/CoRN/metrics/Equiv/id_is_isopsmetry.con".
-inline cic:/CoRN/metrics/Equiv/comp_resp_isopsmetry.con.
+inline "cic:/CoRN/metrics/Equiv/comp_resp_isopsmetry.con".
-inline cic:/CoRN/metrics/Equiv/inv_isopsmetry.con.
+inline "cic:/CoRN/metrics/Equiv/inv_isopsmetry.con".
-inline cic:/CoRN/metrics/Equiv/MSequivalent.con.
+inline "cic:/CoRN/metrics/Equiv/MSequivalent.con".
(*#*
Not all pseudo metric spaces are equivalent:
*)
(*#*
Not all pseudo metric spaces are equivalent:
*)
-inline cic:/CoRN/metrics/Equiv/MSequivalent_discr.con.
+inline "cic:/CoRN/metrics/Equiv/MSequivalent_discr.con".
(* UNEXPORTED
End equivalent.
(* UNEXPORTED
End equivalent.
set "baseuri" "cic:/matita/CoRN-Decl/metrics/IR_CPMSpace".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/IR_CPMSpace".
(* $Id: IR_CPMSpace.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
(* $Id: IR_CPMSpace.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
-(* INCLUDE
-ContFunctions
-*)
+include "metrics/ContFunctions.ma".
(* UNEXPORTED
Section Reals.
(* UNEXPORTED
Section Reals.
The real numbers with the usual distance form a pseudo metric space.
*)
The real numbers with the usual distance form a pseudo metric space.
*)
-inline cic:/CoRN/metrics/IR_CPMSpace/dIR.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_dIR.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_dIR.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/dIR_as_CSetoid_fun.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_as_CSetoid_fun.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/dIR_com.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_com.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/dIR_tri_ineq.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/dIR_tri_ineq.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/X.var.
+inline "cic:/CoRN/metrics/IR_CPMSpace/X.var".
-inline cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con".
(*#*
A pseudo metric is Lipschitz. Hence it is uniformly continuous and continuous.
*)
(*#*
A pseudo metric is Lipschitz. Hence it is uniformly continuous and continuous.
*)
-inline cic:/CoRN/metrics/IR_CPMSpace/d_is_lipschitz.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_lipschitz.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con".
Lipschitz/uniformly continuous/continuous.
*)
Lipschitz/uniformly continuous/continuous.
*)
-inline cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con".
-inline cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con.
+inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con".
(* UNEXPORTED
End Addition.
(* UNEXPORTED
End Addition.
set "baseuri" "cic:/matita/CoRN-Decl/metrics/Prod_Sub".
set "baseuri" "cic:/matita/CoRN-Decl/metrics/Prod_Sub".
(* $Id: Prod_Sub.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
(* $Id: Prod_Sub.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *)
-(* INCLUDE
-IR_CPMSpace
-*)
+include "metrics/IR_CPMSpace.ma".
(* UNEXPORTED
Section prodpsmetrics.
(* UNEXPORTED
Section prodpsmetrics.
$\RR^{2}$ #IR<SUP>2</SUP># out of the metric of $\RR$ #IR#.
*)
$\RR^{2}$ #IR<SUP>2</SUP># out of the metric of $\RR$ #IR#.
*)
-inline cic:/CoRN/metrics/Prod_Sub/dprod0.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dprod0.con".
-inline cic:/CoRN/metrics/Prod_Sub/dprod0_strext.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dprod0_strext.con".
-inline cic:/CoRN/metrics/Prod_Sub/d_prod0.con.
+inline "cic:/CoRN/metrics/Prod_Sub/d_prod0.con".
-inline cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con".
-inline cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con.
+inline "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con".
(* UNEXPORTED
End prodpsmetrics.
(* UNEXPORTED
End prodpsmetrics.
the pseudo metric on $X$ #X# restricted to $Y$ #Y#.
*)
the pseudo metric on $X$ #X# restricted to $Y$ #Y#.
*)
-inline cic:/CoRN/metrics/Prod_Sub/restr_bin_fun.con.
+inline "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun.con".
(* UNEXPORTED
Implicit Arguments restr_bin_fun [X].
*)
(* UNEXPORTED
Implicit Arguments restr_bin_fun [X].
*)
-inline cic:/CoRN/metrics/Prod_Sub/restr_bin_fun'.con.
+inline "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun'.con".
(* UNEXPORTED
Implicit Arguments restr_bin_fun' [X].
*)
(* UNEXPORTED
Implicit Arguments restr_bin_fun' [X].
*)
-inline cic:/CoRN/metrics/Prod_Sub/restr_bin_fun_strext.con.
+inline "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun_strext.con".
-inline cic:/CoRN/metrics/Prod_Sub/Build_SubCSetoid_bin_fun.con.
+inline "cic:/CoRN/metrics/Prod_Sub/Build_SubCSetoid_bin_fun.con".
-inline cic:/CoRN/metrics/Prod_Sub/dsub.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dsub.con".
(* UNEXPORTED
Implicit Arguments dsub [X].
*)
(* UNEXPORTED
Implicit Arguments dsub [X].
*)
-inline cic:/CoRN/metrics/Prod_Sub/dsub_com.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dsub_com.con".
-inline cic:/CoRN/metrics/Prod_Sub/dsub_nneg.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dsub_nneg.con".
-inline cic:/CoRN/metrics/Prod_Sub/dsub_pos_imp_ap.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dsub_pos_imp_ap.con".
-inline cic:/CoRN/metrics/Prod_Sub/dsub_tri_ineq.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dsub_tri_ineq.con".
-inline cic:/CoRN/metrics/Prod_Sub/is_SubPsMetricSpace.con.
+inline "cic:/CoRN/metrics/Prod_Sub/is_SubPsMetricSpace.con".
-inline cic:/CoRN/metrics/Prod_Sub/SubPsMetricSpace.con.
+inline "cic:/CoRN/metrics/Prod_Sub/SubPsMetricSpace.con".
(* UNEXPORTED
Implicit Arguments SubPsMetricSpace [X].
*)
(* UNEXPORTED
Implicit Arguments SubPsMetricSpace [X].
*)
-inline cic:/CoRN/metrics/Prod_Sub/from_SubPsMetricSpace.con.
+inline "cic:/CoRN/metrics/Prod_Sub/from_SubPsMetricSpace.con".
(*#*
The function [dsub'] is used in the definition of %''located''% #"located"#.
(*#*
The function [dsub'] is used in the definition of %''located''% #"located"#.
pseudo metric space and a certain subspace.
*)
pseudo metric space and a certain subspace.
*)
-inline cic:/CoRN/metrics/Prod_Sub/dsub'.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dsub'.con".
(* UNEXPORTED
Implicit Arguments dsub' [X].
*)
(* UNEXPORTED
Implicit Arguments dsub' [X].
*)
-inline cic:/CoRN/metrics/Prod_Sub/dsub'_strext.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dsub'_strext.con".
-inline cic:/CoRN/metrics/Prod_Sub/dsub'_as_cs_fun.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dsub'_as_cs_fun.con".
(* UNEXPORTED
Implicit Arguments dsub'_as_cs_fun [X].
*)
(* UNEXPORTED
Implicit Arguments dsub'_as_cs_fun [X].
*)
-inline cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con.
+inline "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con".
(* UNEXPORTED
End subpsmetrics.
(* UNEXPORTED
End subpsmetrics.
set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/QSposabgroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/QSposabgroup".
(* $Id: QSposabgroup.v,v 1.5 2004/04/08 08:20:31 lcf Exp $ *)
(* $Id: QSposabgroup.v,v 1.5 2004/04/08 08:20:31 lcf Exp $ *)
-(* INCLUDE
-QSposgroup
-*)
+include "model/groups/QSposgroup.ma".
-(* INCLUDE
-CAbGroups
-*)
+include "algebra/CAbGroups.ma".
(*#* **Example of an abelian group: $\langle$#⟨#[Qpos],$(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#$\rangle$#⟩#
The positive rational numbers form with the operation $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2# an abelian group.
*)
(*#* **Example of an abelian group: $\langle$#⟨#[Qpos],$(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#$\rangle$#⟩#
The positive rational numbers form with the operation $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2# an abelian group.
*)
-inline cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_is_CAbGroup.con.
+inline "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_is_CAbGroup.con".
-inline cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_as_CAbGroup.con.
+inline "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_as_CAbGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/Qabgroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/Qabgroup".
(* $Id: Qabgroup.v,v 1.5 2004/04/08 08:20:31 lcf Exp $ *)
(* $Id: Qabgroup.v,v 1.5 2004/04/08 08:20:31 lcf Exp $ *)
+include "model/groups/Qgroup.ma".
-(* INCLUDE
-CAbGroups
-*)
+include "algebra/CAbGroups.ma".
(*#* **Example of an abelian group: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
*)
(*#* **Example of an abelian group: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
*)
-inline cic:/CoRN/model/abgroups/Qabgroup/Q_is_CAbGroup.con.
+inline "cic:/CoRN/model/abgroups/Qabgroup/Q_is_CAbGroup.con".
-inline cic:/CoRN/model/abgroups/Qabgroup/Q_as_CAbGroup.con.
+inline "cic:/CoRN/model/abgroups/Qabgroup/Q_as_CAbGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/Qposabgroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/Qposabgroup".
(* $Id: Qposabgroup.v,v 1.6 2004/04/08 08:20:31 lcf Exp $ *)
(* $Id: Qposabgroup.v,v 1.6 2004/04/08 08:20:31 lcf Exp $ *)
-(* INCLUDE
-Qposgroup
-*)
+include "model/groups/Qposgroup.ma".
-(* INCLUDE
-CAbGroups
-*)
+include "algebra/CAbGroups.ma".
(*#* **Example of an abelian group: $\langle$#⟨#[Qpos],[[*]]$\rangle$#⟩#
The positive rationals form with the multiplication a CAbgroup.
*)
(*#* **Example of an abelian group: $\langle$#⟨#[Qpos],[[*]]$\rangle$#⟩#
The positive rationals form with the multiplication a CAbgroup.
*)
-inline cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_is_CAbGroup.con.
+inline "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_is_CAbGroup.con".
-inline cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_as_CAbGroup.con.
+inline "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_as_CAbGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/Zabgroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/Zabgroup".
(* $Id: Zabgroup.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *)
(* $Id: Zabgroup.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *)
+include "model/groups/Zgroup.ma".
-(* INCLUDE
-CAbGroups
-*)
+include "algebra/CAbGroups.ma".
(*#* **Example of an abelian group: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
*)
(*#* **Example of an abelian group: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
*)
-inline cic:/CoRN/model/abgroups/Zabgroup/Z_is_CAbGroup.con.
+inline "cic:/CoRN/model/abgroups/Zabgroup/Z_is_CAbGroup.con".
-inline cic:/CoRN/model/abgroups/Zabgroup/Z_as_CAbGroup.con.
+inline "cic:/CoRN/model/abgroups/Zabgroup/Z_as_CAbGroup.con".
(*#* The term [Z_as_CAbGroup] is of type [CAbGroup]. Hence we have proven that [Z] is a constructive Abelian group. *)
(*#* The term [Z_as_CAbGroup] is of type [CAbGroup]. Hence we have proven that [Z] is a constructive Abelian group. *)
set "baseuri" "cic:/matita/CoRN-Decl/model/fields/Qfield".
set "baseuri" "cic:/matita/CoRN-Decl/model/fields/Qfield".
(* $Id: Qfield.v,v 1.8 2004/04/08 08:20:32 lcf Exp $ *)
(* $Id: Qfield.v,v 1.8 2004/04/08 08:20:32 lcf Exp $ *)
+include "model/rings/Qring.ma".
+include "algebra/CFields.ma".
(*#* **Example of a field: $\langle$#⟨#[Q],[[+]],[[*]]$\rangle$#⟩#
As we have seen, there is a inverse for the multiplication for non-zeroes.
So, [Q] not only forms a ring, but even a field.
*)
(*#* **Example of a field: $\langle$#⟨#[Q],[[+]],[[*]]$\rangle$#⟩#
As we have seen, there is a inverse for the multiplication for non-zeroes.
So, [Q] not only forms a ring, but even a field.
*)
-inline cic:/CoRN/model/fields/Qfield/Q_is_CField.con.
+inline "cic:/CoRN/model/fields/Qfield/Q_is_CField.con".
-inline cic:/CoRN/model/fields/Qfield/Q_as_CField.con.
+inline "cic:/CoRN/model/fields/Qfield/Q_as_CField.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/groups/QSposgroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/groups/QSposgroup".
(* $Id: QSposgroup.v,v 1.6 2004/04/08 08:20:32 lcf Exp $ *)
(* $Id: QSposgroup.v,v 1.6 2004/04/08 08:20:32 lcf Exp $ *)
-(* INCLUDE
-QSposmonoid
-*)
+include "model/monoids/QSposmonoid.ma".
+include "algebra/CGroups.ma".
(*#* **Example of a group: $\langle$#⟨#[Qpos],$(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#$\rangle$#⟩#
The positive rationals form with the operation $(x,y) \mapsto xy/2$
#(x,y) ↦ xy/2# a CGroup.
*)
(*#* **Example of a group: $\langle$#⟨#[Qpos],$(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#$\rangle$#⟩#
The positive rationals form with the operation $(x,y) \mapsto xy/2$
#(x,y) ↦ xy/2# a CGroup.
*)
-inline cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_is_CGroup.con.
+inline "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_is_CGroup.con".
-inline cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_as_CGroup.con.
+inline "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_as_CGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/groups/Qgroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/groups/Qgroup".
(* $Id: Qgroup.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *)
(* $Id: Qgroup.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *)
+include "model/monoids/Qmonoid.ma".
+include "algebra/CGroups.ma".
(*#* **Example of a group: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
The rational numbers with addition form a group. The inverse function is taking the opposite.
*)
(*#* **Example of a group: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
The rational numbers with addition form a group. The inverse function is taking the opposite.
*)
-inline cic:/CoRN/model/groups/Qgroup/Q_is_CGroup.con.
+inline "cic:/CoRN/model/groups/Qgroup/Q_is_CGroup.con".
-inline cic:/CoRN/model/groups/Qgroup/Q_as_CGroup.con.
+inline "cic:/CoRN/model/groups/Qgroup/Q_as_CGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/groups/Qposgroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/groups/Qposgroup".
(* $Id: Qposgroup.v,v 1.6 2004/04/08 08:20:32 lcf Exp $ *)
(* $Id: Qposgroup.v,v 1.6 2004/04/08 08:20:32 lcf Exp $ *)
-(* INCLUDE
-Qposmonoid
-*)
+include "model/monoids/Qposmonoid.ma".
+include "algebra/CGroups.ma".
(*#* **Example of a group: $\langle$#⟨#[Qpos],[[*]]$\rangle$#⟩#
The positive rational numbers form a multiplicative group.
*)
(*#* **Example of a group: $\langle$#⟨#[Qpos],[[*]]$\rangle$#⟩#
The positive rational numbers form a multiplicative group.
*)
-inline cic:/CoRN/model/groups/Qposgroup/Qpos_is_CGroup.con.
+inline "cic:/CoRN/model/groups/Qposgroup/Qpos_is_CGroup.con".
-inline cic:/CoRN/model/groups/Qposgroup/Qpos_as_CGroup.con.
+inline "cic:/CoRN/model/groups/Qposgroup/Qpos_as_CGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/groups/Zgroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/groups/Zgroup".
(* $Id: Zgroup.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *)
(* $Id: Zgroup.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *)
+include "model/monoids/Zmonoid.ma".
+include "algebra/CGroups.ma".
(*#* **Example of a group: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
*)
(*#* **Example of a group: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
*)
-inline cic:/CoRN/model/groups/Zgroup/Z_is_CGroup.con.
+inline "cic:/CoRN/model/groups/Zgroup/Z_is_CGroup.con".
-inline cic:/CoRN/model/groups/Zgroup/Z_as_CGroup.con.
+inline "cic:/CoRN/model/groups/Zgroup/Z_as_CGroup.con".
(*#* The term [Z_as_CGroup] is of type [CGroup]. Hence we have proven that [Z] is a constructive group. *)
(*#* The term [Z_as_CGroup] is of type [CGroup]. Hence we have proven that [Z] is a constructive group. *)
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Nmonoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Nmonoid".
(* $Id: Nmonoid.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *)
(* $Id: Nmonoid.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *)
-(* INCLUDE
-Nsemigroup
-*)
+include "model/semigroups/Nsemigroup.ma".
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
(*#* **Example of a monoid: $\langle$#⟨#[nat],[[+]]$\rangle$#⟩#
Zero is an unit for the addition.
*)
(*#* **Example of a monoid: $\langle$#⟨#[nat],[[+]]$\rangle$#⟩#
Zero is an unit for the addition.
*)
-inline cic:/CoRN/model/monoids/Nmonoid/O_as_rht_unit.con.
+inline "cic:/CoRN/model/monoids/Nmonoid/O_as_rht_unit.con".
-inline cic:/CoRN/model/monoids/Nmonoid/O_as_lft_unit.con.
+inline "cic:/CoRN/model/monoids/Nmonoid/O_as_lft_unit.con".
-inline cic:/CoRN/model/monoids/Nmonoid/nat_is_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Nmonoid/nat_is_CMonoid.con".
(*#*
Whence we can define #<i>#%\emph{%the monoid of natural numbers%}%#</i>#:
*)
(*#*
Whence we can define #<i>#%\emph{%the monoid of natural numbers%}%#</i>#:
*)
-inline cic:/CoRN/model/monoids/Nmonoid/nat_as_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Nmonoid/nat_as_CMonoid.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Nposmonoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Nposmonoid".
(* $Id: Nposmonoid.v,v 1.6 2004/04/08 08:20:33 lcf Exp $ *)
(* $Id: Nposmonoid.v,v 1.6 2004/04/08 08:20:33 lcf Exp $ *)
-(* INCLUDE
-Npossemigroup
-*)
+include "model/semigroups/Npossemigroup.ma".
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
(*#* **Example of a monoid: $\langle$#⟨#[Npos],[[*]]$\rangle$#⟩#
One is the right unit as well as the left unit of the multiplication on the
positive natural numbers.
*)
(*#* **Example of a monoid: $\langle$#⟨#[Npos],[[*]]$\rangle$#⟩#
One is the right unit as well as the left unit of the multiplication on the
positive natural numbers.
*)
-inline cic:/CoRN/model/monoids/Nposmonoid/rhtunitNpos.con.
+inline "cic:/CoRN/model/monoids/Nposmonoid/rhtunitNpos.con".
-inline cic:/CoRN/model/monoids/Nposmonoid/lftunitNpos.con.
+inline "cic:/CoRN/model/monoids/Nposmonoid/lftunitNpos.con".
(*#* So, the positive natural numbers with multiplication form a CMonoid.
*)
(*#* So, the positive natural numbers with multiplication form a CMonoid.
*)
-inline cic:/CoRN/model/monoids/Nposmonoid/Nposmult_is_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_is_CMonoid.con".
-inline cic:/CoRN/model/monoids/Nposmonoid/Nposmult_as_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_as_CMonoid.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/QSposmonoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/QSposmonoid".
(* $Id: QSposmonoid.v,v 1.5 2004/04/08 08:20:33 lcf Exp $ *)
(* $Id: QSposmonoid.v,v 1.5 2004/04/08 08:20:33 lcf Exp $ *)
-(* INCLUDE
-QSpossemigroup
-*)
+include "model/semigroups/QSpossemigroup.ma".
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
(*#* **Example of a monoid: $\langle$#⟨#[Qpos],$(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#$\rangle$#⟩#
Two is the unit of the operation $(x,y) \mapsto xy/2$ #(x,y)
↦ xy/2# on the positive rationals. So we have another monoid structure on the positive rational numbers.
*)
(*#* **Example of a monoid: $\langle$#⟨#[Qpos],$(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#$\rangle$#⟩#
Two is the unit of the operation $(x,y) \mapsto xy/2$ #(x,y)
↦ xy/2# on the positive rationals. So we have another monoid structure on the positive rational numbers.
*)
-inline cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_rht_unit.con.
+inline "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_rht_unit.con".
-inline cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_lft_unit.con.
+inline "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_lft_unit.con".
-inline cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_is_CMonoid.con.
+inline "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_is_CMonoid.con".
-inline cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_as_CMonoid.con.
+inline "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_as_CMonoid.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Qmonoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Qmonoid".
(* $Id: Qmonoid.v,v 1.7 2004/04/08 08:20:33 lcf Exp $ *)
(* $Id: Qmonoid.v,v 1.7 2004/04/08 08:20:33 lcf Exp $ *)
-(* INCLUDE
-Qsemigroup
-*)
+include "model/semigroups/Qsemigroup.ma".
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
(*#* **Examples of a monoid: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
The rational numbers form with addition a CMonoid. [QZERO] is the unit.
*)
(*#* **Examples of a monoid: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
The rational numbers form with addition a CMonoid. [QZERO] is the unit.
*)
-inline cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_rht_unit3.con.
+inline "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_rht_unit3.con".
-inline cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_lft_unit3.con.
+inline "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_lft_unit3.con".
-inline cic:/CoRN/model/monoids/Qmonoid/Q_is_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Qmonoid/Q_is_CMonoid.con".
-inline cic:/CoRN/model/monoids/Qmonoid/Q_as_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Qmonoid/Q_as_CMonoid.con".
(*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
Also with multiplication Q forms a CMonoid. Here, the unit is [QONE].
*)
(*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
Also with multiplication Q forms a CMonoid. Here, the unit is [QONE].
*)
-inline cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_rht_unit.con.
+inline "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_rht_unit.con".
-inline cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_lft_unit.con.
+inline "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_lft_unit.con".
-inline cic:/CoRN/model/monoids/Qmonoid/Q_mul_is_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Qmonoid/Q_mul_is_CMonoid.con".
-inline cic:/CoRN/model/monoids/Qmonoid/Q_mul_as_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Qmonoid/Q_mul_as_CMonoid.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Qposmonoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Qposmonoid".
(* $Id: Qposmonoid.v,v 1.7 2004/04/08 08:20:33 lcf Exp $ *)
(* $Id: Qposmonoid.v,v 1.7 2004/04/08 08:20:33 lcf Exp $ *)
-(* INCLUDE
-Qpossemigroup
-*)
+include "model/semigroups/Qpossemigroup.ma".
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
(*#* **Example of a monoid: $\langle$#⟨#[Qpos],[[*]]$\rangle$#⟩#
One is the unit for multiplication on positive integers. Therefore the positive rational numbers together with the multiplication are a CMonoid.
*)
(*#* **Example of a monoid: $\langle$#⟨#[Qpos],[[*]]$\rangle$#⟩#
One is the unit for multiplication on positive integers. Therefore the positive rational numbers together with the multiplication are a CMonoid.
*)
-inline cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_rht_unit.con.
+inline "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_rht_unit.con".
-inline cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_lft_unit.con.
+inline "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_lft_unit.con".
-inline cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_is_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_is_CMonoid.con".
-inline cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_as_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_as_CMonoid.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Zmonoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Zmonoid".
(* $Id: Zmonoid.v,v 1.6 2004/04/08 08:20:33 lcf Exp $ *)
(* $Id: Zmonoid.v,v 1.6 2004/04/08 08:20:33 lcf Exp $ *)
-(* INCLUDE
-Zsemigroup
-*)
+include "model/semigroups/Zsemigroup.ma".
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
(*#* **Examples of monoids: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Z],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
(*#* **Examples of monoids: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Z],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
-inline cic:/CoRN/model/monoids/Zmonoid/ZERO_as_rht_unit.con.
+inline "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_rht_unit.con".
-inline cic:/CoRN/model/monoids/Zmonoid/ZERO_as_lft_unit.con.
+inline "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_lft_unit.con".
-inline cic:/CoRN/model/monoids/Zmonoid/Z_is_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Zmonoid/Z_is_CMonoid.con".
-inline cic:/CoRN/model/monoids/Zmonoid/Z_as_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Zmonoid/Z_as_CMonoid.con".
(*#* The term [Z_as_CMonoid] is of type [CMonoid]. Hence we have proven that [Z] is a constructive monoid.
(*#* The term [Z_as_CMonoid] is of type [CMonoid]. Hence we have proven that [Z] is a constructive monoid.
the representation we have for integers.
*)
the representation we have for integers.
*)
-inline cic:/CoRN/model/monoids/Zmonoid/ONE_as_rht_unit.con.
+inline "cic:/CoRN/model/monoids/Zmonoid/ONE_as_rht_unit.con".
-inline cic:/CoRN/model/monoids/Zmonoid/ONE_as_lft_unit.con.
+inline "cic:/CoRN/model/monoids/Zmonoid/ONE_as_lft_unit.con".
-inline cic:/CoRN/model/monoids/Zmonoid/Z_mul_is_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Zmonoid/Z_mul_is_CMonoid.con".
-inline cic:/CoRN/model/monoids/Zmonoid/Z_mul_as_CMonoid.con.
+inline "cic:/CoRN/model/monoids/Zmonoid/Z_mul_as_CMonoid.con".
(*#* The term [Z_mul_as_CMonoid] is another term of type [CMonoid]. *)
(*#* The term [Z_mul_as_CMonoid] is another term of type [CMonoid]. *)
set "baseuri" "cic:/matita/CoRN-Decl/model/non_examples/N_no_group".
set "baseuri" "cic:/matita/CoRN-Decl/model/non_examples/N_no_group".
(* $Id: N_no_group.v,v 1.5 2004/04/08 08:20:33 lcf Exp $ *)
(* $Id: N_no_group.v,v 1.5 2004/04/08 08:20:33 lcf Exp $ *)
+include "model/monoids/Nmonoid.ma".
+include "algebra/CGroups.ma".
(*#* **Non-example of a group: $\langle$#⟨#[nat],[[+]]$\rangle$#⟩#
There is no inverse function for the natural numbers with addition.
*)
(*#* **Non-example of a group: $\langle$#⟨#[nat],[[+]]$\rangle$#⟩#
There is no inverse function for the natural numbers with addition.
*)
-inline cic:/CoRN/model/non_examples/N_no_group/no_inverse_nat_plus.con.
+inline "cic:/CoRN/model/non_examples/N_no_group/no_inverse_nat_plus.con".
(*#* Hence they do not form a CGroup.
*)
(*#* Hence they do not form a CGroup.
*)
-inline cic:/CoRN/model/non_examples/N_no_group/no_group_nat_plus.con.
+inline "cic:/CoRN/model/non_examples/N_no_group/no_group_nat_plus.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/non_examples/Npos_no_group".
set "baseuri" "cic:/matita/CoRN-Decl/model/non_examples/Npos_no_group".
(* $Id: Npos_no_group.v,v 1.6 2004/04/08 08:20:33 lcf Exp $ *)
(* $Id: Npos_no_group.v,v 1.6 2004/04/08 08:20:33 lcf Exp $ *)
+include "algebra/CGroups.ma".
-(* INCLUDE
-Nposmonoid
-*)
+include "model/monoids/Nposmonoid.ma".
(*#* **Non-example of a group: $\langle$#⟨#[Npos],[[+]]$\rangle$#⟩#
There is no inverse for multiplication on the positive natural numbers.
*)
(*#* **Non-example of a group: $\langle$#⟨#[Npos],[[+]]$\rangle$#⟩#
There is no inverse for multiplication on the positive natural numbers.
*)
-inline cic:/CoRN/model/non_examples/Npos_no_group/no_inverse_Nposmult.con.
+inline "cic:/CoRN/model/non_examples/Npos_no_group/no_inverse_Nposmult.con".
(*#* Hence the natural numbers with multiplication do not form a group.
*)
(*#* Hence the natural numbers with multiplication do not form a group.
*)
-inline cic:/CoRN/model/non_examples/Npos_no_group/no_group_Nposmult.con.
+inline "cic:/CoRN/model/non_examples/Npos_no_group/no_group_Nposmult.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/non_examples/Npos_no_monoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/non_examples/Npos_no_monoid".
(* $Id: Npos_no_monoid.v,v 1.5 2004/04/08 08:20:34 lcf Exp $ *)
(* $Id: Npos_no_monoid.v,v 1.5 2004/04/08 08:20:34 lcf Exp $ *)
-(* INCLUDE
-Npossemigroup
-*)
+include "model/semigroups/Npossemigroup.ma".
-(* INCLUDE
-CMonoids
-*)
+include "algebra/CMonoids.ma".
(*#* **Non-example of a monoid: $\langle$#⟨#[Npos],[[+]]$\rangle$#⟩#
There is no right unit for the addition on the positive natural numbers.
*)
(*#* **Non-example of a monoid: $\langle$#⟨#[Npos],[[+]]$\rangle$#⟩#
There is no right unit for the addition on the positive natural numbers.
*)
-inline cic:/CoRN/model/non_examples/Npos_no_monoid/no_rht_unit_Npos.con.
+inline "cic:/CoRN/model/non_examples/Npos_no_monoid/no_rht_unit_Npos.con".
(*#* Therefore the set of positive natural numbers doesn't form a group with
addition.
*)
(*#* Therefore the set of positive natural numbers doesn't form a group with
addition.
*)
-inline cic:/CoRN/model/non_examples/Npos_no_monoid/no_monoid_Npos.con.
+inline "cic:/CoRN/model/non_examples/Npos_no_monoid/no_monoid_Npos.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/ordfields/Qordfield".
set "baseuri" "cic:/matita/CoRN-Decl/model/ordfields/Qordfield".
(* $Id: Qordfield.v,v 1.9 2004/04/23 10:01:03 lcf Exp $ *)
(* $Id: Qordfield.v,v 1.9 2004/04/23 10:01:03 lcf Exp $ *)
+include "model/fields/Qfield.ma".
-(* INCLUDE
-COrdFields
-*)
+include "algebra/COrdFields.ma".
(*#* **Example of an ordered field: $\langle$#⟨#[Q],[[+]],[[*]],[[<]]$\rangle$#⟩#
[Q] is an archemaedian ordered field.
*)
(*#* **Example of an ordered field: $\langle$#⟨#[Q],[[+]],[[*]],[[<]]$\rangle$#⟩#
[Q] is an archemaedian ordered field.
*)
-inline cic:/CoRN/model/ordfields/Qordfield/Qlt_is_strict_order.con.
+inline "cic:/CoRN/model/ordfields/Qordfield/Qlt_is_strict_order.con".
-inline cic:/CoRN/model/ordfields/Qordfield/Q_is_COrdField.con.
+inline "cic:/CoRN/model/ordfields/Qordfield/Q_is_COrdField.con".
-inline cic:/CoRN/model/ordfields/Qordfield/Q_as_COrdField.con.
+inline "cic:/CoRN/model/ordfields/Qordfield/Q_as_COrdField.con".
-inline cic:/CoRN/model/ordfields/Qordfield/Q_is_archemaedian.con.
+inline "cic:/CoRN/model/ordfields/Qordfield/Q_is_archemaedian.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/reals/Cauchy_IR".
set "baseuri" "cic:/matita/CoRN-Decl/model/reals/Cauchy_IR".
(* $Id: Cauchy_IR.v,v 1.2 2004/04/06 15:46:03 lcf Exp $ *)
(* $Id: Cauchy_IR.v,v 1.2 2004/04/06 15:46:03 lcf Exp $ *)
-(* INCLUDE
-Qordfield
-*)
+include "model/ordfields/Qordfield.ma".
-(* INCLUDE
-Cauchy_CReals
-*)
+include "reals/Cauchy_CReals.ma".
(*#* * Cauchy Real Numbers
Earlier we defined a construction of a real number structure from an
(*#* * Cauchy Real Numbers
Earlier we defined a construction of a real number structure from an
of the real numbers as Cauchy sequences of rationals.
*)
of the real numbers as Cauchy sequences of rationals.
*)
-inline cic:/CoRN/model/reals/Cauchy_IR/Cauchy_IR.con.
+inline "cic:/CoRN/model/reals/Cauchy_IR/Cauchy_IR.con".
(*#* The term [Cauchy_IR] is of type [CReals]. *)
(*#* The term [Cauchy_IR] is of type [CReals]. *)
set "baseuri" "cic:/matita/CoRN-Decl/model/rings/Qring".
set "baseuri" "cic:/matita/CoRN-Decl/model/rings/Qring".
(* $Id: Qring.v,v 1.8 2004/04/23 10:01:03 lcf Exp $ *)
(* $Id: Qring.v,v 1.8 2004/04/23 10:01:03 lcf Exp $ *)
-(* INCLUDE
-Qabgroup
-*)
+include "model/abgroups/Qabgroup.ma".
+include "algebra/CRings.ma".
+include "model/rings/Zring.ma".
(*#* **Example of a ring: $\langle$#⟨#[Q],[[+]],[[*]]$\rangle$#⟩#
Because [Q] forms an abelian group with addition, a monoid with
multiplication and it satisfies the distributive law, it is a ring.
*)
(*#* **Example of a ring: $\langle$#⟨#[Q],[[+]],[[*]]$\rangle$#⟩#
Because [Q] forms an abelian group with addition, a monoid with
multiplication and it satisfies the distributive law, it is a ring.
*)
-inline cic:/CoRN/model/rings/Qring/Q_mult_plus_is_dist.con.
+inline "cic:/CoRN/model/rings/Qring/Q_mult_plus_is_dist.con".
-inline cic:/CoRN/model/rings/Qring/Q_is_CRing.con.
+inline "cic:/CoRN/model/rings/Qring/Q_is_CRing.con".
-inline cic:/CoRN/model/rings/Qring/Q_as_CRing.con.
+inline "cic:/CoRN/model/rings/Qring/Q_as_CRing.con".
(*#* The following lemmas are used in the proof that [Q] is Archimeadian.
*)
(*#* The following lemmas are used in the proof that [Q] is Archimeadian.
*)
-inline cic:/CoRN/model/rings/Qring/injz_Nring.con.
-
-inline cic:/CoRN/model/rings/Qring/injZ_eq.con.
+inline "cic:/CoRN/model/rings/Qring/injz_Nring.con".
+inline "cic:/CoRN/model/rings/Qring/injZ_eq.con".
-inline cic:/CoRN/model/rings/Qring/nring_Q.con.
+inline "cic:/CoRN/model/rings/Qring/nring_Q.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/rings/Zring".
set "baseuri" "cic:/matita/CoRN-Decl/model/rings/Zring".
(* $Id: Zring.v,v 1.6 2004/04/08 08:20:34 lcf Exp $ *)
(* $Id: Zring.v,v 1.6 2004/04/08 08:20:34 lcf Exp $ *)
-(* INCLUDE
-Zabgroup
-*)
+include "model/abgroups/Zabgroup.ma".
+include "algebra/CRings.ma".
(*#* **Example of a ring: $\langle$#⟨#[Z],[[+]],[[*]]$\rangle$#⟩#
The multiplication and the addition are distributive.
*)
(*#* **Example of a ring: $\langle$#⟨#[Z],[[+]],[[*]]$\rangle$#⟩#
The multiplication and the addition are distributive.
*)
-inline cic:/CoRN/model/rings/Zring/Z_mult_plus_is_dist.con.
+inline "cic:/CoRN/model/rings/Zring/Z_mult_plus_is_dist.con".
-inline cic:/CoRN/model/rings/Zring/Z_is_CRing.con.
+inline "cic:/CoRN/model/rings/Zring/Z_is_CRing.con".
-inline cic:/CoRN/model/rings/Zring/Z_as_CRing.con.
+inline "cic:/CoRN/model/rings/Zring/Z_as_CRing.con".
(*#* The term [Z_as_CRing] is of type [CRing]. Hence we have proven that [Z] is a constructive ring. *)
(*#* The term [Z_as_CRing] is of type [CRing]. Hence we have proven that [Z] is a constructive ring. *)
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Npossemigroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Npossemigroup".
(* $Id: Npossemigroup.v,v 1.6 2004/04/08 08:20:34 lcf Exp $ *)
(* $Id: Npossemigroup.v,v 1.6 2004/04/08 08:20:34 lcf Exp $ *)
-(* INCLUDE
-CSemiGroups
-*)
+include "algebra/CSemiGroups.ma".
-(* INCLUDE
-Nsemigroup
-*)
+include "model/semigroups/Nsemigroup.ma".
-(* INCLUDE
-Npossetoid
-*)
+include "model/setoids/Npossetoid.ma".
(*#* **Examples of semi-groups: $\langle$#⟨#[Npos],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Npos],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Npos],[[+]]$\rangle$#⟩#
(*#* **Examples of semi-groups: $\langle$#⟨#[Npos],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Npos],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Npos],[[+]]$\rangle$#⟩#
of the semigroup of the natural numbers with addition.
*)
of the semigroup of the natural numbers with addition.
*)
-inline cic:/CoRN/model/semigroups/Npossemigroup/Npos_as_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/Npossemigroup/Npos_as_CSemiGroup.con".
(*#* ***$\langle$#⟨#[Npos],[[*]]$\rangle$#⟩#
Also together with multiplication, the positive numbers form a semigroup.
*)
(*#* ***$\langle$#⟨#[Npos],[[*]]$\rangle$#⟩#
Also together with multiplication, the positive numbers form a semigroup.
*)
-inline cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_is_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_is_CSemiGroup.con".
-inline cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_as_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_as_CSemiGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Nsemigroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Nsemigroup".
(* $Id: Nsemigroup.v,v 1.6 2004/04/08 08:20:34 lcf Exp $ *)
(* $Id: Nsemigroup.v,v 1.6 2004/04/08 08:20:34 lcf Exp $ *)
+include "model/setoids/Nsetoid.ma".
-(* INCLUDE
-CSemiGroups
-*)
+include "algebra/CSemiGroups.ma".
(*#* **Example of a semi-group: $\langle$#⟨#[nat],[[+]]$\rangle$#⟩#
*)
(*#* **Example of a semi-group: $\langle$#⟨#[nat],[[+]]$\rangle$#⟩#
*)
(*#* Because addition is associative, the natural numbers form a CSemiGroup.
*)
(*#* Because addition is associative, the natural numbers form a CSemiGroup.
*)
-inline cic:/CoRN/model/semigroups/Nsemigroup/nat_as_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/Nsemigroup/nat_as_CSemiGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/QSpossemigroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/QSpossemigroup".
(* $Id: QSpossemigroup.v,v 1.5 2004/04/08 08:20:35 lcf Exp $ *)
(* $Id: QSpossemigroup.v,v 1.5 2004/04/08 08:20:35 lcf Exp $ *)
-(* INCLUDE
-Qpossetoid
-*)
+include "model/setoids/Qpossetoid.ma".
-(* INCLUDE
-CSemiGroups
-*)
+include "algebra/CSemiGroups.ma".
(*#* **Example of a semi-group: $\langle$#⟨#[Qpos],$(x,y) \mapsto xy/2$#(x,y) ↦ xy/2#$\rangle$#⟩#
The positive rationals form with the operation
$(x,y) \mapsto xy/2$#(x,y) ↦ xy/2# a CSemiGroup.
*)
(*#* **Example of a semi-group: $\langle$#⟨#[Qpos],$(x,y) \mapsto xy/2$#(x,y) ↦ xy/2#$\rangle$#⟩#
The positive rationals form with the operation
$(x,y) \mapsto xy/2$#(x,y) ↦ xy/2# a CSemiGroup.
*)
-inline cic:/CoRN/model/semigroups/QSpossemigroup/Qpos_multdiv2_as_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/QSpossemigroup/Qpos_multdiv2_as_CSemiGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Qpossemigroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Qpossemigroup".
(* $Id: Qpossemigroup.v,v 1.6 2004/04/08 08:20:35 lcf Exp $ *)
(* $Id: Qpossemigroup.v,v 1.6 2004/04/08 08:20:35 lcf Exp $ *)
-(* INCLUDE
-Qpossetoid
-*)
+include "model/setoids/Qpossetoid.ma".
-(* INCLUDE
-CSemiGroups
-*)
+include "algebra/CSemiGroups.ma".
(*#* **Example of a semi-group: $\langle$#⟨#[Qpos],[[*]]$\rangle$#⟩#
The positive rationals form with the multiplication a CSemiGroup.
*)
(*#* **Example of a semi-group: $\langle$#⟨#[Qpos],[[*]]$\rangle$#⟩#
The positive rationals form with the multiplication a CSemiGroup.
*)
-inline cic:/CoRN/model/semigroups/Qpossemigroup/Qpos_mult_as_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/Qpossemigroup/Qpos_mult_as_CSemiGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Qsemigroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Qsemigroup".
(* $Id: Qsemigroup.v,v 1.6 2004/04/08 08:20:35 lcf Exp $ *)
(* $Id: Qsemigroup.v,v 1.6 2004/04/08 08:20:35 lcf Exp $ *)
+include "model/setoids/Qsetoid.ma".
-(* INCLUDE
-CSemiGroups
-*)
+include "algebra/CSemiGroups.ma".
(*#* **Examples of semi-groups: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
*)
(*#* **Examples of semi-groups: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
*)
-inline cic:/CoRN/model/semigroups/Qsemigroup/Q_as_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/Qsemigroup/Q_as_CSemiGroup.con".
(*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
*)
(*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
*)
-inline cic:/CoRN/model/semigroups/Qsemigroup/Q_mul_as_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/Qsemigroup/Q_mul_as_CSemiGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Zsemigroup".
set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Zsemigroup".
(* $Id: Zsemigroup.v,v 1.6 2004/04/08 08:20:35 lcf Exp $ *)
(* $Id: Zsemigroup.v,v 1.6 2004/04/08 08:20:35 lcf Exp $ *)
+include "model/setoids/Zsetoid.ma".
-(* INCLUDE
-CSemiGroups
-*)
+include "algebra/CSemiGroups.ma".
(*#* **Examples of semi-groups: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Z],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
*)
(*#* **Examples of semi-groups: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Z],[[*]]$\rangle$#⟩#
***$\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
*)
-inline cic:/CoRN/model/semigroups/Zsemigroup/Z_as_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/Zsemigroup/Z_as_CSemiGroup.con".
(*#* The term [Z_as_CSemiGroup] is of type [CSemiGroup]. Hence we have proven that [Z] is a constructive semi-group. *)
(*#* ***$\langle$#⟨#[Z],[[*]]$\rangle$#⟩#
*)
(*#* The term [Z_as_CSemiGroup] is of type [CSemiGroup]. Hence we have proven that [Z] is a constructive semi-group. *)
(*#* ***$\langle$#⟨#[Z],[[*]]$\rangle$#⟩#
*)
-inline cic:/CoRN/model/semigroups/Zsemigroup/Z_mul_as_CSemiGroup.con.
+inline "cic:/CoRN/model/semigroups/Zsemigroup/Z_mul_as_CSemiGroup.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Npossetoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Npossetoid".
(* $Id: Npossetoid.v,v 1.3 2004/04/06 15:46:04 lcf Exp $ *)
(* $Id: Npossetoid.v,v 1.3 2004/04/06 15:46:04 lcf Exp $ *)
+include "model/setoids/Nsetoid.ma".
+include "model/structures/Npossec.ma".
-(* INCLUDE
-CSetoidFun
-*)
+include "algebra/CSetoidFun.ma".
(*#* **Example of a setoid: [Npos]
(*#* **Example of a setoid: [Npos]
-inline cic:/CoRN/model/setoids/Npossetoid/Npos.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/Npos.con".
-inline cic:/CoRN/model/setoids/Npossetoid/NposP.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/NposP.con".
(*#* One and two are elements of it.
*)
(*#* One and two are elements of it.
*)
-inline cic:/CoRN/model/setoids/Npossetoid/ONEpos.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/ONEpos.con".
-inline cic:/CoRN/model/setoids/Npossetoid/TWOpos.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/TWOpos.con".
(*#* ***Addition and multiplication
Because addition and multiplication preserve positivity, we can define
them on this subsetoid.
*)
(*#* ***Addition and multiplication
Because addition and multiplication preserve positivity, we can define
them on this subsetoid.
*)
-inline cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con".
-inline cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con".
-inline cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con".
-inline cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con".
(*#* The addition has no right unit on this set.
*)
(*#* The addition has no right unit on this set.
*)
-inline cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con".
(*#* And the multiplication doesn't have an inverse, because there can't be an
inverse for 2.
*)
(*#* And the multiplication doesn't have an inverse, because there can't be an
inverse for 2.
*)
-inline cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con.
+inline "cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Nsetoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Nsetoid".
(* $Id: Nsetoid.v,v 1.4 2004/04/06 15:46:04 lcf Exp $ *)
(* $Id: Nsetoid.v,v 1.4 2004/04/06 15:46:04 lcf Exp $ *)
+include "model/structures/Nsec.ma".
-(* INCLUDE
-CSetoidFun
-*)
+include "algebra/CSetoidFun.ma".
(*#* **Example of a setoid: [nat]
We will show that the natural numbers form a CSetoid.
*)
(*#* **Example of a setoid: [nat]
We will show that the natural numbers form a CSetoid.
*)
-inline cic:/CoRN/model/setoids/Nsetoid/ap_nat_irreflexive.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_irreflexive.con".
-inline cic:/CoRN/model/setoids/Nsetoid/ap_nat_symmetric.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_symmetric.con".
-inline cic:/CoRN/model/setoids/Nsetoid/ap_nat_cotransitive.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_cotransitive.con".
-inline cic:/CoRN/model/setoids/Nsetoid/ap_nat_tight.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_tight.con".
-inline cic:/CoRN/model/setoids/Nsetoid/ap_nat_is_apartness.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/ap_nat_is_apartness.con".
-inline cic:/CoRN/model/setoids/Nsetoid/nat_as_CSetoid.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/nat_as_CSetoid.con".
-inline cic:/CoRN/model/setoids/Nsetoid/plus_wd.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/plus_wd.con".
-inline cic:/CoRN/model/setoids/Nsetoid/plus_strext.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/plus_strext.con".
-inline cic:/CoRN/model/setoids/Nsetoid/plus_is_bin_fun.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/plus_is_bin_fun.con".
(*#* It is associative and commutative.
*)
(*#* It is associative and commutative.
*)
-inline cic:/CoRN/model/setoids/Nsetoid/plus_is_assoc.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/plus_is_assoc.con".
-inline cic:/CoRN/model/setoids/Nsetoid/plus_is_commut.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/plus_is_commut.con".
(*#* ***Multiplication
*)
(*#* ***Multiplication
*)
-inline cic:/CoRN/model/setoids/Nsetoid/mult_strext.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/mult_strext.con".
-inline cic:/CoRN/model/setoids/Nsetoid/mult_as_bin_fun.con.
+inline "cic:/CoRN/model/setoids/Nsetoid/mult_as_bin_fun.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Qpossetoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Qpossetoid".
(* $Id: Qpossetoid.v,v 1.4 2004/04/06 15:46:05 lcf Exp $ *)
(* $Id: Qpossetoid.v,v 1.4 2004/04/06 15:46:05 lcf Exp $ *)
+include "model/setoids/Qsetoid.ma".
-(* INCLUDE
-CSetoidFun
-*)
+include "algebra/CSetoidFun.ma".
+include "model/structures/Qpossec.ma".
(*#* **Example of a setoid: [Qpos]
***Setoid
(*#* **Example of a setoid: [Qpos]
***Setoid
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/QposP.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/QposP.con".
(*#* One, two and four are elements of it.
*)
(*#* One, two and four are elements of it.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con".
(*#* ***Multiplication
As we have seen, multiplication preserves positivity, so we can restrict it
(*#* ***Multiplication
As we have seen, multiplication preserves positivity, so we can restrict it
-inline cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con".
(*#* ***Inverse
We restrict the domain of the inverse to the set of positive rationals.
*)
(*#* ***Inverse
We restrict the domain of the inverse to the set of positive rationals.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con".
(*#* The restricted inverse preserves positivity.
*)
(*#* The restricted inverse preserves positivity.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con".
(*#* Now, we can also restrict the co-domain.
*)
(*#* Now, we can also restrict the co-domain.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con".
(*#* This restricted inverse map appears a setoid function.
*)
(*#* This restricted inverse map appears a setoid function.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con".
(*#* ***Special multiplication and inverse
We define [multdiv2]: $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#.
*)
(*#* ***Special multiplication and inverse
We define [multdiv2]: $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con".
(*#* And its inverse [multdiv4]: $x \mapsto 4/x$ #x ↦ 4/x#.
*)
(*#* And its inverse [multdiv4]: $x \mapsto 4/x$ #x ↦ 4/x#.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/mult4.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/mult4.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/divmult4.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/divmult4.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Qsetoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Qsetoid".
(* $Id: Qsetoid.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
(* $Id: Qsetoid.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
+include "model/structures/Qsec.ma".
-(* INCLUDE
-CSetoidFun
-*)
+include "algebra/CSetoidFun.ma".
(*#* **Example of a setoid: [Q]
***Setoid
*)
(*#* **Example of a setoid: [Q]
***Setoid
*)
-inline cic:/CoRN/model/setoids/Qsetoid/ap_Q_irreflexive1.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/ap_Q_irreflexive1.con".
-inline cic:/CoRN/model/setoids/Qsetoid/ap_Q_symmetric1.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/ap_Q_symmetric1.con".
-inline cic:/CoRN/model/setoids/Qsetoid/ap_Q_cotransitive1.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/ap_Q_cotransitive1.con".
-inline cic:/CoRN/model/setoids/Qsetoid/ap_Q_tight1.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/ap_Q_tight1.con".
-inline cic:/CoRN/model/setoids/Qsetoid/ap_Q_is_apartness.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/ap_Q_is_apartness.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Q_as_CSetoid.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Q_as_CSetoid.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qplus_wd.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qplus_wd.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qplus_strext1.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qplus_strext1.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qplus_is_bin_fun.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_bin_fun.con".
(*#* It is associative and commutative.
*)
(*#* It is associative and commutative.
*)
-inline cic:/CoRN/model/setoids/Qsetoid/Qplus_is_assoc.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_assoc.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qplus_is_commut1.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_commut1.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qopp_wd.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qopp_wd.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qopp_strext.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qopp_strext.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qopp_is_fun.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qopp_is_fun.con".
(*#* ***Multiplication
*)
(*#* ***Multiplication
*)
-inline cic:/CoRN/model/setoids/Qsetoid/Qmult_wd.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qmult_wd.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qmult_strext1.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qmult_strext1.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qmult_is_bin_fun.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_bin_fun.con".
(*#* It is associative and commutative.
*)
(*#* It is associative and commutative.
*)
-inline cic:/CoRN/model/setoids/Qsetoid/Qmult_is_assoc.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_assoc.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qmult_is_commut.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_commut.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qlt_strext.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qlt_strext.con".
-inline cic:/CoRN/model/setoids/Qsetoid/Qlt_is_CSetoid_relation.con.
+inline "cic:/CoRN/model/setoids/Qsetoid/Qlt_is_CSetoid_relation.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Zsetoid".
set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Zsetoid".
(* $Id: Zsetoid.v,v 1.5 2004/04/07 15:08:08 lcf Exp $ *)
(* $Id: Zsetoid.v,v 1.5 2004/04/07 15:08:08 lcf Exp $ *)
+include "model/structures/Zsec.ma".
-(* INCLUDE
-CSetoidFun
-*)
+include "algebra/CSetoidFun.ma".
(*#* **Example of a setoid: [Z]
*** [Z]
*)
(*#* **Example of a setoid: [Z]
*** [Z]
*)
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_irreflexive.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_irreflexive.con".
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.con".
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_cotransitive.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_cotransitive.con".
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.con".
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_is_apartness.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_is_apartness.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.con".
(*#* The term [Z_as_CSetoid] is of type [CSetoid]. Hence we have proven that [Z] is a constructive setoid.
***Addition
We will prove now that the addition on the integers is a setoid function.
*)
(*#* The term [Z_as_CSetoid] is of type [CSetoid]. Hence we have proven that [Z] is a constructive setoid.
***Addition
We will prove now that the addition on the integers is a setoid function.
*)
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_wd.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_wd.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.con".
(*#* What's more: the addition is also associative and commutative.
*)
(*#* What's more: the addition is also associative and commutative.
*)
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_is_assoc.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_assoc.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.con".
(*#* ***Opposite
Taking the opposite of an integer is a setoid function.
*)
(*#* ***Opposite
Taking the opposite of an integer is a setoid function.
*)
-inline cic:/CoRN/model/setoids/Zsetoid/Zopp_wd.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_wd.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.con".
(*#* ***Multiplication
Finally the multiplication is a setoid function and is associative and commutative.
*)
(*#* ***Multiplication
Finally the multiplication is a setoid function and is associative and commutative.
*)
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_wd.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_wd.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_is_bin_fun.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_bin_fun.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Npossec".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Npossec".
(* $Id: Npossec.v,v 1.3 2004/04/06 15:46:05 lcf Exp $ *)
(*#* printing Npos $\mathbb{N}^{+}$ #N<SUP>+</SUP># *)
(* $Id: Npossec.v,v 1.3 2004/04/06 15:46:05 lcf Exp $ *)
(*#* printing Npos $\mathbb{N}^{+}$ #N<SUP>+</SUP># *)
-(* INCLUDE
-Nsec
-*)
-
-(* INCLUDE
-Arith
-*)
+include "model/structures/Nsec.ma".
(*#* **[Npos]
The positive natural numbers have some nice properties. Addition as well
as multiplication preserve the feature of being positive.
*)
(*#* **[Npos]
The positive natural numbers have some nice properties. Addition as well
as multiplication preserve the feature of being positive.
*)
-inline cic:/CoRN/model/structures/Npossec/plus_resp_Npos0.con.
+inline "cic:/CoRN/model/structures/Npossec/plus_resp_Npos0.con".
-inline cic:/CoRN/model/structures/Npossec/Npos_is_suc.con.
+inline "cic:/CoRN/model/structures/Npossec/Npos_is_suc.con".
-inline cic:/CoRN/model/structures/Npossec/mult_resp_Npos0.con.
+inline "cic:/CoRN/model/structures/Npossec/mult_resp_Npos0.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Nsec".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Nsec".
(* $Id: Nsec.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
(*#* printing {#N} $\ensuremath{\mathrel\#_{\mathbb N}}$ *)
(* $Id: Nsec.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
(*#* printing {#N} $\ensuremath{\mathrel\#_{\mathbb N}}$ *)
-(* INCLUDE
-Peano_dec
-*)
-
-(* INCLUDE
-Relations
-*)
-
-(* INCLUDE
-CLogic
-*)
+include "algebra/CLogic.ma".
(*#* *[nat]
**About [nat]
(*#* *[nat]
**About [nat]
A variant of [0_S] from the standard library
*)
A variant of [0_S] from the standard library
*)
-inline cic:/CoRN/model/structures/Nsec/S_O.con.
+inline "cic:/CoRN/model/structures/Nsec/S_O.con".
-inline cic:/CoRN/model/structures/Nsec/ap_nat.con.
+inline "cic:/CoRN/model/structures/Nsec/ap_nat.con".
-inline cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con.
+inline "cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con".
-inline cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con.
+inline "cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con".
-inline cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con.
+inline "cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con".
-inline cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con.
+inline "cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con".
-inline cic:/CoRN/model/structures/Nsec/plus_strext0.con.
+inline "cic:/CoRN/model/structures/Nsec/plus_strext0.con".
(*#* There is no inverse for addition, because every candidate will fail for 2
*)
(*#* There is no inverse for addition, because every candidate will fail for 2
*)
-inline cic:/CoRN/model/structures/Nsec/no_inverse0.con.
+inline "cic:/CoRN/model/structures/Nsec/no_inverse0.con".
(*#* ***Multiplication
*)
(*#* ***Multiplication
*)
-inline cic:/CoRN/model/structures/Nsec/mult_strext0.con.
+inline "cic:/CoRN/model/structures/Nsec/mult_strext0.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Qpossec".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Qpossec".
(* $Id: Qpossec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
(*#* printing Qpos $\mathbb{Q}^{+}$ #Q<SUP>+</SUP># *)
(* $Id: Qpossec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
(*#* printing Qpos $\mathbb{Q}^{+}$ #Q<SUP>+</SUP># *)
+include "model/structures/Qsec.ma".
+include "algebra/CLogic.ma".
(*#* **About [Qpos]
We will prove some lemmas concerning rationals bigger than 0.
(*#* **About [Qpos]
We will prove some lemmas concerning rationals bigger than 0.
One, two and four are all bigger than zero.
*)
One, two and four are all bigger than zero.
*)
-inline cic:/CoRN/model/structures/Qpossec/pos_QONE.con.
+inline "cic:/CoRN/model/structures/Qpossec/pos_QONE.con".
-inline cic:/CoRN/model/structures/Qpossec/pos_QTWO.con.
+inline "cic:/CoRN/model/structures/Qpossec/pos_QTWO.con".
-inline cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con.
+inline "cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con".
(*#* A positive rational is not zero.
*)
(*#* A positive rational is not zero.
*)
-inline cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con.
+inline "cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con".
(*#* ***Multiplication
The product of two positive rationals is again positive.
*)
(*#* ***Multiplication
The product of two positive rationals is again positive.
*)
-inline cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con.
+inline "cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con".
(*#* ***Inverse
The inverse of a positive rational is again positive.
*)
(*#* ***Inverse
The inverse of a positive rational is again positive.
*)
-inline cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con.
+inline "cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con".
(*#* ***Special multiplication
Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y)
(*#* ***Special multiplication
Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y)
\mapsto 4/x$ #x ↦ 4/x#.
*)
\mapsto 4/x$ #x ↦ 4/x#.
*)
-inline cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con.
+inline "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con".
-inline cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con.
+inline "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con".
-inline cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con.
+inline "cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Qsec".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Qsec".
(* $Id: Qsec.v,v 1.7 2004/04/08 08:20:35 lcf Exp $ *)
(*#* printing Q %\ensuremath{\mathbb{Q}}% *)
(* $Id: Qsec.v,v 1.7 2004/04/08 08:20:35 lcf Exp $ *)
(*#* printing Q %\ensuremath{\mathbb{Q}}% *)
(*#* printing QFOUR %\ensuremath{4_\mathbb{Q}}% #4<sub>Q</sub># *)
(*#* printing QFOUR %\ensuremath{4_\mathbb{Q}}% #4<sub>Q</sub># *)
-(* INCLUDE
-CLogic
-*)
-
-(* INCLUDE
-Arith
-*)
-
-(* INCLUDE
-Peano_dec
-*)
+include "algebra/CLogic.ma".
+include "model/structures/Zsec.ma".
-inline cic:/CoRN/model/structures/Qsec/Q.ind.
+inline "cic:/CoRN/model/structures/Qsec/Q.ind".
-inline cic:/CoRN/model/structures/Qsec/Qeq.con.
+inline "cic:/CoRN/model/structures/Qsec/Qeq.con".
-inline cic:/CoRN/model/structures/Qsec/Qap.con.
+inline "cic:/CoRN/model/structures/Qsec/Qap.con".
-inline cic:/CoRN/model/structures/Qsec/Qlt.con.
+inline "cic:/CoRN/model/structures/Qsec/Qlt.con".
-inline cic:/CoRN/model/structures/Qsec/Qplus.con.
+inline "cic:/CoRN/model/structures/Qsec/Qplus.con".
-inline cic:/CoRN/model/structures/Qsec/Qmult.con.
+inline "cic:/CoRN/model/structures/Qsec/Qmult.con".
-inline cic:/CoRN/model/structures/Qsec/Qopp.con.
+inline "cic:/CoRN/model/structures/Qsec/Qopp.con".
-inline cic:/CoRN/model/structures/Qsec/QZERO.con.
+inline "cic:/CoRN/model/structures/Qsec/QZERO.con".
-inline cic:/CoRN/model/structures/Qsec/QONE.con.
+inline "cic:/CoRN/model/structures/Qsec/QONE.con".
-inline cic:/CoRN/model/structures/Qsec/Qinv.con.
+inline "cic:/CoRN/model/structures/Qsec/Qinv.con".
-inline cic:/CoRN/model/structures/Qsec/QTWO.con.
+inline "cic:/CoRN/model/structures/Qsec/QTWO.con".
-inline cic:/CoRN/model/structures/Qsec/QFOUR.con.
+inline "cic:/CoRN/model/structures/Qsec/QFOUR.con".
(*#* ***Equality
Here we prove that [QONE] is #<i>#%\emph{%not equal%}%#</i># to [QZERO]:
*)
(*#* ***Equality
Here we prove that [QONE] is #<i>#%\emph{%not equal%}%#</i># to [QZERO]:
*)
-inline cic:/CoRN/model/structures/Qsec/ONEQ_neq_ZEROQ.con.
+inline "cic:/CoRN/model/structures/Qsec/ONEQ_neq_ZEROQ.con".
-inline cic:/CoRN/model/structures/Qsec/refl_Qeq.con.
+inline "cic:/CoRN/model/structures/Qsec/refl_Qeq.con".
-inline cic:/CoRN/model/structures/Qsec/sym_Qeq.con.
+inline "cic:/CoRN/model/structures/Qsec/sym_Qeq.con".
-inline cic:/CoRN/model/structures/Qsec/trans_Qeq.con.
+inline "cic:/CoRN/model/structures/Qsec/trans_Qeq.con".
(*#*
The equality is decidable:
*)
(*#*
The equality is decidable:
*)
-inline cic:/CoRN/model/structures/Qsec/dec_Qeq.con.
+inline "cic:/CoRN/model/structures/Qsec/dec_Qeq.con".
-inline cic:/CoRN/model/structures/Qsec/Q_non_zero.con.
+inline "cic:/CoRN/model/structures/Qsec/Q_non_zero.con".
-inline cic:/CoRN/model/structures/Qsec/ap_Q_irreflexive0.con.
+inline "cic:/CoRN/model/structures/Qsec/ap_Q_irreflexive0.con".
-inline cic:/CoRN/model/structures/Qsec/ap_Q_symmetric0.con.
+inline "cic:/CoRN/model/structures/Qsec/ap_Q_symmetric0.con".
-inline cic:/CoRN/model/structures/Qsec/ap_Q_cotransitive0.con.
+inline "cic:/CoRN/model/structures/Qsec/ap_Q_cotransitive0.con".
-inline cic:/CoRN/model/structures/Qsec/ap_Q_tight0.con.
+inline "cic:/CoRN/model/structures/Qsec/ap_Q_tight0.con".
-inline cic:/CoRN/model/structures/Qsec/Qplus_simpl.con.
+inline "cic:/CoRN/model/structures/Qsec/Qplus_simpl.con".
(*#*
Addition is associative:
*)
(*#*
Addition is associative:
*)
-inline cic:/CoRN/model/structures/Qsec/Qplus_assoc.con.
+inline "cic:/CoRN/model/structures/Qsec/Qplus_assoc.con".
(*#*
[QZERO] as the neutral element for addition:
*)
(*#*
[QZERO] as the neutral element for addition:
*)
-inline cic:/CoRN/model/structures/Qsec/QZERO_right.con.
+inline "cic:/CoRN/model/structures/Qsec/QZERO_right.con".
(*#*
Commutativity of addition:
*)
(*#*
Commutativity of addition:
*)
-inline cic:/CoRN/model/structures/Qsec/Qplus_sym.con.
+inline "cic:/CoRN/model/structures/Qsec/Qplus_sym.con".
-inline cic:/CoRN/model/structures/Qsec/Qplus_strext0.con.
+inline "cic:/CoRN/model/structures/Qsec/Qplus_strext0.con".
-inline cic:/CoRN/model/structures/Qsec/ZEROQ_as_rht_unit0.con.
+inline "cic:/CoRN/model/structures/Qsec/ZEROQ_as_rht_unit0.con".
-inline cic:/CoRN/model/structures/Qsec/ZEROQ_as_lft_unit0.con.
+inline "cic:/CoRN/model/structures/Qsec/ZEROQ_as_lft_unit0.con".
-inline cic:/CoRN/model/structures/Qsec/Qplus_is_commut0.con.
+inline "cic:/CoRN/model/structures/Qsec/Qplus_is_commut0.con".
(*#* ***Opposite
[{-Q}] is a well defined unary operation:
*)
(*#* ***Opposite
[{-Q}] is a well defined unary operation:
*)
-inline cic:/CoRN/model/structures/Qsec/Qopp_simpl.con.
+inline "cic:/CoRN/model/structures/Qsec/Qopp_simpl.con".
(*#*
The group equation for [{-Q}]
*)
(*#*
The group equation for [{-Q}]
*)
-inline cic:/CoRN/model/structures/Qsec/Qplus_inverse_r.con.
+inline "cic:/CoRN/model/structures/Qsec/Qplus_inverse_r.con".
(*#* ***Multiplication
Next we shall prove the properties of multiplication. First we prove
that [{*Q}] is well-defined
*)
(*#* ***Multiplication
Next we shall prove the properties of multiplication. First we prove
that [{*Q}] is well-defined
*)
-inline cic:/CoRN/model/structures/Qsec/Qmult_simpl.con.
+inline "cic:/CoRN/model/structures/Qsec/Qmult_simpl.con".
(*#*
and it is associative:
*)
(*#*
and it is associative:
*)
-inline cic:/CoRN/model/structures/Qsec/Qmult_assoc.con.
+inline "cic:/CoRN/model/structures/Qsec/Qmult_assoc.con".
(*#*
[QONE] is the neutral element for multiplication:
*)
(*#*
[QONE] is the neutral element for multiplication:
*)
-inline cic:/CoRN/model/structures/Qsec/Qmult_n_1.con.
+inline "cic:/CoRN/model/structures/Qsec/Qmult_n_1.con".
(*#*
The commutativity for [{*Q}]:
*)
(*#*
The commutativity for [{*Q}]:
*)
-inline cic:/CoRN/model/structures/Qsec/Qmult_sym.con.
+inline "cic:/CoRN/model/structures/Qsec/Qmult_sym.con".
-inline cic:/CoRN/model/structures/Qsec/Qmult_plus_distr_r.con.
+inline "cic:/CoRN/model/structures/Qsec/Qmult_plus_distr_r.con".
(*#*
And a property of multiplication which says if [x [~=] Zero] and [xy [=] Zero] then [y [=] Zero]:
*)
(*#*
And a property of multiplication which says if [x [~=] Zero] and [xy [=] Zero] then [y [=] Zero]:
*)
-inline cic:/CoRN/model/structures/Qsec/Qmult_eq.con.
+inline "cic:/CoRN/model/structures/Qsec/Qmult_eq.con".
-inline cic:/CoRN/model/structures/Qsec/Qmult_strext0.con.
+inline "cic:/CoRN/model/structures/Qsec/Qmult_strext0.con".
-inline cic:/CoRN/model/structures/Qsec/nonZero.con.
+inline "cic:/CoRN/model/structures/Qsec/nonZero.con".
-inline cic:/CoRN/model/structures/Qsec/Qinv_strext.con.
+inline "cic:/CoRN/model/structures/Qsec/Qinv_strext.con".
-inline cic:/CoRN/model/structures/Qsec/Qinv_is_inv.con.
+inline "cic:/CoRN/model/structures/Qsec/Qinv_is_inv.con".
-inline cic:/CoRN/model/structures/Qsec/Qlt_wd_right.con.
+inline "cic:/CoRN/model/structures/Qsec/Qlt_wd_right.con".
-inline cic:/CoRN/model/structures/Qsec/Qlt_wd_left.con.
+inline "cic:/CoRN/model/structures/Qsec/Qlt_wd_left.con".
-inline cic:/CoRN/model/structures/Qsec/Qlt_eq_gt_dec.con.
+inline "cic:/CoRN/model/structures/Qsec/Qlt_eq_gt_dec.con".
-inline cic:/CoRN/model/structures/Qsec/Qlt_is_transitive_unfolded.con.
+inline "cic:/CoRN/model/structures/Qsec/Qlt_is_transitive_unfolded.con".
-inline cic:/CoRN/model/structures/Qsec/Qlt_strext_unfolded.con.
+inline "cic:/CoRN/model/structures/Qsec/Qlt_strext_unfolded.con".
-inline cic:/CoRN/model/structures/Qsec/Qlt_is_irreflexive_unfolded.con.
+inline "cic:/CoRN/model/structures/Qsec/Qlt_is_irreflexive_unfolded.con".
-inline cic:/CoRN/model/structures/Qsec/Qlt_is_antisymmetric_unfolded.con.
+inline "cic:/CoRN/model/structures/Qsec/Qlt_is_antisymmetric_unfolded.con".
-inline cic:/CoRN/model/structures/Qsec/Qplus_resp_Qlt.con.
+inline "cic:/CoRN/model/structures/Qsec/Qplus_resp_Qlt.con".
-inline cic:/CoRN/model/structures/Qsec/Qmult_resp_pos_Qlt.con.
+inline "cic:/CoRN/model/structures/Qsec/Qmult_resp_pos_Qlt.con".
-inline cic:/CoRN/model/structures/Qsec/Qlt_gives_apartness.con.
+inline "cic:/CoRN/model/structures/Qsec/Qlt_gives_apartness.con".
(*#* ***Miscellaneous
We consider the injection [inject_Z] from [Z] to [Q] as a coercion.
*)
(*#* ***Miscellaneous
We consider the injection [inject_Z] from [Z] to [Q] as a coercion.
*)
-inline cic:/CoRN/model/structures/Qsec/inject_Z.con.
+inline "cic:/CoRN/model/structures/Qsec/inject_Z.con".
+
+coercion "cic:/matita/CoRN-Decl/model/structures/Qsec/inject_Z.con" 0 (* compounds *).
-inline cic:/CoRN/model/structures/Qsec/injz_plus.con.
+inline "cic:/CoRN/model/structures/Qsec/injz_plus.con".
-inline cic:/CoRN/model/structures/Qsec/injZ_One.con.
+inline "cic:/CoRN/model/structures/Qsec/injZ_One.con".
(*#* We can always find a natural number that is bigger than a given rational
number.
*)
(*#* We can always find a natural number that is bigger than a given rational
number.
*)
-inline cic:/CoRN/model/structures/Qsec/Q_is_archemaedian0.con.
+inline "cic:/CoRN/model/structures/Qsec/Q_is_archemaedian0.con".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Zsec".
set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Zsec".
(* $Id: Zsec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
(*#* printing {#Z} %\ensuremath{\mathrel\#_{\mathbb Z}}% *)
(* $Id: Zsec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
(*#* printing {#Z} %\ensuremath{\mathrel\#_{\mathbb Z}}% *)
-(* INCLUDE
-ZArith
-*)
-
-(* INCLUDE
-CLogic
-*)
+include "algebra/CLogic.ma".
We define the apartness as the negation of the Leibniz equality:
*)
We define the apartness as the negation of the Leibniz equality:
*)
-inline cic:/CoRN/model/structures/Zsec/ap_Z.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z.con".
(*#* Some properties of apartness:
*)
(*#* Some properties of apartness:
*)
-inline cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con".
-inline cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con".
-inline cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con".
-inline cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con".
-inline cic:/CoRN/model/structures/Zsec/ONE_neq_O.con.
+inline "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con".
(*#* ***Addition
Some properties of the addition. [Zplus] is also defined in the standard
library.
*)
(*#* ***Addition
Some properties of the addition. [Zplus] is also defined in the standard
library.
*)
-inline cic:/CoRN/model/structures/Zsec/Zplus_wd0.con.
+inline "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con".
-inline cic:/CoRN/model/structures/Zsec/Zplus_strext0.con.
+inline "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con".
(*#* ***Multiplication
The multiplication is extensional:
*)
(*#* ***Multiplication
The multiplication is extensional:
*)
-inline cic:/CoRN/model/structures/Zsec/Zmult_strext0.con.
+inline "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con".
-inline cic:/CoRN/model/structures/Zsec/Zpos.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos.con".
+coercion "cic:/matita/CoRN-Decl/model/structures/Zsec/Zpos.con" 0 (* compounds *).
+
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con".
-inline cic:/CoRN/model/structures/Zsec/Zpos_pos.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos_pos.con".
-inline cic:/CoRN/model/structures/Zsec/Zpos_neg.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos_neg.con".
-inline cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con".
-inline cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB".
(* begin hide *)
(* file : least_upper_bound_principle.v *)
(* begin hide *)
(* file : least_upper_bound_principle.v *)
(* description : proof of the Bridges' least upper bound principle *)
(* description : proof of the Bridges' least upper bound principle *)
-(* INCLUDE
-iso_CReals
-*)
+include "reals/iso_CReals.ma".
+include "algebra/Expon.ma".
(* UNEXPORTED
Section LUBP.
*)
(* UNEXPORTED
Section LUBP.
*)
-inline cic:/CoRN/reals/Bridges_LUB/R1.var.
+inline "cic:/CoRN/reals/Bridges_LUB/R1.var".
(* SUBSECTION ON GENRAL DEFINITIONS *)
(* SUBSECTION ON GENRAL DEFINITIONS *)
Section lub_definitions.
*)
Section lub_definitions.
*)
-inline cic:/CoRN/reals/Bridges_LUB/OF.var.
+inline "cic:/CoRN/reals/Bridges_LUB/OF.var".
-inline cic:/CoRN/reals/Bridges_LUB/SS.var.
+inline "cic:/CoRN/reals/Bridges_LUB/SS.var".
-inline cic:/CoRN/reals/Bridges_LUB/member.con.
+inline "cic:/CoRN/reals/Bridges_LUB/member.con".
-inline cic:/CoRN/reals/Bridges_LUB/Pmember.con.
+inline "cic:/CoRN/reals/Bridges_LUB/Pmember.con".
-inline cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con.
+inline "cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con".
-inline cic:/CoRN/reals/Bridges_LUB/l_u_b.con.
+inline "cic:/CoRN/reals/Bridges_LUB/l_u_b.con".
-inline cic:/CoRN/reals/Bridges_LUB/supremum.con.
+inline "cic:/CoRN/reals/Bridges_LUB/supremum.con".
-inline cic:/CoRN/reals/Bridges_LUB/Psupremum.con.
+inline "cic:/CoRN/reals/Bridges_LUB/Psupremum.con".
(* the following definitions are not used in *)
(* this file but later we will need them *)
(* the following definitions are not used in *)
(* this file but later we will need them *)
-inline cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con.
+inline "cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con".
-inline cic:/CoRN/reals/Bridges_LUB/g_l_b.con.
+inline "cic:/CoRN/reals/Bridges_LUB/g_l_b.con".
-inline cic:/CoRN/reals/Bridges_LUB/infimum.con.
+inline "cic:/CoRN/reals/Bridges_LUB/infimum.con".
-inline cic:/CoRN/reals/Bridges_LUB/Pinfimum.con.
+inline "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con".
(* UNEXPORTED
End lub_definitions.
(* UNEXPORTED
End lub_definitions.
Section upper_bound_sequence.
*)
Section upper_bound_sequence.
*)
-inline cic:/CoRN/reals/Bridges_LUB/A.var.
+inline "cic:/CoRN/reals/Bridges_LUB/A.var".
-inline cic:/CoRN/reals/Bridges_LUB/is_inhabitted.var.
+inline "cic:/CoRN/reals/Bridges_LUB/is_inhabitted.var".
-inline cic:/CoRN/reals/Bridges_LUB/bounded_above.var.
+inline "cic:/CoRN/reals/Bridges_LUB/bounded_above.var".
-inline cic:/CoRN/reals/Bridges_LUB/located.var.
+inline "cic:/CoRN/reals/Bridges_LUB/located.var".
-inline cic:/CoRN/reals/Bridges_LUB/s.con.
+inline "cic:/CoRN/reals/Bridges_LUB/s.con".
-inline cic:/CoRN/reals/Bridges_LUB/Ps.con.
+inline "cic:/CoRN/reals/Bridges_LUB/Ps.con".
-inline cic:/CoRN/reals/Bridges_LUB/b0.con.
+inline "cic:/CoRN/reals/Bridges_LUB/b0.con".
-inline cic:/CoRN/reals/Bridges_LUB/Pb0.con.
+inline "cic:/CoRN/reals/Bridges_LUB/Pb0.con".
-inline cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con.
+inline "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con".
-inline cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con.
+inline "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con".
-inline cic:/CoRN/reals/Bridges_LUB/dstart_l.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dstart_l.con".
-inline cic:/CoRN/reals/Bridges_LUB/dstart_r.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dstart_r.con".
-inline cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con".
-inline cic:/CoRN/reals/Bridges_LUB/shrink23d.con.
+inline "cic:/CoRN/reals/Bridges_LUB/shrink23d.con".
-inline cic:/CoRN/reals/Bridges_LUB/shrink13d.con.
+inline "cic:/CoRN/reals/Bridges_LUB/shrink13d.con".
-inline cic:/CoRN/reals/Bridges_LUB/shrink24d.con.
+inline "cic:/CoRN/reals/Bridges_LUB/shrink24d.con".
-inline cic:/CoRN/reals/Bridges_LUB/Real_Interval.con.
+inline "cic:/CoRN/reals/Bridges_LUB/Real_Interval.con".
-inline cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con".
-inline cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con".
-inline cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con".
-inline cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con".
-inline cic:/CoRN/reals/Bridges_LUB/dIntrvl.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con".
-inline cic:/CoRN/reals/Bridges_LUB/U.con.
+inline "cic:/CoRN/reals/Bridges_LUB/U.con".
-inline cic:/CoRN/reals/Bridges_LUB/V.con.
+inline "cic:/CoRN/reals/Bridges_LUB/V.con".
-inline cic:/CoRN/reals/Bridges_LUB/W.con.
+inline "cic:/CoRN/reals/Bridges_LUB/W.con".
-inline cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con.
+inline "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con".
-inline cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con.
+inline "cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con".
-inline cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con".
-inline cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con.
+inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con".
-inline cic:/CoRN/reals/Bridges_LUB/V_increase.con.
+inline "cic:/CoRN/reals/Bridges_LUB/V_increase.con".
-inline cic:/CoRN/reals/Bridges_LUB/W_decrease.con.
+inline "cic:/CoRN/reals/Bridges_LUB/W_decrease.con".
-inline cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con.
+inline "cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con".
-inline cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con.
+inline "cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con".
(* These lemma are *very* similar to those in *)
(* Cauchy_rationals_approach_reals.v *)
(* These lemma are *very* similar to those in *)
(* Cauchy_rationals_approach_reals.v *)
-inline cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con.
+inline "cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con".
-inline cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con.
+inline "cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con".
-inline cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con.
+inline "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con".
-inline cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con.
+inline "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con".
-inline cic:/CoRN/reals/Bridges_LUB/B.con.
+inline "cic:/CoRN/reals/Bridges_LUB/B.con".
-inline cic:/CoRN/reals/Bridges_LUB/U_minus_V.con.
+inline "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con".
-inline cic:/CoRN/reals/Bridges_LUB/U_minus_W.con.
+inline "cic:/CoRN/reals/Bridges_LUB/U_minus_W.con".
-inline cic:/CoRN/reals/Bridges_LUB/U_V_upper.con.
+inline "cic:/CoRN/reals/Bridges_LUB/U_V_upper.con".
-inline cic:/CoRN/reals/Bridges_LUB/U_W_lower.con.
+inline "cic:/CoRN/reals/Bridges_LUB/U_W_lower.con".
-inline cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con.
+inline "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con".
-inline cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con.
+inline "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con".
(* Two properties of exponentiation in COrdFields *)
(* Two properties of exponentiation in COrdFields *)
-inline cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con.
+inline "cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con".
-inline cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con.
+inline "cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con".
(* A consequence of Archimedean property - *)
(* the every basis of definition of e=lim(1+1/n)^n *)
(* A consequence of Archimedean property - *)
(* the every basis of definition of e=lim(1+1/n)^n *)
-inline cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con.
+inline "cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con".
-inline cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con.
+inline "cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con".
-inline cic:/CoRN/reals/Bridges_LUB/B_limit_V.con.
+inline "cic:/CoRN/reals/Bridges_LUB/B_limit_V.con".
-inline cic:/CoRN/reals/Bridges_LUB/B_limit_W.con.
+inline "cic:/CoRN/reals/Bridges_LUB/B_limit_W.con".
-inline cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con.
+inline "cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con".
-inline cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con.
+inline "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con".
-inline cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con.
+inline "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con".
(* UNEXPORTED
End upper_bound_sequence.
(* UNEXPORTED
End upper_bound_sequence.
set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_iso".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_iso".
(* begin hide *)
(* file : bridges_gives_our.v *)
(* begin hide *)
(* file : bridges_gives_our.v *)
(* description : Bridges' proof of Cauchy completeness in TCS-219 *)
(* description : Bridges' proof of Cauchy completeness in TCS-219 *)
-(* INCLUDE
-Bridges_LUB
-*)
+include "reals/Bridges_LUB.ma".
(* This lemma comes from lemmas.v of Martijn Oostdijk *)
(* This lemma comes from lemmas.v of Martijn Oostdijk *)
-inline cic:/CoRN/reals/Bridges_iso/le_witness_informative.con.
+inline "cic:/CoRN/reals/Bridges_iso/le_witness_informative.con".
(* UNEXPORTED
Section bridges_axioms_imply_ours.
*)
(* UNEXPORTED
Section bridges_axioms_imply_ours.
*)
-inline cic:/CoRN/reals/Bridges_iso/OF.var.
+inline "cic:/CoRN/reals/Bridges_iso/OF.var".
-inline cic:/CoRN/reals/Bridges_iso/lubp.var.
+inline "cic:/CoRN/reals/Bridges_iso/lubp.var".
-inline cic:/CoRN/reals/Bridges_iso/is_Archimedes.var.
+inline "cic:/CoRN/reals/Bridges_iso/is_Archimedes.var".
-inline cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con.
+inline "cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con".
(* UNEXPORTED
Section proofs_in_TCS.
*)
(* UNEXPORTED
Section proofs_in_TCS.
*)
-inline cic:/CoRN/reals/Bridges_iso/leEq_geEq.con.
+inline "cic:/CoRN/reals/Bridges_iso/leEq_geEq.con".
-inline cic:/CoRN/reals/Bridges_iso/glbp.con.
+inline "cic:/CoRN/reals/Bridges_iso/glbp.con".
(* UNEXPORTED
Section supremum.
*)
(* UNEXPORTED
Section supremum.
*)
-inline cic:/CoRN/reals/Bridges_iso/P.var.
+inline "cic:/CoRN/reals/Bridges_iso/P.var".
-inline cic:/CoRN/reals/Bridges_iso/inequality1.con.
+inline "cic:/CoRN/reals/Bridges_iso/inequality1.con".
-inline cic:/CoRN/reals/Bridges_iso/inequality2.con.
+inline "cic:/CoRN/reals/Bridges_iso/inequality2.con".
-inline cic:/CoRN/reals/Bridges_iso/inequality3.con.
+inline "cic:/CoRN/reals/Bridges_iso/inequality3.con".
-inline cic:/CoRN/reals/Bridges_iso/inequality4.con.
+inline "cic:/CoRN/reals/Bridges_iso/inequality4.con".
-inline cic:/CoRN/reals/Bridges_iso/Hum.con.
+inline "cic:/CoRN/reals/Bridges_iso/Hum.con".
-inline cic:/CoRN/reals/Bridges_iso/bound_tk1.con.
+inline "cic:/CoRN/reals/Bridges_iso/bound_tk1.con".
-inline cic:/CoRN/reals/Bridges_iso/bound_tk2.con.
+inline "cic:/CoRN/reals/Bridges_iso/bound_tk2.con".
-inline cic:/CoRN/reals/Bridges_iso/trick.con.
+inline "cic:/CoRN/reals/Bridges_iso/trick.con".
-inline cic:/CoRN/reals/Bridges_iso/trick'.con.
+inline "cic:/CoRN/reals/Bridges_iso/trick'.con".
-inline cic:/CoRN/reals/Bridges_iso/up_bound_for_n_element.con.
+inline "cic:/CoRN/reals/Bridges_iso/up_bound_for_n_element.con".
-inline cic:/CoRN/reals/Bridges_iso/low_bound_for_n_element.con.
+inline "cic:/CoRN/reals/Bridges_iso/low_bound_for_n_element.con".
-inline cic:/CoRN/reals/Bridges_iso/saghf.con.
+inline "cic:/CoRN/reals/Bridges_iso/saghf.con".
-inline cic:/CoRN/reals/Bridges_iso/Psaghf.con.
+inline "cic:/CoRN/reals/Bridges_iso/Psaghf.con".
-inline cic:/CoRN/reals/Bridges_iso/kaf.con.
+inline "cic:/CoRN/reals/Bridges_iso/kaf.con".
-inline cic:/CoRN/reals/Bridges_iso/Pkaf.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pkaf.con".
-inline cic:/CoRN/reals/Bridges_iso/is_finite_P.var.
+inline "cic:/CoRN/reals/Bridges_iso/is_finite_P.var".
-inline cic:/CoRN/reals/Bridges_iso/card.con.
+inline "cic:/CoRN/reals/Bridges_iso/card.con".
-inline cic:/CoRN/reals/Bridges_iso/Pcard1.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pcard1.con".
-inline cic:/CoRN/reals/Bridges_iso/seq.con.
+inline "cic:/CoRN/reals/Bridges_iso/seq.con".
-inline cic:/CoRN/reals/Bridges_iso/Pseq1.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pseq1.con".
-inline cic:/CoRN/reals/Bridges_iso/Pseq1_unfolded.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pseq1_unfolded.con".
-inline cic:/CoRN/reals/Bridges_iso/indeks.con.
+inline "cic:/CoRN/reals/Bridges_iso/indeks.con".
-inline cic:/CoRN/reals/Bridges_iso/Pindeks.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pindeks.con".
-inline cic:/CoRN/reals/Bridges_iso/is_onto_seq_P.var.
+inline "cic:/CoRN/reals/Bridges_iso/is_onto_seq_P.var".
-inline cic:/CoRN/reals/Bridges_iso/P_is_inhabited.con.
+inline "cic:/CoRN/reals/Bridges_iso/P_is_inhabited.con".
(*
Lemma bounded_quantifier:(N:nat;phi,psi:nat->Prop)
(*
Lemma bounded_quantifier:(N:nat;phi,psi:nat->Prop)
-inline cic:/CoRN/reals/Bridges_iso/bounded_quantifier_informative.con.
+inline "cic:/CoRN/reals/Bridges_iso/bounded_quantifier_informative.con".
-inline cic:/CoRN/reals/Bridges_iso/bridges_lemma1a.con.
+inline "cic:/CoRN/reals/Bridges_iso/bridges_lemma1a.con".
-inline cic:/CoRN/reals/Bridges_iso/P_is_strongly_extensional.var.
+inline "cic:/CoRN/reals/Bridges_iso/P_is_strongly_extensional.var".
-inline cic:/CoRN/reals/Bridges_iso/bridges_lemma1b.con.
+inline "cic:/CoRN/reals/Bridges_iso/bridges_lemma1b.con".
(* UNEXPORTED
End supremum.
(* UNEXPORTED
End supremum.
Section Every_Cauchy_Sequence_is_bounded.
*)
Section Every_Cauchy_Sequence_is_bounded.
*)
-inline cic:/CoRN/reals/Bridges_iso/seq2set.con.
+inline "cic:/CoRN/reals/Bridges_iso/seq2set.con".
-inline cic:/CoRN/reals/Bridges_iso/g.var.
+inline "cic:/CoRN/reals/Bridges_iso/g.var".
-inline cic:/CoRN/reals/Bridges_iso/g_.con.
+inline "cic:/CoRN/reals/Bridges_iso/g_.con".
-inline cic:/CoRN/reals/Bridges_iso/pg.con.
+inline "cic:/CoRN/reals/Bridges_iso/pg.con".
-inline cic:/CoRN/reals/Bridges_iso/P.con.
+inline "cic:/CoRN/reals/Bridges_iso/P.con".
-inline cic:/CoRN/reals/Bridges_iso/fin_is_fin.con.
+inline "cic:/CoRN/reals/Bridges_iso/fin_is_fin.con".
-inline cic:/CoRN/reals/Bridges_iso/card_fin.con.
+inline "cic:/CoRN/reals/Bridges_iso/card_fin.con".
-inline cic:/CoRN/reals/Bridges_iso/finite_seq.con.
+inline "cic:/CoRN/reals/Bridges_iso/finite_seq.con".
-inline cic:/CoRN/reals/Bridges_iso/bridges_lemma2a.con.
+inline "cic:/CoRN/reals/Bridges_iso/bridges_lemma2a.con".
-inline cic:/CoRN/reals/Bridges_iso/sup.con.
+inline "cic:/CoRN/reals/Bridges_iso/sup.con".
-inline cic:/CoRN/reals/Bridges_iso/Psup.con.
+inline "cic:/CoRN/reals/Bridges_iso/Psup.con".
-inline cic:/CoRN/reals/Bridges_iso/Psup_proj1.con.
+inline "cic:/CoRN/reals/Bridges_iso/Psup_proj1.con".
-inline cic:/CoRN/reals/Bridges_iso/Psup_unfolded1.con.
+inline "cic:/CoRN/reals/Bridges_iso/Psup_unfolded1.con".
-inline cic:/CoRN/reals/Bridges_iso/Psup_unfolded2.con.
+inline "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2.con".
-inline cic:/CoRN/reals/Bridges_iso/bridges_lemma2b.con.
+inline "cic:/CoRN/reals/Bridges_iso/bridges_lemma2b.con".
-inline cic:/CoRN/reals/Bridges_iso/inf.con.
+inline "cic:/CoRN/reals/Bridges_iso/inf.con".
-inline cic:/CoRN/reals/Bridges_iso/Pinf.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pinf.con".
-inline cic:/CoRN/reals/Bridges_iso/Pinf_proj1.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pinf_proj1.con".
-inline cic:/CoRN/reals/Bridges_iso/Pinf_unfolded1.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded1.con".
-inline cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2.con".
(* I tried very much not to mention this lemma! *)
(* I tried very much not to mention this lemma! *)
-inline cic:/CoRN/reals/Bridges_iso/sup_leEq.con.
+inline "cic:/CoRN/reals/Bridges_iso/sup_leEq.con".
-inline cic:/CoRN/reals/Bridges_iso/inf_geEq.con.
+inline "cic:/CoRN/reals/Bridges_iso/inf_geEq.con".
-inline cic:/CoRN/reals/Bridges_iso/tail_is_Cauchy.con.
+inline "cic:/CoRN/reals/Bridges_iso/tail_is_Cauchy.con".
-inline cic:/CoRN/reals/Bridges_iso/tail_seq.con.
+inline "cic:/CoRN/reals/Bridges_iso/tail_seq.con".
(* UNEXPORTED
End Every_Cauchy_Sequence_is_bounded.
*)
(* UNEXPORTED
End Every_Cauchy_Sequence_is_bounded.
*)
-inline cic:/CoRN/reals/Bridges_iso/g.var.
+inline "cic:/CoRN/reals/Bridges_iso/g.var".
-inline cic:/CoRN/reals/Bridges_iso/g_.con.
+inline "cic:/CoRN/reals/Bridges_iso/g_.con".
-inline cic:/CoRN/reals/Bridges_iso/pg.con.
+inline "cic:/CoRN/reals/Bridges_iso/pg.con".
-inline cic:/CoRN/reals/Bridges_iso/sup_tail.con.
+inline "cic:/CoRN/reals/Bridges_iso/sup_tail.con".
-inline cic:/CoRN/reals/Bridges_iso/sup_tail_leEq.con.
+inline "cic:/CoRN/reals/Bridges_iso/sup_tail_leEq.con".
-inline cic:/CoRN/reals/Bridges_iso/sup_tail_is_Cauchy.con.
+inline "cic:/CoRN/reals/Bridges_iso/sup_tail_is_Cauchy.con".
-inline cic:/CoRN/reals/Bridges_iso/sup_tail_as_Cauchy.con.
+inline "cic:/CoRN/reals/Bridges_iso/sup_tail_as_Cauchy.con".
-inline cic:/CoRN/reals/Bridges_iso/L.con.
+inline "cic:/CoRN/reals/Bridges_iso/L.con".
-inline cic:/CoRN/reals/Bridges_iso/sup_tail_decrease.con.
+inline "cic:/CoRN/reals/Bridges_iso/sup_tail_decrease.con".
-inline cic:/CoRN/reals/Bridges_iso/L_less_sup_n.con.
+inline "cic:/CoRN/reals/Bridges_iso/L_less_sup_n.con".
-inline cic:/CoRN/reals/Bridges_iso/Psup_unfolded2_informative.con.
+inline "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2_informative.con".
-inline cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2_informative.con.
+inline "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2_informative.con".
-inline cic:/CoRN/reals/Bridges_iso/convergent_subseq.con.
+inline "cic:/CoRN/reals/Bridges_iso/convergent_subseq.con".
(* very elegant proof almost as short as text version! *)
(* very elegant proof almost as short as text version! *)
-inline cic:/CoRN/reals/Bridges_iso/lubp_gives_Cauchy.con.
+inline "cic:/CoRN/reals/Bridges_iso/lubp_gives_Cauchy.con".
(* UNEXPORTED
End proofs_in_TCS.
*)
(* UNEXPORTED
End proofs_in_TCS.
*)
-inline cic:/CoRN/reals/Bridges_iso/Bridges_R_is_CReals.con.
+inline "cic:/CoRN/reals/Bridges_iso/Bridges_R_is_CReals.con".
-inline cic:/CoRN/reals/Bridges_iso/Bridges_R_as_CReals.con.
+inline "cic:/CoRN/reals/Bridges_iso/Bridges_R_as_CReals.con".
(* UNEXPORTED
End bridges_axioms_imply_ours.
(* UNEXPORTED
End bridges_axioms_imply_ours.
set "baseuri" "cic:/matita/CoRN-Decl/reals/CMetricFields".
set "baseuri" "cic:/matita/CoRN-Decl/reals/CMetricFields".
(* $Id: CMetricFields.v,v 1.6 2004/04/23 10:01:03 lcf Exp $ *)
(* $Id: CMetricFields.v,v 1.6 2004/04/23 10:01:03 lcf Exp $ *)
+include "reals/CReals1.ma".
(* UNEXPORTED
Section CMetric_Fields.
(* UNEXPORTED
Section CMetric_Fields.
-inline cic:/CoRN/reals/CMetricFields/is_CMetricField.ind.
+inline "cic:/CoRN/reals/CMetricFields/is_CMetricField.ind".
-inline cic:/CoRN/reals/CMetricFields/CMetricField.ind.
+inline "cic:/CoRN/reals/CMetricFields/CMetricField.ind".
+
+coercion "cic:/matita/CoRN-Decl/reals/CMetricFields/cmf_crr.con" 0 (* compounds *).
(* UNEXPORTED
End CMetric_Fields.
(* UNEXPORTED
End CMetric_Fields.
-inline cic:/CoRN/reals/CMetricFields/MAbs_one.con.
+inline "cic:/CoRN/reals/CMetricFields/MAbs_one.con".
-inline cic:/CoRN/reals/CMetricFields/Hulp.con.
+inline "cic:/CoRN/reals/CMetricFields/Hulp.con".
-inline cic:/CoRN/reals/CMetricFields/MAbs_one_recip_one.con.
+inline "cic:/CoRN/reals/CMetricFields/MAbs_one_recip_one.con".
Section CMetric_Field_Cauchy.
*)
Section CMetric_Field_Cauchy.
*)
-inline cic:/CoRN/reals/CMetricFields/F.var.
+inline "cic:/CoRN/reals/CMetricFields/F.var".
(*#*
%\begin{convention}% Let [F:CMetricField].
%\end{convention}%
*)
(*#*
%\begin{convention}% Let [F:CMetricField].
%\end{convention}%
*)
-inline cic:/CoRN/reals/CMetricFields/MCauchy_prop.con.
+inline "cic:/CoRN/reals/CMetricFields/MCauchy_prop.con".
+
+inline "cic:/CoRN/reals/CMetricFields/MCauchySeq.ind".
-inline cic:/CoRN/reals/CMetricFields/MCauchySeq.ind.
+coercion "cic:/matita/CoRN-Decl/reals/CMetricFields/MCS_seq.con" 0 (* compounds *).
-inline cic:/CoRN/reals/CMetricFields/MseqLimit.con.
+inline "cic:/CoRN/reals/CMetricFields/MseqLimit.con".
-inline cic:/CoRN/reals/CMetricFields/is_MCauchyCompl.con.
+inline "cic:/CoRN/reals/CMetricFields/is_MCauchyCompl.con".
(* UNEXPORTED
End CMetric_Field_Cauchy.
(* UNEXPORTED
End CMetric_Field_Cauchy.
set "baseuri" "cic:/matita/CoRN-Decl/reals/CPoly_Contin".
set "baseuri" "cic:/matita/CoRN-Decl/reals/CPoly_Contin".
(* $Id: CPoly_Contin.v,v 1.6 2004/04/23 10:01:03 lcf Exp $ *)
(*#* * Continuity of polynomials *)
(* $Id: CPoly_Contin.v,v 1.6 2004/04/23 10:01:03 lcf Exp $ *)
(*#* * Continuity of polynomials *)
-(* INCLUDE
-RealFuncts
-*)
+include "reals/RealFuncts.ma".
-inline cic:/CoRN/reals/CPoly_Contin/plus_op_contin.con.
+inline "cic:/CoRN/reals/CPoly_Contin/plus_op_contin.con".
-inline cic:/CoRN/reals/CPoly_Contin/mult_op_contin.con.
+inline "cic:/CoRN/reals/CPoly_Contin/mult_op_contin.con".
-inline cic:/CoRN/reals/CPoly_Contin/linear_op_contin.con.
+inline "cic:/CoRN/reals/CPoly_Contin/linear_op_contin.con".
-inline cic:/CoRN/reals/CPoly_Contin/cpoly_op_contin.con.
+inline "cic:/CoRN/reals/CPoly_Contin/cpoly_op_contin.con".
set "baseuri" "cic:/matita/CoRN-Decl/reals/CReals".
set "baseuri" "cic:/matita/CoRN-Decl/reals/CReals".
(* $Id: CReals.v,v 1.2 2004/04/05 11:35:38 lcf Exp $ *)
(*#* printing Lim %\ensuremath{\lim}% *)
(* $Id: CReals.v,v 1.2 2004/04/05 11:35:38 lcf Exp $ *)
(*#* printing Lim %\ensuremath{\lim}% *)
-(* INCLUDE
-COrdCauchy
-*)
+include "algebra/COrdCauchy.ma".
(*#* * Definition of the notion of reals
The reals are defined as a Cauchy-closed Archimedean constructive
(*#* * Definition of the notion of reals
The reals are defined as a Cauchy-closed Archimedean constructive
-inline cic:/CoRN/reals/CReals/is_CReals.ind.
+inline "cic:/CoRN/reals/CReals/is_CReals.ind".
+
+inline "cic:/CoRN/reals/CReals/CReals.ind".
-inline cic:/CoRN/reals/CReals/CReals.ind.
+coercion "cic:/matita/CoRN-Decl/reals/CReals/crl_crr.con" 0 (* compounds *).
-inline cic:/CoRN/reals/CReals/Lim.con.
+inline "cic:/CoRN/reals/CReals/Lim.con".
(* UNEXPORTED
Implicit Arguments Lim [IR].
(* UNEXPORTED
Implicit Arguments Lim [IR].
set "baseuri" "cic:/matita/CoRN-Decl/reals/CReals1".
set "baseuri" "cic:/matita/CoRN-Decl/reals/CReals1".
(* $Id: CReals1.v,v 1.4 2004/04/23 10:01:04 lcf Exp $ *)
(* $Id: CReals1.v,v 1.4 2004/04/23 10:01:04 lcf Exp $ *)
-(* INCLUDE
-Max_AbsIR
-*)
+include "reals/Max_AbsIR.ma".
+include "algebra/Expon.ma".
-(* INCLUDE
-CPoly_ApZero
-*)
+include "algebra/CPoly_ApZero.ma".
(* UNEXPORTED
Section More_Cauchy_Props.
(* UNEXPORTED
Section More_Cauchy_Props.
The sequence defined by $x_n=\frac2{n+1}$#x(n)=2/(n+1)#.
*)
The sequence defined by $x_n=\frac2{n+1}$#x(n)=2/(n+1)#.
*)
-inline cic:/CoRN/reals/CReals1/twice_inv_seq_Lim.con.
+inline "cic:/CoRN/reals/CReals1/twice_inv_seq_Lim.con".
-inline cic:/CoRN/reals/CReals1/twice_inv_seq.con.
+inline "cic:/CoRN/reals/CReals1/twice_inv_seq.con".
(*#*
Next, we prove that the sequence of absolute values of a Cauchy
sequence is also Cauchy.
*)
(*#*
Next, we prove that the sequence of absolute values of a Cauchy
sequence is also Cauchy.
*)
-inline cic:/CoRN/reals/CReals1/Cauchy_Lim_abs.con.
+inline "cic:/CoRN/reals/CReals1/Cauchy_Lim_abs.con".
-inline cic:/CoRN/reals/CReals1/Cauchy_abs.con.
+inline "cic:/CoRN/reals/CReals1/Cauchy_abs.con".
-inline cic:/CoRN/reals/CReals1/Lim_abs.con.
+inline "cic:/CoRN/reals/CReals1/Lim_abs.con".
(* UNEXPORTED
End More_Cauchy_Props.
(* UNEXPORTED
End More_Cauchy_Props.
-inline cic:/CoRN/reals/CReals1/seq1.var.
+inline "cic:/CoRN/reals/CReals1/seq1.var".
-inline cic:/CoRN/reals/CReals1/seq2.var.
+inline "cic:/CoRN/reals/CReals1/seq2.var".
-inline cic:/CoRN/reals/CReals1/f.var.
+inline "cic:/CoRN/reals/CReals1/f.var".
-inline cic:/CoRN/reals/CReals1/monF.var.
+inline "cic:/CoRN/reals/CReals1/monF.var".
-inline cic:/CoRN/reals/CReals1/crescF.var.
+inline "cic:/CoRN/reals/CReals1/crescF.var".
-inline cic:/CoRN/reals/CReals1/subseq.var.
+inline "cic:/CoRN/reals/CReals1/subseq.var".
-inline cic:/CoRN/reals/CReals1/mon_seq2.var.
+inline "cic:/CoRN/reals/CReals1/mon_seq2.var".
-inline cic:/CoRN/reals/CReals1/unbnd_f.con.
+inline "cic:/CoRN/reals/CReals1/unbnd_f.con".
-inline cic:/CoRN/reals/CReals1/mon_F'.con.
+inline "cic:/CoRN/reals/CReals1/mon_F'.con".
-inline cic:/CoRN/reals/CReals1/conv_subseq_imp_conv_seq.con.
+inline "cic:/CoRN/reals/CReals1/conv_subseq_imp_conv_seq.con".
-inline cic:/CoRN/reals/CReals1/Cprop2_seq_imp_Cprop2_subseq.con.
+inline "cic:/CoRN/reals/CReals1/Cprop2_seq_imp_Cprop2_subseq.con".
-inline cic:/CoRN/reals/CReals1/conv_seq_imp_conv_subseq.con.
+inline "cic:/CoRN/reals/CReals1/conv_seq_imp_conv_subseq.con".
-inline cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con.
+inline "cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con".
(* UNEXPORTED
End Subsequences.
(* UNEXPORTED
End Subsequences.
Section Cauchy_Subsequences.
*)
Section Cauchy_Subsequences.
*)
-inline cic:/CoRN/reals/CReals1/seq1.var.
+inline "cic:/CoRN/reals/CReals1/seq1.var".
-inline cic:/CoRN/reals/CReals1/seq2.var.
+inline "cic:/CoRN/reals/CReals1/seq2.var".
-inline cic:/CoRN/reals/CReals1/f.var.
+inline "cic:/CoRN/reals/CReals1/f.var".
-inline cic:/CoRN/reals/CReals1/monF.var.
+inline "cic:/CoRN/reals/CReals1/monF.var".
-inline cic:/CoRN/reals/CReals1/crescF.var.
+inline "cic:/CoRN/reals/CReals1/crescF.var".
-inline cic:/CoRN/reals/CReals1/subseq.var.
+inline "cic:/CoRN/reals/CReals1/subseq.var".
-inline cic:/CoRN/reals/CReals1/mon_seq2.var.
+inline "cic:/CoRN/reals/CReals1/mon_seq2.var".
-inline cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con.
+inline "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con".
-inline cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con.
+inline "cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con".
(* UNEXPORTED
End Cauchy_Subsequences.
(* UNEXPORTED
End Cauchy_Subsequences.
Finally, we prove that [x[^]n] grows to infinity if [x [>] One].
*)
Finally, we prove that [x[^]n] grows to infinity if [x [>] One].
*)
-inline cic:/CoRN/reals/CReals1/power_big'.con.
+inline "cic:/CoRN/reals/CReals1/power_big'.con".
-inline cic:/CoRN/reals/CReals1/power_big.con.
+inline "cic:/CoRN/reals/CReals1/power_big.con".
-inline cic:/CoRN/reals/CReals1/qi_yields_zero.con.
+inline "cic:/CoRN/reals/CReals1/qi_yields_zero.con".
-inline cic:/CoRN/reals/CReals1/qi_lim_zero.con.
+inline "cic:/CoRN/reals/CReals1/qi_lim_zero.con".
(* UNEXPORTED
End Properties_of_Exponentiation.
(* UNEXPORTED
End Properties_of_Exponentiation.
(*#* *** [IR] has characteristic zero *)
(*#* *** [IR] has characteristic zero *)
-inline cic:/CoRN/reals/CReals1/char0_IR.con.
+inline "cic:/CoRN/reals/CReals1/char0_IR.con".
-inline cic:/CoRN/reals/CReals1/poly_apzero_IR.con.
+inline "cic:/CoRN/reals/CReals1/poly_apzero_IR.con".
-inline cic:/CoRN/reals/CReals1/poly_IR_extensional.con.
+inline "cic:/CoRN/reals/CReals1/poly_IR_extensional.con".
set "baseuri" "cic:/matita/CoRN-Decl/reals/CSumsReals".
set "baseuri" "cic:/matita/CoRN-Decl/reals/CSumsReals".
(* $Id: CSumsReals.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
(* $Id: CSumsReals.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
+include "reals/CReals1.ma".
Section Sums_over_Reals.
*)
Section Sums_over_Reals.
*)
-inline cic:/CoRN/reals/CSumsReals/c.var.
+inline "cic:/CoRN/reals/CSumsReals/c.var".
-inline cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con".
(* UNEXPORTED
Hint Resolve Sum0_c_exp.
*)
(* UNEXPORTED
Hint Resolve Sum0_c_exp.
*)
-inline cic:/CoRN/reals/CSumsReals/Sum_c_exp.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con".
(* UNEXPORTED
Hint Resolve Sum_c_exp.
(* UNEXPORTED
Hint Resolve Sum_c_exp.
(*#* The following formulation is often more useful if [c [<] 1]. *)
(*#* The following formulation is often more useful if [c [<] 1]. *)
-inline cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con".
(* UNEXPORTED
Hint Resolve Sum_c_exp'.
(* UNEXPORTED
Hint Resolve Sum_c_exp'.
Hint Resolve Sum0_c_exp Sum_c_exp Sum_c_exp': algebra.
*)
Hint Resolve Sum0_c_exp Sum_c_exp Sum_c_exp': algebra.
*)
-inline cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con.
+inline "cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con".
-inline cic:/CoRN/reals/CSumsReals/diff_is_sum.con.
+inline "cic:/CoRN/reals/CSumsReals/diff_is_sum.con".
-inline cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con".
-inline cic:/CoRN/reals/CSumsReals/Sum_pres_less.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum_pres_less.con".
-inline cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con".
-inline cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con".
(* UNEXPORTED
Hint Resolve Sum0_comm_scal: algebra.
*)
(* UNEXPORTED
Hint Resolve Sum0_comm_scal: algebra.
*)
-inline cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con".
-inline cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con".
-inline cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con".
-inline cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con.
+inline "cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con".
-inline cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con.
+inline "cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con".
set "baseuri" "cic:/matita/CoRN-Decl/reals/CauchySeq".
set "baseuri" "cic:/matita/CoRN-Decl/reals/CauchySeq".
(* $Id: CauchySeq.v,v 1.8 2004/04/23 10:01:04 lcf Exp $ *)
(*#* printing IR %\ensuremath{\mathbb R}% *)
(* $Id: CauchySeq.v,v 1.8 2004/04/23 10:01:04 lcf Exp $ *)
(*#* printing IR %\ensuremath{\mathbb R}% *)
(*#* printing AbsIR %\ensuremath{|\cdot|_{\mathbb R}}% *)
(*#* printing AbsIR %\ensuremath{|\cdot|_{\mathbb R}}% *)
+include "reals/CReals.ma".
(*#* *Real Number Structures
%\begin{convention}% Let [IR] be a structure for real numbers.
(*#* *Real Number Structures
%\begin{convention}% Let [IR] be a structure for real numbers.
-inline cic:/CoRN/reals/CauchySeq/IR.var.
+inline "cic:/CoRN/reals/CauchySeq/IR.var".
-(* INCLUDE
-Transparent_algebra
-*)
+include "tactics/Transparent_algebra.ma".
(*#* ** [CReals] axioms *)
(*#* ** [CReals] axioms *)
-inline cic:/CoRN/reals/CauchySeq/CReals_is_CReals.con.
+inline "cic:/CoRN/reals/CauchySeq/CReals_is_CReals.con".
(*#* First properties which follow trivially from the axioms. *)
(*#* First properties which follow trivially from the axioms. *)
-inline cic:/CoRN/reals/CauchySeq/Lim_Cauchy.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_Cauchy.con".
-inline cic:/CoRN/reals/CauchySeq/Archimedes.con.
+inline "cic:/CoRN/reals/CauchySeq/Archimedes.con".
-inline cic:/CoRN/reals/CauchySeq/Archimedes'.con.
+inline "cic:/CoRN/reals/CauchySeq/Archimedes'.con".
(*#* A stronger version, which often comes in useful. *)
(*#* A stronger version, which often comes in useful. *)
-inline cic:/CoRN/reals/CauchySeq/str_Archimedes.con.
+inline "cic:/CoRN/reals/CauchySeq/str_Archimedes.con".
-inline cic:/CoRN/reals/CauchySeq/CauchySeqR.con.
+inline "cic:/CoRN/reals/CauchySeq/CauchySeqR.con".
(* UNEXPORTED
End CReals_axioms.
(* UNEXPORTED
End CReals_axioms.
sometimes easier and program extraction much more efficient.
*)
sometimes easier and program extraction much more efficient.
*)
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop1.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop1.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop2.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop2.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop3.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop3.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop4.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop4.con".
(* UNEXPORTED
End Cauchy_Defs.
(* UNEXPORTED
End Cauchy_Defs.
The next lemma is equal to lemma [Lim_Cauchy]. *)
The next lemma is equal to lemma [Lim_Cauchy]. *)
-inline cic:/CoRN/reals/CauchySeq/Cauchy_complete.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_complete.con".
-inline cic:/CoRN/reals/CauchySeq/less_Lim_so_less_seq.con.
+inline "cic:/CoRN/reals/CauchySeq/less_Lim_so_less_seq.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_less_so_seq_less.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_less_so_seq_less.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_less_Lim_so_seq_less_seq.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_less_Lim_so_seq_less_seq.con".
(*#* The next lemma follows from [less_Lim_so_less_seq] with [y := (y[+] (Lim seq)) [/]TwoNZ]. *)
(*#* The next lemma follows from [less_Lim_so_less_seq] with [y := (y[+] (Lim seq)) [/]TwoNZ]. *)
-inline cic:/CoRN/reals/CauchySeq/less_Lim_so.con.
+inline "cic:/CoRN/reals/CauchySeq/less_Lim_so.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_less_so.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_less_so.con".
-inline cic:/CoRN/reals/CauchySeq/leEq_seq_so_leEq_Lim.con.
+inline "cic:/CoRN/reals/CauchySeq/leEq_seq_so_leEq_Lim.con".
-inline cic:/CoRN/reals/CauchySeq/str_leEq_seq_so_leEq_Lim.con.
+inline "cic:/CoRN/reals/CauchySeq/str_leEq_seq_so_leEq_Lim.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_leEq_Lim.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_leEq_Lim.con".
-inline cic:/CoRN/reals/CauchySeq/seq_leEq_so_Lim_leEq.con.
+inline "cic:/CoRN/reals/CauchySeq/seq_leEq_so_Lim_leEq.con".
-inline cic:/CoRN/reals/CauchySeq/str_seq_leEq_so_Lim_leEq.con.
+inline "cic:/CoRN/reals/CauchySeq/str_seq_leEq_so_Lim_leEq.con".
-inline cic:/CoRN/reals/CauchySeq/Limits_unique.con.
+inline "cic:/CoRN/reals/CauchySeq/Limits_unique.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_wd.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_wd.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_strext.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_strext.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap'.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap'.con".
(* UNEXPORTED
End Inequalities.
(* UNEXPORTED
End Inequalities.
(*#* *** Equivalence of formulations of Cauchy *)
(*#* *** Equivalence of formulations of Cauchy *)
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop1_prop.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop1_prop.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop2_prop.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop2_prop.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3_prop2.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3_prop2.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop2.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop2.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop.con".
-inline cic:/CoRN/reals/CauchySeq/Build_CauchySeq1.con.
+inline "cic:/CoRN/reals/CauchySeq/Build_CauchySeq1.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop3.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop3.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop2.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop2.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop3.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop3.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop.con".
-inline cic:/CoRN/reals/CauchySeq/Build_CauchySeq4.con.
+inline "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4.con".
-inline cic:/CoRN/reals/CauchySeq/Build_CauchySeq4_y.con.
+inline "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4_y.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_CauchySeq4.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq4.con".
-inline cic:/CoRN/reals/CauchySeq/Build_CauchySeq2.con.
+inline "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2.con".
-inline cic:/CoRN/reals/CauchySeq/Build_CauchySeq2_y.con.
+inline "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2_y.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_CauchySeq2.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq2.con".
(*#* Well definedness. *)
(*#* Well definedness. *)
-inline cic:/CoRN/reals/CauchySeq/Cauchy_prop_wd.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop_wd.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2_wd.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2_wd.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_wd'.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_wd'.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_unique.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_unique.con".
(* UNEXPORTED
End Equiv_Cauchy.
(* UNEXPORTED
End Equiv_Cauchy.
We begin by defining the constant sequence and proving that it is Cauchy with the expected limit.
*)
We begin by defining the constant sequence and proving that it is Cauchy with the expected limit.
*)
-inline cic:/CoRN/reals/CauchySeq/Cauchy_const.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_const.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_const.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_const.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_plus.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_plus.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_plus.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_plus.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_plus.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_plus.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_inv.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_inv.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_inv.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_inv.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_inv.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_inv.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_minus.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_minus.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_minus.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_minus.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_minus.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_minus.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_Lim_mult.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_mult.con".
-inline cic:/CoRN/reals/CauchySeq/Cauchy_mult.con.
+inline "cic:/CoRN/reals/CauchySeq/Cauchy_mult.con".
-inline cic:/CoRN/reals/CauchySeq/Lim_mult.con.
+inline "cic:/CoRN/reals/CauchySeq/Lim_mult.con".
(* UNEXPORTED
End Cauchy_props.
(* UNEXPORTED
End Cauchy_props.
set "baseuri" "cic:/matita/CoRN-Decl/reals/Cauchy_CReals".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Cauchy_CReals".
(* $Id: Cauchy_CReals.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
(* $Id: Cauchy_CReals.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
-(* INCLUDE
-Cauchy_COF
-*)
+include "algebra/Cauchy_COF.ma".
+include "reals/CReals.ma".
(* UNEXPORTED
Section R_CReals.
(* UNEXPORTED
Section R_CReals.
-inline cic:/CoRN/reals/Cauchy_CReals/F.var.
+inline "cic:/CoRN/reals/Cauchy_CReals/F.var".
-inline cic:/CoRN/reals/Cauchy_CReals/inject_Q.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/inject_Q.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_eq.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_eq.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_plus.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_plus.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_min.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_min.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_lt.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_lt.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_ap.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_ap.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_cancel_eq.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_eq.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_cancel_less.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_less.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_le.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_le.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_cancel_leEq.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_leEq.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_cancel_AbsSmall.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_AbsSmall.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_One.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_One.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_nring'.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_nring'.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_nring.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_nring.con".
-inline cic:/CoRN/reals/Cauchy_CReals/ing_mult.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_mult.con".
(* UNEXPORTED
Opaque R_COrdField.
*)
(* UNEXPORTED
Opaque R_COrdField.
*)
-inline cic:/CoRN/reals/Cauchy_CReals/ing_div_three.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_div_three.con".
(* UNEXPORTED
Transparent R_COrdField.
*)
(* UNEXPORTED
Transparent R_COrdField.
*)
-inline cic:/CoRN/reals/Cauchy_CReals/ing_n.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/ing_n.con".
-inline cic:/CoRN/reals/Cauchy_CReals/expand_Q_R.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R.con".
-inline cic:/CoRN/reals/Cauchy_CReals/conv_modulus.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/conv_modulus.con".
-inline cic:/CoRN/reals/Cauchy_CReals/T.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/T.con".
(*#* We now assume our original field is archimedean and prove that the
resulting one is, too.
*)
(*#* We now assume our original field is archimedean and prove that the
resulting one is, too.
*)
-inline cic:/CoRN/reals/Cauchy_CReals/F_is_archemaedian.var.
+inline "cic:/CoRN/reals/Cauchy_CReals/F_is_archemaedian.var".
-inline cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con".
-inline cic:/CoRN/reals/Cauchy_CReals/PT.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/PT.con".
-inline cic:/CoRN/reals/Cauchy_CReals/modulus_property.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/modulus_property.con".
-inline cic:/CoRN/reals/Cauchy_CReals/modulus_property_2.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/modulus_property_2.con".
-inline cic:/CoRN/reals/Cauchy_CReals/expand_Q_R_2.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R_2.con".
-inline cic:/CoRN/reals/Cauchy_CReals/CS_seq_diagonal.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/CS_seq_diagonal.con".
(*#* ** Cauchy Completeness
We can also define a limit operator.
*)
(*#* ** Cauchy Completeness
We can also define a limit operator.
*)
-inline cic:/CoRN/reals/Cauchy_CReals/Q_dense_in_R.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/Q_dense_in_R.con".
-inline cic:/CoRN/reals/Cauchy_CReals/LimR_CauchySeq.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/LimR_CauchySeq.con".
-inline cic:/CoRN/reals/Cauchy_CReals/R_is_complete.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/R_is_complete.con".
-inline cic:/CoRN/reals/Cauchy_CReals/R_is_CReals.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/R_is_CReals.con".
-inline cic:/CoRN/reals/Cauchy_CReals/R_as_CReals.con.
+inline "cic:/CoRN/reals/Cauchy_CReals/R_as_CReals.con".
(* UNEXPORTED
End R_CReals.
(* UNEXPORTED
End R_CReals.
set "baseuri" "cic:/matita/CoRN-Decl/reals/IVT".
set "baseuri" "cic:/matita/CoRN-Decl/reals/IVT".
(* $Id: IVT.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
(* $Id: IVT.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *)
-(* INCLUDE
-CPoly_Contin
-*)
+include "reals/CPoly_Contin.ma".
(* UNEXPORTED
Section Nested_Intervals.
(* UNEXPORTED
Section Nested_Intervals.
-inline cic:/CoRN/reals/IVT/a.var.
+inline "cic:/CoRN/reals/IVT/a.var".
-inline cic:/CoRN/reals/IVT/b.var.
+inline "cic:/CoRN/reals/IVT/b.var".
-inline cic:/CoRN/reals/IVT/a_mon.var.
+inline "cic:/CoRN/reals/IVT/a_mon.var".
-inline cic:/CoRN/reals/IVT/b_mon.var.
+inline "cic:/CoRN/reals/IVT/b_mon.var".
-inline cic:/CoRN/reals/IVT/a_b.var.
+inline "cic:/CoRN/reals/IVT/a_b.var".
-inline cic:/CoRN/reals/IVT/b_a.var.
+inline "cic:/CoRN/reals/IVT/b_a.var".
-inline cic:/CoRN/reals/IVT/a_mon'.con.
+inline "cic:/CoRN/reals/IVT/a_mon'.con".
-inline cic:/CoRN/reals/IVT/b_mon'.con.
+inline "cic:/CoRN/reals/IVT/b_mon'.con".
-inline cic:/CoRN/reals/IVT/a_b'.con.
+inline "cic:/CoRN/reals/IVT/a_b'.con".
-inline cic:/CoRN/reals/IVT/intervals_cauchy.con.
+inline "cic:/CoRN/reals/IVT/intervals_cauchy.con".
-inline cic:/CoRN/reals/IVT/a'.con.
+inline "cic:/CoRN/reals/IVT/a'.con".
-inline cic:/CoRN/reals/IVT/Cnested_intervals_limit.con.
+inline "cic:/CoRN/reals/IVT/Cnested_intervals_limit.con".
(*#* %\begin{convention}% Let [f] be a continuous real function.
%\end{convention}%
*)
(*#* %\begin{convention}% Let [f] be a continuous real function.
%\end{convention}%
*)
-inline cic:/CoRN/reals/IVT/f.var.
+inline "cic:/CoRN/reals/IVT/f.var".
-inline cic:/CoRN/reals/IVT/f_contin.var.
+inline "cic:/CoRN/reals/IVT/f_contin.var".
-inline cic:/CoRN/reals/IVT/f_contin_pos.con.
+inline "cic:/CoRN/reals/IVT/f_contin_pos.con".
-inline cic:/CoRN/reals/IVT/f_contin_neg.con.
+inline "cic:/CoRN/reals/IVT/f_contin_neg.con".
(*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *)
(*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *)
-inline cic:/CoRN/reals/IVT/f_a.var.
+inline "cic:/CoRN/reals/IVT/f_a.var".
-inline cic:/CoRN/reals/IVT/f_b.var.
+inline "cic:/CoRN/reals/IVT/f_b.var".
-inline cic:/CoRN/reals/IVT/Cnested_intervals_zero.con.
+inline "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con".
(* UNEXPORTED
End Nested_Intervals.
(* UNEXPORTED
End Nested_Intervals.
-inline cic:/CoRN/reals/IVT/f.var.
+inline "cic:/CoRN/reals/IVT/f.var".
-inline cic:/CoRN/reals/IVT/f_apzero_interval.var.
+inline "cic:/CoRN/reals/IVT/f_apzero_interval.var".
-inline cic:/CoRN/reals/IVT/a.var.
+inline "cic:/CoRN/reals/IVT/a.var".
-inline cic:/CoRN/reals/IVT/b.var.
+inline "cic:/CoRN/reals/IVT/b.var".
-inline cic:/CoRN/reals/IVT/a_b.var.
+inline "cic:/CoRN/reals/IVT/a_b.var".
-inline cic:/CoRN/reals/IVT/f_a.var.
+inline "cic:/CoRN/reals/IVT/f_a.var".
-inline cic:/CoRN/reals/IVT/f_b.var.
+inline "cic:/CoRN/reals/IVT/f_b.var".
(*#*
%\begin{convention}% Let [Small] denote [Two[/]ThreeNZ], [lft] be [(Two[*]a[+]b) [/]ThreeNZ] and [rht] be [(a[+]Two[*]b) [/]ThreeNZ].
(*#*
%\begin{convention}% Let [Small] denote [Two[/]ThreeNZ], [lft] be [(Two[*]a[+]b) [/]ThreeNZ] and [rht] be [(a[+]Two[*]b) [/]ThreeNZ].
-inline cic:/CoRN/reals/IVT/Small.con.
+inline "cic:/CoRN/reals/IVT/Small.con".
-inline cic:/CoRN/reals/IVT/lft.con.
+inline "cic:/CoRN/reals/IVT/lft.con".
-inline cic:/CoRN/reals/IVT/rht.con.
+inline "cic:/CoRN/reals/IVT/rht.con".
-inline cic:/CoRN/reals/IVT/a_lft.con.
+inline "cic:/CoRN/reals/IVT/a_lft.con".
-inline cic:/CoRN/reals/IVT/rht_b.con.
+inline "cic:/CoRN/reals/IVT/rht_b.con".
-inline cic:/CoRN/reals/IVT/lft_rht.con.
+inline "cic:/CoRN/reals/IVT/lft_rht.con".
-inline cic:/CoRN/reals/IVT/smaller_lft.con.
+inline "cic:/CoRN/reals/IVT/smaller_lft.con".
-inline cic:/CoRN/reals/IVT/smaller_rht.con.
+inline "cic:/CoRN/reals/IVT/smaller_rht.con".
(* UNEXPORTED
Hint Resolve smaller_lft smaller_rht: algebra.
*)
(* UNEXPORTED
Hint Resolve smaller_lft smaller_rht: algebra.
*)
-inline cic:/CoRN/reals/IVT/Cbisect'.con.
+inline "cic:/CoRN/reals/IVT/Cbisect'.con".
(* UNEXPORTED
End Bisection.
(* UNEXPORTED
End Bisection.
Section Bisect_Interval.
*)
Section Bisect_Interval.
*)
-inline cic:/CoRN/reals/IVT/f.var.
+inline "cic:/CoRN/reals/IVT/f.var".
-inline cic:/CoRN/reals/IVT/C_f_apzero_interval.var.
+inline "cic:/CoRN/reals/IVT/C_f_apzero_interval.var".
-inline cic:/CoRN/reals/IVT/Small.con.
+inline "cic:/CoRN/reals/IVT/Small.con".
-inline cic:/CoRN/reals/IVT/bisect_interval.ind.
+inline "cic:/CoRN/reals/IVT/bisect_interval.ind".
-inline cic:/CoRN/reals/IVT/Cbisect_exists.con.
+inline "cic:/CoRN/reals/IVT/Cbisect_exists.con".
-inline cic:/CoRN/reals/IVT/bisect.con.
+inline "cic:/CoRN/reals/IVT/bisect.con".
-inline cic:/CoRN/reals/IVT/bisect_prop.con.
+inline "cic:/CoRN/reals/IVT/bisect_prop.con".
(* UNEXPORTED
End Bisect_Interval.
(* UNEXPORTED
End Bisect_Interval.
Same conventions as before.
*)
Same conventions as before.
*)
-inline cic:/CoRN/reals/IVT/f.var.
+inline "cic:/CoRN/reals/IVT/f.var".
-inline cic:/CoRN/reals/IVT/f_contin.var.
+inline "cic:/CoRN/reals/IVT/f_contin.var".
-inline cic:/CoRN/reals/IVT/f_apzero_interval.var.
+inline "cic:/CoRN/reals/IVT/f_apzero_interval.var".
-inline cic:/CoRN/reals/IVT/a.var.
+inline "cic:/CoRN/reals/IVT/a.var".
-inline cic:/CoRN/reals/IVT/b.var.
+inline "cic:/CoRN/reals/IVT/b.var".
-inline cic:/CoRN/reals/IVT/a_b.var.
+inline "cic:/CoRN/reals/IVT/a_b.var".
-inline cic:/CoRN/reals/IVT/f_a.var.
+inline "cic:/CoRN/reals/IVT/f_a.var".
-inline cic:/CoRN/reals/IVT/f_b.var.
+inline "cic:/CoRN/reals/IVT/f_b.var".
-inline cic:/CoRN/reals/IVT/Small.con.
+inline "cic:/CoRN/reals/IVT/Small.con".
-inline cic:/CoRN/reals/IVT/interval_sequence.con.
+inline "cic:/CoRN/reals/IVT/interval_sequence.con".
-inline cic:/CoRN/reals/IVT/a_.con.
+inline "cic:/CoRN/reals/IVT/a_.con".
-inline cic:/CoRN/reals/IVT/b_.con.
+inline "cic:/CoRN/reals/IVT/b_.con".
-inline cic:/CoRN/reals/IVT/intervals_smaller.con.
+inline "cic:/CoRN/reals/IVT/intervals_smaller.con".
-inline cic:/CoRN/reals/IVT/intervals_small''.con.
+inline "cic:/CoRN/reals/IVT/intervals_small''.con".
-inline cic:/CoRN/reals/IVT/intervals_small'.con.
+inline "cic:/CoRN/reals/IVT/intervals_small'.con".
-inline cic:/CoRN/reals/IVT/intervals_small.con.
+inline "cic:/CoRN/reals/IVT/intervals_small.con".
-inline cic:/CoRN/reals/IVT/Civt_op.con.
+inline "cic:/CoRN/reals/IVT/Civt_op.con".
(* UNEXPORTED
End IVT_Op.
(* UNEXPORTED
End IVT_Op.
(*#* ** IVT for polynomials *)
(*#* ** IVT for polynomials *)
-inline cic:/CoRN/reals/IVT/Civt_poly.con.
+inline "cic:/CoRN/reals/IVT/Civt_poly.con".
(* UNEXPORTED
End IVT_Poly.
(* UNEXPORTED
End IVT_Poly.
set "baseuri" "cic:/matita/CoRN-Decl/reals/Intervals".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Intervals".
(* $Id: Intervals.v,v 1.10 2004/04/23 10:01:04 lcf Exp $ *)
(* $Id: Intervals.v,v 1.10 2004/04/23 10:01:04 lcf Exp $ *)
-(* INCLUDE
-CSetoidInc
-*)
+include "algebra/CSetoidInc.ma".
-(* INCLUDE
-RealLists
-*)
+include "reals/RealLists.ma".
(* UNEXPORTED
Section Intervals.
(* UNEXPORTED
Section Intervals.
require [a [<=] b], as we want to work only in nonempty intervals.
*)
require [a [<=] b], as we want to work only in nonempty intervals.
*)
-inline cic:/CoRN/reals/Intervals/compact.con.
+inline "cic:/CoRN/reals/Intervals/compact.con".
(*#*
%\begin{convention}% Let [a,b : IR] and [Hab : a [<=] b].
(*#*
%\begin{convention}% Let [a,b : IR] and [Hab : a [<=] b].
members of the interval [[Min(a,b),Max(a,b)]].
*)
members of the interval [[Min(a,b),Max(a,b)]].
*)
-inline cic:/CoRN/reals/Intervals/a.var.
+inline "cic:/CoRN/reals/Intervals/a.var".
-inline cic:/CoRN/reals/Intervals/b.var.
+inline "cic:/CoRN/reals/Intervals/b.var".
-inline cic:/CoRN/reals/Intervals/Hab.var.
+inline "cic:/CoRN/reals/Intervals/Hab.var".
-inline cic:/CoRN/reals/Intervals/compact_inc_lft.con.
+inline "cic:/CoRN/reals/Intervals/compact_inc_lft.con".
-inline cic:/CoRN/reals/Intervals/compact_inc_rht.con.
+inline "cic:/CoRN/reals/Intervals/compact_inc_rht.con".
-inline cic:/CoRN/reals/Intervals/compact_Min_lft.con.
+inline "cic:/CoRN/reals/Intervals/compact_Min_lft.con".
-inline cic:/CoRN/reals/Intervals/compact_Min_rht.con.
+inline "cic:/CoRN/reals/Intervals/compact_Min_rht.con".
(*#*
As we will be interested in taking functions with domain in a compact
interval, we want this predicate to be well defined.
*)
(*#*
As we will be interested in taking functions with domain in a compact
interval, we want this predicate to be well defined.
*)
-inline cic:/CoRN/reals/Intervals/compact_wd.con.
+inline "cic:/CoRN/reals/Intervals/compact_wd.con".
(*#*
Also, it will sometimes be necessary to rewrite the endpoints of an interval.
*)
(*#*
Also, it will sometimes be necessary to rewrite the endpoints of an interval.
*)
-inline cic:/CoRN/reals/Intervals/compact_wd'.con.
+inline "cic:/CoRN/reals/Intervals/compact_wd'.con".
(*#*
As we identify subsets with predicates, inclusion is simply implication.
(*#*
As we identify subsets with predicates, inclusion is simply implication.
returns the restriction $F|_P$# of F to P#.
*)
returns the restriction $F|_P$# of F to P#.
*)
-inline cic:/CoRN/reals/Intervals/Frestr.con.
+inline "cic:/CoRN/reals/Intervals/Frestr.con".
(* UNEXPORTED
End Intervals.
(* UNEXPORTED
End Intervals.
Section More_Intervals.
*)
Section More_Intervals.
*)
-inline cic:/CoRN/reals/Intervals/included_refl'.con.
+inline "cic:/CoRN/reals/Intervals/included_refl'.con".
(*#* We prove some inclusions of compact intervals. *)
(*#* We prove some inclusions of compact intervals. *)
-inline cic:/CoRN/reals/Intervals/compact_map1.con.
+inline "cic:/CoRN/reals/Intervals/compact_map1.con".
-inline cic:/CoRN/reals/Intervals/compact_map2.con.
+inline "cic:/CoRN/reals/Intervals/compact_map2.con".
-inline cic:/CoRN/reals/Intervals/compact_map3.con.
+inline "cic:/CoRN/reals/Intervals/compact_map3.con".
(* UNEXPORTED
End More_Intervals.
(* UNEXPORTED
End More_Intervals.
Notice the use of lists for quantification.
*)
Notice the use of lists for quantification.
*)
-inline cic:/CoRN/reals/Intervals/totally_bounded.con.
+inline "cic:/CoRN/reals/Intervals/totally_bounded.con".
(*#*
This definition is classically, but not constructively, equivalent to
(*#*
This definition is classically, but not constructively, equivalent to
and that we defined compacts as we did.
*)
and that we defined compacts as we did.
*)
-inline cic:/CoRN/reals/Intervals/compact_is_totally_bounded.con.
+inline "cic:/CoRN/reals/Intervals/compact_is_totally_bounded.con".
(*#*
Suprema and infima will be needed throughout; we define them here both
for arbitrary subsets of [IR] and for images of functions.
*)
(*#*
Suprema and infima will be needed throughout; we define them here both
for arbitrary subsets of [IR] and for images of functions.
*)
-inline cic:/CoRN/reals/Intervals/set_glb_IR.con.
+inline "cic:/CoRN/reals/Intervals/set_glb_IR.con".
-inline cic:/CoRN/reals/Intervals/set_lub_IR.con.
+inline "cic:/CoRN/reals/Intervals/set_lub_IR.con".
-inline cic:/CoRN/reals/Intervals/fun_image.con.
+inline "cic:/CoRN/reals/Intervals/fun_image.con".
-inline cic:/CoRN/reals/Intervals/fun_glb_IR.con.
+inline "cic:/CoRN/reals/Intervals/fun_glb_IR.con".
-inline cic:/CoRN/reals/Intervals/fun_lub_IR.con.
+inline "cic:/CoRN/reals/Intervals/fun_lub_IR.con".
-inline cic:/CoRN/reals/Intervals/aux_seq_lub.con.
+inline "cic:/CoRN/reals/Intervals/aux_seq_lub.con".
-inline cic:/CoRN/reals/Intervals/aux_seq_lub_prop.con.
+inline "cic:/CoRN/reals/Intervals/aux_seq_lub_prop.con".
The following are probably the most important results in this section.
*)
The following are probably the most important results in this section.
*)
-inline cic:/CoRN/reals/Intervals/totally_bounded_has_lub.con.
+inline "cic:/CoRN/reals/Intervals/totally_bounded_has_lub.con".
-inline cic:/CoRN/reals/Intervals/aux_seq_glb.con.
+inline "cic:/CoRN/reals/Intervals/aux_seq_glb.con".
-inline cic:/CoRN/reals/Intervals/aux_seq_glb_prop.con.
+inline "cic:/CoRN/reals/Intervals/aux_seq_glb_prop.con".
-inline cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con.
+inline "cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con".
(* UNEXPORTED
End Totally_Bounded.
(* UNEXPORTED
End Totally_Bounded.
The following characterization of inclusion can be very useful:
*)
The following characterization of inclusion can be very useful:
*)
-inline cic:/CoRN/reals/Intervals/included_compact.con.
+inline "cic:/CoRN/reals/Intervals/included_compact.con".
(*#*
At several points in our future development of a theory we will need
(*#*
At several points in our future development of a theory we will need
-inline cic:/CoRN/reals/Intervals/a.var.
+inline "cic:/CoRN/reals/Intervals/a.var".
-inline cic:/CoRN/reals/Intervals/b.var.
+inline "cic:/CoRN/reals/Intervals/b.var".
-inline cic:/CoRN/reals/Intervals/Hab.var.
+inline "cic:/CoRN/reals/Intervals/Hab.var".
-inline cic:/CoRN/reals/Intervals/I.con.
+inline "cic:/CoRN/reals/Intervals/I.con".
-inline cic:/CoRN/reals/Intervals/Hab'.var.
+inline "cic:/CoRN/reals/Intervals/Hab'.var".
-inline cic:/CoRN/reals/Intervals/e.var.
+inline "cic:/CoRN/reals/Intervals/e.var".
-inline cic:/CoRN/reals/Intervals/He.var.
+inline "cic:/CoRN/reals/Intervals/He.var".
(*#*
We start by finding a natural number [n] such that [(b[-]a) [/] n [<] e].
*)
(*#*
We start by finding a natural number [n] such that [(b[-]a) [/] n [<] e].
*)
-inline cic:/CoRN/reals/Intervals/compact_nat.con.
+inline "cic:/CoRN/reals/Intervals/compact_nat.con".
(*#* Obviously such an [n] must be greater than zero.*)
(*#* Obviously such an [n] must be greater than zero.*)
-inline cic:/CoRN/reals/Intervals/pos_compact_nat.con.
+inline "cic:/CoRN/reals/Intervals/pos_compact_nat.con".
(*#*
We now define a sequence on [n] points in [[a,b]] by
(*#*
We now define a sequence on [n] points in [[a,b]] by
prove that all of its points are really in that interval.
*)
prove that all of its points are really in that interval.
*)
-inline cic:/CoRN/reals/Intervals/compact_part.con.
+inline "cic:/CoRN/reals/Intervals/compact_part.con".
-inline cic:/CoRN/reals/Intervals/compact_part_hyp.con.
+inline "cic:/CoRN/reals/Intervals/compact_part_hyp.con".
(*#*
This sequence is strictly increasing and each two consecutive points
are apart by less than [e].*)
(*#*
This sequence is strictly increasing and each two consecutive points
are apart by less than [e].*)
-inline cic:/CoRN/reals/Intervals/compact_less.con.
+inline "cic:/CoRN/reals/Intervals/compact_less.con".
-inline cic:/CoRN/reals/Intervals/compact_leEq.con.
+inline "cic:/CoRN/reals/Intervals/compact_leEq.con".
(*#* When we proceed to integration, this lemma will also be useful: *)
(*#* When we proceed to integration, this lemma will also be useful: *)
-inline cic:/CoRN/reals/Intervals/compact_partition_lemma.con.
+inline "cic:/CoRN/reals/Intervals/compact_partition_lemma.con".
(*#* The next lemma provides an upper bound for the distance between two points in an interval: *)
(*#* The next lemma provides an upper bound for the distance between two points in an interval: *)
-inline cic:/CoRN/reals/Intervals/compact_elements.con.
+inline "cic:/CoRN/reals/Intervals/compact_elements.con".
(* UNEXPORTED
Opaque Min Max.
(* UNEXPORTED
Opaque Min Max.
(*#* The following is a variation on the previous lemma: *)
(*#* The following is a variation on the previous lemma: *)
-inline cic:/CoRN/reals/Intervals/compact_elements'.con.
+inline "cic:/CoRN/reals/Intervals/compact_elements'.con".
(*#* The following lemma is a bit more specific: it shows that we can
also estimate the distance from the center of a compact interval to
any of its points. *)
(*#* The following lemma is a bit more specific: it shows that we can
also estimate the distance from the center of a compact interval to
any of its points. *)
-inline cic:/CoRN/reals/Intervals/compact_bnd_AbsIR.con.
+inline "cic:/CoRN/reals/Intervals/compact_bnd_AbsIR.con".
(*#* Finally, two more useful lemmas to prove inclusion of compact
intervals. They will be necessary for the definition and proof of the
elementary properties of the integral. *)
(*#* Finally, two more useful lemmas to prove inclusion of compact
intervals. They will be necessary for the definition and proof of the
elementary properties of the integral. *)
-inline cic:/CoRN/reals/Intervals/included2_compact.con.
+inline "cic:/CoRN/reals/Intervals/included2_compact.con".
-inline cic:/CoRN/reals/Intervals/included3_compact.con.
+inline "cic:/CoRN/reals/Intervals/included3_compact.con".
(* UNEXPORTED
End Compact.
(* UNEXPORTED
End Compact.
set "baseuri" "cic:/matita/CoRN-Decl/reals/Max_AbsIR".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Max_AbsIR".
(* $Id: Max_AbsIR.v,v 1.13 2004/04/23 10:01:04 lcf Exp $ *)
(*#* printing Max %\ensuremath{\max}% *)
(*#* printing Min %\ensuremath{\min}% *)
(* $Id: Max_AbsIR.v,v 1.13 2004/04/23 10:01:04 lcf Exp $ *)
(*#* printing Max %\ensuremath{\max}% *)
(*#* printing Min %\ensuremath{\min}% *)
-(* INCLUDE
-CauchySeq
-*)
+include "reals/CauchySeq.ma".
(* UNEXPORTED
Section Maximum.
(* UNEXPORTED
Section Maximum.
-inline cic:/CoRN/reals/Max_AbsIR/x.var.
+inline "cic:/CoRN/reals/Max_AbsIR/x.var".
-inline cic:/CoRN/reals/Max_AbsIR/y.var.
+inline "cic:/CoRN/reals/Max_AbsIR/y.var".
-inline cic:/CoRN/reals/Max_AbsIR/Max_seq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_seq.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_seq_char.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_seq_char.con".
-inline cic:/CoRN/reals/Max_AbsIR/Cauchy_Max_seq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Cauchy_Max_seq.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_CauchySeq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_CauchySeq.con".
-inline cic:/CoRN/reals/Max_AbsIR/MAX.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MAX.con".
(*#*
Constructively, the elementary properties of the maximum function are:
(*#*
Constructively, the elementary properties of the maximum function are:
(So [Max] is [MAX] coupled with some proofs.)
*)
(So [Max] is [MAX] coupled with some proofs.)
*)
-inline cic:/CoRN/reals/Max_AbsIR/lft_leEq_MAX.con.
+inline "cic:/CoRN/reals/Max_AbsIR/lft_leEq_MAX.con".
-inline cic:/CoRN/reals/Max_AbsIR/rht_leEq_MAX.con.
+inline "cic:/CoRN/reals/Max_AbsIR/rht_leEq_MAX.con".
-inline cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con.
+inline "cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con".
(* UNEXPORTED
End Max_function.
*)
(* UNEXPORTED
End Max_function.
*)
-inline cic:/CoRN/reals/Max_AbsIR/MAX_strext.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MAX_strext.con".
-inline cic:/CoRN/reals/Max_AbsIR/MAX_wd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MAX_wd.con".
(* UNEXPORTED
Section properties_of_Max.
(* UNEXPORTED
Section properties_of_Max.
-inline cic:/CoRN/reals/Max_AbsIR/Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_wd_unfolded.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_wd_unfolded.con".
-inline cic:/CoRN/reals/Max_AbsIR/lft_leEq_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/lft_leEq_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/rht_leEq_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/rht_leEq_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/less_Max_imp.con.
+inline "cic:/CoRN/reals/Max_AbsIR/less_Max_imp.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_leEq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_leEq.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_less.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_less.con".
-inline cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_max.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_id.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_id.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_comm.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_comm.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_imp_Max_is_rht.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Max_is_rht.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_is_rht_imp_leEq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_is_rht_imp_leEq.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_minus_eps_leEq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_minus_eps_leEq.con".
-inline cic:/CoRN/reals/Max_AbsIR/max_one_ap_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/max_one_ap_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/pos_max_one.con.
+inline "cic:/CoRN/reals/Max_AbsIR/pos_max_one.con".
-inline cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con.
+inline "cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con".
(* UNEXPORTED
End properties_of_Max.
(* UNEXPORTED
End properties_of_Max.
[Min(x,y) [=] [--]Max( [--]x,[--]y)].
*)
[Min(x,y) [=] [--]Max( [--]x,[--]y)].
*)
-inline cic:/CoRN/reals/Max_AbsIR/MIN.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MIN.con".
-inline cic:/CoRN/reals/Max_AbsIR/MIN_wd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MIN_wd.con".
-inline cic:/CoRN/reals/Max_AbsIR/MIN_strext.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MIN_strext.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_wd_unfolded.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_wd_unfolded.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_strext_unfolded.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_strext_unfolded.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_leEq_lft.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_lft.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_leEq_rht.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_rht.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_less_imp.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_less_imp.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_Min.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_Min.con".
-inline cic:/CoRN/reals/Max_AbsIR/less_Min.con.
+inline "cic:/CoRN/reals/Max_AbsIR/less_Min.con".
-inline cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_min.con.
+inline "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_min.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_id.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_id.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_comm.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_comm.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_imp_Min_is_lft.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Min_is_lft.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_is_lft_imp_leEq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_is_lft_imp_leEq.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con".
-inline cic:/CoRN/reals/Max_AbsIR/a.var.
+inline "cic:/CoRN/reals/Max_AbsIR/a.var".
-inline cic:/CoRN/reals/Max_AbsIR/b.var.
+inline "cic:/CoRN/reals/Max_AbsIR/b.var".
-inline cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max'.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min3_leEq_Max3.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min3_leEq_Max3.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_less_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_less_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/ap_imp_Min_less_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/ap_imp_Min_less_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con".
(* UNEXPORTED
End Minimum.
(* UNEXPORTED
End Minimum.
(*#* *** Absolute value *)
(*#* *** Absolute value *)
-inline cic:/CoRN/reals/Max_AbsIR/ABSIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/ABSIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/ABSIR_strext.con.
+inline "cic:/CoRN/reals/Max_AbsIR/ABSIR_strext.con".
-inline cic:/CoRN/reals/Max_AbsIR/ABSIR_wd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/ABSIR_wd.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_wd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_wd.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_wdl.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdl.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_wdr.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdr.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIRz_isz.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIRz_isz.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_nonneg.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_nonneg.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_pos.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_pos.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_cancel_ap_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_cancel_ap_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_resp_ap_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_resp_ap_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/inv_leEq_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/inv_leEq_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsSmall_e.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsSmall_e.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsSmall_imp_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsSmall_imp_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_AbsSmall.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_AbsSmall.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_imp_AbsSmall.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_imp_AbsSmall.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsSmall_transitive.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsSmall_transitive.con".
-inline cic:/CoRN/reals/Max_AbsIR/zero_less_AbsIR_plus_one.con.
+inline "cic:/CoRN/reals/Max_AbsIR/zero_less_AbsIR_plus_one.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_inv.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_inv.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_minus.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_minus.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_x.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_x.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_inv_x.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_inv_x.con".
-inline cic:/CoRN/reals/Max_AbsIR/less_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/less_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_distr_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_distr_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_approach_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_approach_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/Abs_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Abs_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_str_bnd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_str_bnd.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con".
(* UNEXPORTED
End Absolute.
(* UNEXPORTED
End Absolute.
-inline cic:/CoRN/reals/Max_AbsIR/F.var.
+inline "cic:/CoRN/reals/Max_AbsIR/F.var".
-inline cic:/CoRN/reals/Max_AbsIR/G.var.
+inline "cic:/CoRN/reals/Max_AbsIR/G.var".
-inline cic:/CoRN/reals/Max_AbsIR/P.con.
+inline "cic:/CoRN/reals/Max_AbsIR/P.con".
-inline cic:/CoRN/reals/Max_AbsIR/Q.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Q.con".
-inline cic:/CoRN/reals/Max_AbsIR/part_function_Max_strext.con.
+inline "cic:/CoRN/reals/Max_AbsIR/part_function_Max_strext.con".
-inline cic:/CoRN/reals/Max_AbsIR/FMax.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FMax.con".
(* UNEXPORTED
End Part_Function_Max.
(* UNEXPORTED
End Part_Function_Max.
Section Part_Function_Abs.
*)
Section Part_Function_Abs.
*)
-inline cic:/CoRN/reals/Max_AbsIR/F.var.
+inline "cic:/CoRN/reals/Max_AbsIR/F.var".
-inline cic:/CoRN/reals/Max_AbsIR/G.var.
+inline "cic:/CoRN/reals/Max_AbsIR/G.var".
-inline cic:/CoRN/reals/Max_AbsIR/P.con.
+inline "cic:/CoRN/reals/Max_AbsIR/P.con".
-inline cic:/CoRN/reals/Max_AbsIR/Q.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Q.con".
-inline cic:/CoRN/reals/Max_AbsIR/FMin.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FMin.con".
-inline cic:/CoRN/reals/Max_AbsIR/FAbs.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FAbs.con".
(* UNEXPORTED
Opaque Max.
*)
(* UNEXPORTED
Opaque Max.
*)
-inline cic:/CoRN/reals/Max_AbsIR/FMin_char.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FMin_char.con".
(* UNEXPORTED
Transparent Max.
*)
(* UNEXPORTED
Transparent Max.
*)
-inline cic:/CoRN/reals/Max_AbsIR/FAbs_char.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FAbs_char.con".
(* UNEXPORTED
End Part_Function_Abs.
(* UNEXPORTED
End Part_Function_Abs.
Hint Resolve FAbs_char: algebra.
*)
Hint Resolve FAbs_char: algebra.
*)
-inline cic:/CoRN/reals/Max_AbsIR/FAbs_char'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FAbs_char'.con".
-inline cic:/CoRN/reals/Max_AbsIR/FAbs_nonneg.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FAbs_nonneg.con".
(* UNEXPORTED
Hint Resolve FAbs_char': algebra.
(* UNEXPORTED
Hint Resolve FAbs_char': algebra.
-inline cic:/CoRN/reals/Max_AbsIR/F.var.
+inline "cic:/CoRN/reals/Max_AbsIR/F.var".
-inline cic:/CoRN/reals/Max_AbsIR/G.var.
+inline "cic:/CoRN/reals/Max_AbsIR/G.var".
-inline cic:/CoRN/reals/Max_AbsIR/P.con.
+inline "cic:/CoRN/reals/Max_AbsIR/P.con".
-inline cic:/CoRN/reals/Max_AbsIR/Q.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Q.con".
-inline cic:/CoRN/reals/Max_AbsIR/R.var.
+inline "cic:/CoRN/reals/Max_AbsIR/R.var".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMax.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMax.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMax'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMax'.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMax''.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMax''.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMin.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMin.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMin'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMin'.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMin''.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMin''.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FAbs.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FAbs.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con".
(* UNEXPORTED
End Inclusion.
(* UNEXPORTED
End Inclusion.
set "baseuri" "cic:/matita/CoRN-Decl/reals/NRootIR".
set "baseuri" "cic:/matita/CoRN-Decl/reals/NRootIR".
(* $Id: NRootIR.v,v 1.5 2004/04/23 10:01:05 lcf Exp $ *)
(*#* printing NRoot %\ensuremath{\sqrt[n]{\cdot}}% *)
(*#* printing sqrt %\ensuremath{\sqrt{\cdot}}% *)
(* $Id: NRootIR.v,v 1.5 2004/04/23 10:01:05 lcf Exp $ *)
(*#* printing NRoot %\ensuremath{\sqrt[n]{\cdot}}% *)
(*#* printing sqrt %\ensuremath{\sqrt{\cdot}}% *)
-(* INCLUDE
-OddPolyRootIR
-*)
+include "reals/OddPolyRootIR.ma".
(*#* * Roots of Real Numbers *)
(*#* * Roots of Real Numbers *)
-inline cic:/CoRN/reals/NRootIR/n.var.
+inline "cic:/CoRN/reals/NRootIR/n.var".
-inline cic:/CoRN/reals/NRootIR/n_pos.var.
+inline "cic:/CoRN/reals/NRootIR/n_pos.var".
-inline cic:/CoRN/reals/NRootIR/c.var.
+inline "cic:/CoRN/reals/NRootIR/c.var".
-inline cic:/CoRN/reals/NRootIR/c_nonneg.var.
+inline "cic:/CoRN/reals/NRootIR/c_nonneg.var".
-inline cic:/CoRN/reals/NRootIR/p.con.
+inline "cic:/CoRN/reals/NRootIR/p.con".
-inline cic:/CoRN/reals/NRootIR/CnrootIR.con.
+inline "cic:/CoRN/reals/NRootIR/CnrootIR.con".
-inline cic:/CoRN/reals/NRootIR/nroot.con.
+inline "cic:/CoRN/reals/NRootIR/nroot.con".
-inline cic:/CoRN/reals/NRootIR/NRoot.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot.con".
-inline cic:/CoRN/reals/NRootIR/NRoot_power.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_power.con".
(* UNEXPORTED
Hint Resolve NRoot_power: algebra.
*)
(* UNEXPORTED
Hint Resolve NRoot_power: algebra.
*)
-inline cic:/CoRN/reals/NRootIR/NRoot_nonneg.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_nonneg.con".
-inline cic:/CoRN/reals/NRootIR/NRoot_pos.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_pos.con".
-inline cic:/CoRN/reals/NRootIR/NRoot_power'.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_power'.con".
-inline cic:/CoRN/reals/NRootIR/NRoot_pres_less.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_pres_less.con".
-inline cic:/CoRN/reals/NRootIR/NRoot_less_one.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_less_one.con".
-inline cic:/CoRN/reals/NRootIR/NRoot_cancel.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_cancel.con".
(*#* %\begin{convention}% Let [x,y] be nonnegative real numbers.
%\end{convention}% *)
(*#* %\begin{convention}% Let [x,y] be nonnegative real numbers.
%\end{convention}% *)
-inline cic:/CoRN/reals/NRootIR/x.var.
+inline "cic:/CoRN/reals/NRootIR/x.var".
-inline cic:/CoRN/reals/NRootIR/y.var.
+inline "cic:/CoRN/reals/NRootIR/y.var".
-inline cic:/CoRN/reals/NRootIR/Hx.var.
+inline "cic:/CoRN/reals/NRootIR/Hx.var".
-inline cic:/CoRN/reals/NRootIR/Hy.var.
+inline "cic:/CoRN/reals/NRootIR/Hy.var".
-inline cic:/CoRN/reals/NRootIR/NRoot_wd.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_wd.con".
-inline cic:/CoRN/reals/NRootIR/NRoot_unique.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_unique.con".
(* UNEXPORTED
End Nth_Root.
(* UNEXPORTED
End Nth_Root.
Hint Resolve NRoot_power NRoot_power': algebra.
*)
Hint Resolve NRoot_power NRoot_power': algebra.
*)
-inline cic:/CoRN/reals/NRootIR/NRoot_resp_leEq.con.
+inline "cic:/CoRN/reals/NRootIR/NRoot_resp_leEq.con".
(*#**********************************)
(*#**********************************)
-inline cic:/CoRN/reals/NRootIR/sqrt.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt.con".
-inline cic:/CoRN/reals/NRootIR/sqrt_sqr.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_sqr.con".
(* UNEXPORTED
Hint Resolve sqrt_sqr: algebra.
*)
(* UNEXPORTED
Hint Resolve sqrt_sqr: algebra.
*)
-inline cic:/CoRN/reals/NRootIR/sqrt_nonneg.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_nonneg.con".
-inline cic:/CoRN/reals/NRootIR/sqrt_wd.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_wd.con".
(* UNEXPORTED
Hint Resolve sqrt_wd: algebra_c.
*)
(* UNEXPORTED
Hint Resolve sqrt_wd: algebra_c.
*)
-inline cic:/CoRN/reals/NRootIR/sqrt_to_nonneg.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_to_nonneg.con".
-inline cic:/CoRN/reals/NRootIR/sqrt_to_nonpos.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_to_nonpos.con".
-inline cic:/CoRN/reals/NRootIR/sqrt_mult.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_mult.con".
(* UNEXPORTED
Hint Resolve sqrt_mult: algebra.
*)
(* UNEXPORTED
Hint Resolve sqrt_mult: algebra.
*)
-inline cic:/CoRN/reals/NRootIR/sqrt_mult_wd.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_mult_wd.con".
-inline cic:/CoRN/reals/NRootIR/sqrt_less.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_less.con".
-inline cic:/CoRN/reals/NRootIR/sqrt_less'.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_less'.con".
-inline cic:/CoRN/reals/NRootIR/sqrt_resp_leEq.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_resp_leEq.con".
-inline cic:/CoRN/reals/NRootIR/sqrt_resp_less.con.
+inline "cic:/CoRN/reals/NRootIR/sqrt_resp_less.con".
(* UNEXPORTED
End Square_root.
(* UNEXPORTED
End Square_root.
-inline cic:/CoRN/reals/NRootIR/AbsIR_sqrt_sqr.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_sqrt_sqr.con".
(* UNEXPORTED
Hint Resolve AbsIR_sqrt_sqr: algebra.
*)
(* UNEXPORTED
Hint Resolve AbsIR_sqrt_sqr: algebra.
*)
-inline cic:/CoRN/reals/NRootIR/AbsIR_resp_mult.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_resp_mult.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_mult_pos.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_mult_pos'.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos'.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_nexp.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_nexp.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_nexp_op.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_nexp_op.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_less_square.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_less_square.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_leEq_square.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_leEq_square.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_division.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_division.con".
(*#* Some special cases. *)
(*#* Some special cases. *)
-inline cic:/CoRN/reals/NRootIR/AbsIR_recip.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_recip.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_div_two.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_div_two.con".
(*#* Cauchy-Schwartz for IR and variants on that subject. *)
(*#* Cauchy-Schwartz for IR and variants on that subject. *)
-inline cic:/CoRN/reals/NRootIR/triangle_IR.con.
+inline "cic:/CoRN/reals/NRootIR/triangle_IR.con".
-inline cic:/CoRN/reals/NRootIR/triangle_SumIR.con.
+inline "cic:/CoRN/reals/NRootIR/triangle_SumIR.con".
-inline cic:/CoRN/reals/NRootIR/triangle_IR_minus.con.
+inline "cic:/CoRN/reals/NRootIR/triangle_IR_minus.con".
-inline cic:/CoRN/reals/NRootIR/weird_triangleIR.con.
+inline "cic:/CoRN/reals/NRootIR/weird_triangleIR.con".
-inline cic:/CoRN/reals/NRootIR/triangle_IR_minus'.con.
+inline "cic:/CoRN/reals/NRootIR/triangle_IR_minus'.con".
-inline cic:/CoRN/reals/NRootIR/triangle_SumxIR.con.
+inline "cic:/CoRN/reals/NRootIR/triangle_SumxIR.con".
-inline cic:/CoRN/reals/NRootIR/triangle_Sum2IR.con.
+inline "cic:/CoRN/reals/NRootIR/triangle_Sum2IR.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_str_bnd_AbsIR.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_str_bnd_AbsIR.con".
-inline cic:/CoRN/reals/NRootIR/AbsIR_bnd_AbsIR.con.
+inline "cic:/CoRN/reals/NRootIR/AbsIR_bnd_AbsIR.con".
(* UNEXPORTED
End Absolute_Props.
(* UNEXPORTED
End Absolute_Props.
-inline cic:/CoRN/reals/NRootIR/Cauchy_Lim_recip.con.
+inline "cic:/CoRN/reals/NRootIR/Cauchy_Lim_recip.con".
-inline cic:/CoRN/reals/NRootIR/Cauchy_recip.con.
+inline "cic:/CoRN/reals/NRootIR/Cauchy_recip.con".
-inline cic:/CoRN/reals/NRootIR/Lim_recip.con.
+inline "cic:/CoRN/reals/NRootIR/Lim_recip.con".
(* UNEXPORTED
End Consequences.
(* UNEXPORTED
End Consequences.
set "baseuri" "cic:/matita/CoRN-Decl/reals/OddPolyRootIR".
set "baseuri" "cic:/matita/CoRN-Decl/reals/OddPolyRootIR".
(* $Id: OddPolyRootIR.v,v 1.5 2004/04/23 10:01:05 lcf Exp $ *)
(* $Id: OddPolyRootIR.v,v 1.5 2004/04/23 10:01:05 lcf Exp $ *)
(*#* * Roots of polynomials of odd degree *)
(*#* * Roots of polynomials of odd degree *)
-inline cic:/CoRN/reals/OddPolyRootIR/R.var.
+inline "cic:/CoRN/reals/OddPolyRootIR/R.var".
-inline cic:/CoRN/reals/OddPolyRootIR/RX.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/RX.con".
-inline cic:/CoRN/reals/OddPolyRootIR/Cbigger.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/Cbigger.con".
-inline cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con".
-inline cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con".
-inline cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con".
(* UNEXPORTED
End CPoly_Big.
(* UNEXPORTED
End CPoly_Big.
-inline cic:/CoRN/reals/OddPolyRootIR/R.var.
+inline "cic:/CoRN/reals/OddPolyRootIR/R.var".
-inline cic:/CoRN/reals/OddPolyRootIR/RX.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/RX.con".
-inline cic:/CoRN/reals/OddPolyRootIR/flip.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/flip.con".
-inline cic:/CoRN/reals/OddPolyRootIR/flip_poly.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con".
-inline cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con".
(* UNEXPORTED
Hint Resolve flip_coefficient: algebra.
*)
(* UNEXPORTED
Hint Resolve flip_coefficient: algebra.
*)
-inline cic:/CoRN/reals/OddPolyRootIR/flip_odd.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con".
(* UNEXPORTED
End Flip_Poly.
(* UNEXPORTED
End Flip_Poly.
-inline cic:/CoRN/reals/OddPolyRootIR/R.var.
+inline "cic:/CoRN/reals/OddPolyRootIR/R.var".
-inline cic:/CoRN/reals/OddPolyRootIR/RX.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/RX.con".
-inline cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con".
-inline cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con".
-inline cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con".
(* UNEXPORTED
End OddPoly_Signs.
(* UNEXPORTED
End OddPoly_Signs.
-inline cic:/CoRN/reals/OddPolyRootIR/R.var.
+inline "cic:/CoRN/reals/OddPolyRootIR/R.var".
-inline cic:/CoRN/reals/OddPolyRootIR/RX.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/RX.con".
-inline cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con".
-inline cic:/CoRN/reals/OddPolyRootIR/poly_norm.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm.con".
-inline cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con".
-inline cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con".
(* UNEXPORTED
End Poly_Norm.
(* UNEXPORTED
End Poly_Norm.
(*#* ** Roots of polynomials of odd degree
Polynomials of odd degree over the reals always have a root. *)
(*#* ** Roots of polynomials of odd degree
Polynomials of odd degree over the reals always have a root. *)
-inline cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con".
-inline cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con".
-inline cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con.
+inline "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con".
(* UNEXPORTED
End OddPoly_Root.
(* UNEXPORTED
End OddPoly_Root.
set "baseuri" "cic:/matita/CoRN-Decl/reals/Q_dense".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Q_dense".
-(* INCLUDE
-Q_in_CReals
-*)
+include "reals/Q_in_CReals.ma".
(*#***** Opaque_algebra.v will be loaded in line 151 ******)
(*#***** Opaque_algebra.v will be loaded in line 151 ******)
-inline cic:/CoRN/reals/Q_dense/or_not_and.con.
+inline "cic:/CoRN/reals/Q_dense/or_not_and.con".
(* UNEXPORTED
Section Interval_definition.
*)
(* UNEXPORTED
Section Interval_definition.
*)
-inline cic:/CoRN/reals/Q_dense/OF.var.
+inline "cic:/CoRN/reals/Q_dense/OF.var".
-inline cic:/CoRN/reals/Q_dense/Interval.ind.
+inline "cic:/CoRN/reals/Q_dense/Interval.ind".
-inline cic:/CoRN/reals/Q_dense/Length.con.
+coercion "cic:/matita/CoRN-Decl/reals/Q_dense/pair_crr.con" 0 (* compounds *).
+
+inline "cic:/CoRN/reals/Q_dense/Length.con".
(* UNEXPORTED
End Interval_definition.
*)
(* UNEXPORTED
End Interval_definition.
*)
-inline cic:/CoRN/reals/Q_dense/Rat_Interval.con.
+inline "cic:/CoRN/reals/Q_dense/Rat_Interval.con".
(* we have this in Q_COrdField... *)
(* we have this in Q_COrdField... *)
-inline cic:/CoRN/reals/Q_dense/Qlt_eq_gt_dec'.con.
+inline "cic:/CoRN/reals/Q_dense/Qlt_eq_gt_dec'.con".
(*
Lemma ex_informative_on_Q:(P:Q_as_COrdField->Prop)(Ex [q:Q_as_COrdField](P q))
(*
Lemma ex_informative_on_Q:(P:Q_as_COrdField->Prop)(Ex [q:Q_as_COrdField](P q))
Section COrdField_extra.
*)
Section COrdField_extra.
*)
-inline cic:/CoRN/reals/Q_dense/OF.var.
+inline "cic:/CoRN/reals/Q_dense/OF.var".
-inline cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con.
+inline "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con".
-inline cic:/CoRN/reals/Q_dense/AbsSmall_neg_reflexive.con.
+inline "cic:/CoRN/reals/Q_dense/AbsSmall_neg_reflexive.con".
-inline cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con.
+inline "cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con".
(* UNEXPORTED
End COrdField_extra.
(* UNEXPORTED
End COrdField_extra.
Section Rational_sequence.
*)
Section Rational_sequence.
*)
-(* INCLUDE
-Opaque_algebra
-*)
+include "tactics/Opaque_algebra.ma".
(*#*** WARNING: A file is being loaded *****)
(*#*** WARNING: A file is being loaded *****)
-inline cic:/CoRN/reals/Q_dense/R1.var.
+inline "cic:/CoRN/reals/Q_dense/R1.var".
-inline cic:/CoRN/reals/Q_dense/start_l.con.
+inline "cic:/CoRN/reals/Q_dense/start_l.con".
-inline cic:/CoRN/reals/Q_dense/start_of_sequence2.con.
+inline "cic:/CoRN/reals/Q_dense/start_of_sequence2.con".
-inline cic:/CoRN/reals/Q_dense/start_r.con.
+inline "cic:/CoRN/reals/Q_dense/start_r.con".
-inline cic:/CoRN/reals/Q_dense/start_of_sequence_property.con.
+inline "cic:/CoRN/reals/Q_dense/start_of_sequence_property.con".
-inline cic:/CoRN/reals/Q_dense/l_less_r.con.
+inline "cic:/CoRN/reals/Q_dense/l_less_r.con".
-inline cic:/CoRN/reals/Q_dense/shrink23.con.
+inline "cic:/CoRN/reals/Q_dense/shrink23.con".
-inline cic:/CoRN/reals/Q_dense/shrink13.con.
+inline "cic:/CoRN/reals/Q_dense/shrink13.con".
-inline cic:/CoRN/reals/Q_dense/shrink24.con.
+inline "cic:/CoRN/reals/Q_dense/shrink24.con".
-inline cic:/CoRN/reals/Q_dense/cotrans_analyze.con.
+inline "cic:/CoRN/reals/Q_dense/cotrans_analyze.con".
-inline cic:/CoRN/reals/Q_dense/cotrans_analyze_strong.con.
+inline "cic:/CoRN/reals/Q_dense/cotrans_analyze_strong.con".
-inline cic:/CoRN/reals/Q_dense/trichotomy.con.
+inline "cic:/CoRN/reals/Q_dense/trichotomy.con".
-inline cic:/CoRN/reals/Q_dense/trichotomy_strong1.con.
+inline "cic:/CoRN/reals/Q_dense/trichotomy_strong1.con".
-inline cic:/CoRN/reals/Q_dense/if_cotrans.con.
+inline "cic:/CoRN/reals/Q_dense/if_cotrans.con".
-inline cic:/CoRN/reals/Q_dense/if_cotrans_strong.con.
+inline "cic:/CoRN/reals/Q_dense/if_cotrans_strong.con".
-inline cic:/CoRN/reals/Q_dense/Intrvl.con.
+inline "cic:/CoRN/reals/Q_dense/Intrvl.con".
-inline cic:/CoRN/reals/Q_dense/G.con.
+inline "cic:/CoRN/reals/Q_dense/G.con".
(* UNEXPORTED
Opaque Q_as_CField.
*)
(* UNEXPORTED
Opaque Q_as_CField.
*)
-inline cic:/CoRN/reals/Q_dense/delta_Intrvl.con.
+inline "cic:/CoRN/reals/Q_dense/delta_Intrvl.con".
-inline cic:/CoRN/reals/Q_dense/Length_Intrvl.con.
+inline "cic:/CoRN/reals/Q_dense/Length_Intrvl.con".
-inline cic:/CoRN/reals/Q_dense/Intrvl_inside_l_n.con.
+inline "cic:/CoRN/reals/Q_dense/Intrvl_inside_l_n.con".
-inline cic:/CoRN/reals/Q_dense/Intrvl_inside_r_n.con.
+inline "cic:/CoRN/reals/Q_dense/Intrvl_inside_r_n.con".
-inline cic:/CoRN/reals/Q_dense/G_m_n_lower.con.
+inline "cic:/CoRN/reals/Q_dense/G_m_n_lower.con".
-inline cic:/CoRN/reals/Q_dense/G_m_n_upper.con.
+inline "cic:/CoRN/reals/Q_dense/G_m_n_upper.con".
(* UNEXPORTED
Opaque Q_as_COrdField.
*)
(* UNEXPORTED
Opaque Q_as_COrdField.
*)
-inline cic:/CoRN/reals/Q_dense/a_simple_inequality.con.
+inline "cic:/CoRN/reals/Q_dense/a_simple_inequality.con".
-inline cic:/CoRN/reals/Q_dense/G_conversion_rate2.con.
+inline "cic:/CoRN/reals/Q_dense/G_conversion_rate2.con".
-inline cic:/CoRN/reals/Q_dense/CS_seq_G.con.
+inline "cic:/CoRN/reals/Q_dense/CS_seq_G.con".
-inline cic:/CoRN/reals/Q_dense/G_as_CauchySeq.con.
+inline "cic:/CoRN/reals/Q_dense/G_as_CauchySeq.con".
-inline cic:/CoRN/reals/Q_dense/CS_seq_inj_Q_G.con.
+inline "cic:/CoRN/reals/Q_dense/CS_seq_inj_Q_G.con".
-inline cic:/CoRN/reals/Q_dense/inj_Q_G_as_CauchySeq.con.
+inline "cic:/CoRN/reals/Q_dense/inj_Q_G_as_CauchySeq.con".
-inline cic:/CoRN/reals/Q_dense/x_in_Intrvl_l.con.
+inline "cic:/CoRN/reals/Q_dense/x_in_Intrvl_l.con".
-inline cic:/CoRN/reals/Q_dense/x_in_Intrvl_r.con.
+inline "cic:/CoRN/reals/Q_dense/x_in_Intrvl_r.con".
-inline cic:/CoRN/reals/Q_dense/G_conversion_rate_resp_x.con.
+inline "cic:/CoRN/reals/Q_dense/G_conversion_rate_resp_x.con".
-inline cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con.
+inline "cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con".
(* UNEXPORTED
End Rational_sequence.
(* UNEXPORTED
End Rational_sequence.
set "baseuri" "cic:/matita/CoRN-Decl/reals/Q_in_CReals".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Q_in_CReals".
(* $Id: Q_in_CReals.v,v 1.10 2004/04/23 10:01:05 lcf Exp $ *)
(*#* * On density of the image of [Q] in an arbitrary real number structure
(* $Id: Q_in_CReals.v,v 1.10 2004/04/23 10:01:05 lcf Exp $ *)
(*#* * On density of the image of [Q] in an arbitrary real number structure
in other words we will prove that the image of rational numbers in
dense in any real number structure. *)
in other words we will prove that the image of rational numbers in
dense in any real number structure. *)
-(* INCLUDE
-Cauchy_IR
-*)
+include "model/reals/Cauchy_IR.ma".
+include "model/monoids/Nmonoid.ma".
+include "model/rings/Zring.ma".
(* UNEXPORTED
Section Rational_sequence_prelogue.
(* UNEXPORTED
Section Rational_sequence_prelogue.
-inline cic:/CoRN/reals/Q_in_CReals/R1.var.
+inline "cic:/CoRN/reals/Q_in_CReals/R1.var".
(* We clone these proofs from CReals1.v just because there IR is an axiom *)
(* begin hide *)
(* We clone these proofs from CReals1.v just because there IR is an axiom *)
(* begin hide *)
-inline cic:/CoRN/reals/Q_in_CReals/CReals_is_CReals.con.
+inline "cic:/CoRN/reals/Q_in_CReals/CReals_is_CReals.con".
-inline cic:/CoRN/reals/Q_in_CReals/Lim_Cauchy.con.
+inline "cic:/CoRN/reals/Q_in_CReals/Lim_Cauchy.con".
-inline cic:/CoRN/reals/Q_in_CReals/Archimedes.con.
+inline "cic:/CoRN/reals/Q_in_CReals/Archimedes.con".
-inline cic:/CoRN/reals/Q_in_CReals/Archimedes'.con.
+inline "cic:/CoRN/reals/Q_in_CReals/Archimedes'.con".
(*#**************************************)
(*#**************************************)
+coercion "cic:/matita/CoRN-Decl/reals/Q_in_CReals/nat_of_P.con" 0 (* compounds *).
+
To define the injection we need one elemntary lemma about the denominator:
*)
To define the injection we need one elemntary lemma about the denominator:
*)
-inline cic:/CoRN/reals/Q_in_CReals/den_is_nonzero.con.
+inline "cic:/CoRN/reals/Q_in_CReals/den_is_nonzero.con".
(*#* And we define the injection in the natural way, using [zring] and [nring]. We call this [inj_Q], in contrast with [inject_Q] defined in [Cauchy_CReals]. *)
(*#* And we define the injection in the natural way, using [zring] and [nring]. We call this [inj_Q], in contrast with [inject_Q] defined in [Cauchy_CReals]. *)
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q.con".
(*#* Next we need some properties of [nring], on the setoid of natural numbers: *)
(*#* Next we need some properties of [nring], on the setoid of natural numbers: *)
-inline cic:/CoRN/reals/Q_in_CReals/nring_strext.con.
+inline "cic:/CoRN/reals/Q_in_CReals/nring_strext.con".
-inline cic:/CoRN/reals/Q_in_CReals/nring_wd.con.
+inline "cic:/CoRN/reals/Q_in_CReals/nring_wd.con".
-inline cic:/CoRN/reals/Q_in_CReals/nring_eq.con.
+inline "cic:/CoRN/reals/Q_in_CReals/nring_eq.con".
-inline cic:/CoRN/reals/Q_in_CReals/nring_leEq.con.
+inline "cic:/CoRN/reals/Q_in_CReals/nring_leEq.con".
(*#* Similarly we prove some properties of [zring] on the ring of integers: *)
(*#* Similarly we prove some properties of [zring] on the ring of integers: *)
-inline cic:/CoRN/reals/Q_in_CReals/zring_strext.con.
+inline "cic:/CoRN/reals/Q_in_CReals/zring_strext.con".
-inline cic:/CoRN/reals/Q_in_CReals/zring_wd.con.
+inline "cic:/CoRN/reals/Q_in_CReals/zring_wd.con".
-inline cic:/CoRN/reals/Q_in_CReals/zring_less.con.
+inline "cic:/CoRN/reals/Q_in_CReals/zring_less.con".
(*#* Using the above lemmata we prove the basic properties of [inj_Q], i.e.%\% it is a setoid function and preserves the ring operations and oreder operation. *)
(*#* Using the above lemmata we prove the basic properties of [inj_Q], i.e.%\% it is a setoid function and preserves the ring operations and oreder operation. *)
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_strext.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_strext.con".
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_wd.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_wd.con".
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_plus.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_plus.con".
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_mult.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_mult.con".
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_less.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_less.con".
-inline cic:/CoRN/reals/Q_in_CReals/less_inj_Q.con.
+inline "cic:/CoRN/reals/Q_in_CReals/less_inj_Q.con".
-inline cic:/CoRN/reals/Q_in_CReals/leEq_inj_Q.con.
+inline "cic:/CoRN/reals/Q_in_CReals/leEq_inj_Q.con".
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_leEq.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_leEq.con".
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_min.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_min.con".
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_minus.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_minus.con".
(*#* Moreover, and as expected, the [AbsSmall] predicate is also
preserved under the [inj_Q] *)
(*#* Moreover, and as expected, the [AbsSmall] predicate is also
preserved under the [inj_Q] *)
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_AbsSmall.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_AbsSmall.con".
-inline cic:/CoRN/reals/Q_in_CReals/AbsSmall_inj_Q.con.
+inline "cic:/CoRN/reals/Q_in_CReals/AbsSmall_inj_Q.con".
(*#* ** Injection preserves Cauchy property
We apply the above lemmata to obtain following theorem, which says
that a Cauchy sequence of elemnts of [Q] will be Cauchy in [R1].
*)
(*#* ** Injection preserves Cauchy property
We apply the above lemmata to obtain following theorem, which says
that a Cauchy sequence of elemnts of [Q] will be Cauchy in [R1].
*)
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_Cauchy.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_Cauchy.con".
(*#* Furthermore we prove that applying [nring] (which is adding the
ring unit [n] times) is the same whether we do it in [Q] or in [R1]:
*)
(*#* Furthermore we prove that applying [nring] (which is adding the
ring unit [n] times) is the same whether we do it in [Q] or in [R1]:
*)
-inline cic:/CoRN/reals/Q_in_CReals/inj_Q_nring.con.
+inline "cic:/CoRN/reals/Q_in_CReals/inj_Q_nring.con".
(*#* ** Injection of [Q] is dense
Finally we are able to prove the density of image of [Q] in [R1]. We
(*#* ** Injection of [Q] is dense
Finally we are able to prove the density of image of [Q] in [R1]. We
trisection" argument, which is ubiquitous in constructive analysis.
*)
trisection" argument, which is ubiquitous in constructive analysis.
*)
-inline cic:/CoRN/reals/Q_in_CReals/start_of_sequence.con.
+inline "cic:/CoRN/reals/Q_in_CReals/start_of_sequence.con".
(*#* The second version of the density of [Q] in [R1] states that given
any positive real number, there is a rational number between it and
zero. This lemma can be used to prove the more general fact that there
is a rational number between any two real numbers. *)
(*#* The second version of the density of [Q] in [R1] states that given
any positive real number, there is a rational number between it and
zero. This lemma can be used to prove the more general fact that there
is a rational number between any two real numbers. *)
-inline cic:/CoRN/reals/Q_in_CReals/Q_dense_in_CReals.con.
+inline "cic:/CoRN/reals/Q_in_CReals/Q_dense_in_CReals.con".
(* UNEXPORTED
End Rational_sequence_prelogue.
(* UNEXPORTED
End Rational_sequence_prelogue.
set "baseuri" "cic:/matita/CoRN-Decl/reals/R_morphism".
set "baseuri" "cic:/matita/CoRN-Decl/reals/R_morphism".
(* begin hide *)
(* In this file a notion of morphism between two arbitrary real number
structures, is introduced together with te proofs that this notion of
morphism preserves the basic algebraic structure. *)
(* begin hide *)
(* In this file a notion of morphism between two arbitrary real number
structures, is introduced together with te proofs that this notion of
morphism preserves the basic algebraic structure. *)
+include "reals/CReals.ma".
(* This comes from CReals1.v *)
(* This comes from CReals1.v *)
-inline cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con.
+inline "cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con".
(* UNEXPORTED
Section morphism.
*)
(* UNEXPORTED
Section morphism.
*)
-inline cic:/CoRN/reals/R_morphism/R1.var.
+inline "cic:/CoRN/reals/R_morphism/R1.var".
-inline cic:/CoRN/reals/R_morphism/R2.var.
+inline "cic:/CoRN/reals/R_morphism/R2.var".
(* UNEXPORTED
Section morphism_details.
*)
(* UNEXPORTED
Section morphism_details.
*)
-inline cic:/CoRN/reals/R_morphism/phi.var.
+inline "cic:/CoRN/reals/R_morphism/phi.var".
-inline cic:/CoRN/reals/R_morphism/p1.var.
+inline "cic:/CoRN/reals/R_morphism/p1.var".
-inline cic:/CoRN/reals/R_morphism/p2.var.
+inline "cic:/CoRN/reals/R_morphism/p2.var".
-inline cic:/CoRN/reals/R_morphism/f1.var.
+inline "cic:/CoRN/reals/R_morphism/f1.var".
-inline cic:/CoRN/reals/R_morphism/f2.var.
+inline "cic:/CoRN/reals/R_morphism/f2.var".
-inline cic:/CoRN/reals/R_morphism/g1.var.
+inline "cic:/CoRN/reals/R_morphism/g1.var".
-inline cic:/CoRN/reals/R_morphism/g2.var.
+inline "cic:/CoRN/reals/R_morphism/g2.var".
-inline cic:/CoRN/reals/R_morphism/fun_pres_relation.con.
+inline "cic:/CoRN/reals/R_morphism/fun_pres_relation.con".
-inline cic:/CoRN/reals/R_morphism/fun_pres_un_fun.con.
+inline "cic:/CoRN/reals/R_morphism/fun_pres_un_fun.con".
-inline cic:/CoRN/reals/R_morphism/fun_pres_bin_fun.con.
+inline "cic:/CoRN/reals/R_morphism/fun_pres_bin_fun.con".
(*
Definition fun_pres_partial_fun:=(x:R1;H1:x[#]Zero;H2:(phi x)[#]Zero)
(phi (nzinj R1 (i1 (nzpro R1 x H1))))[=](nzinj R2 (i2 (nzpro R2 (phi x) H2))).
*)
(*
Definition fun_pres_partial_fun:=(x:R1;H1:x[#]Zero;H2:(phi x)[#]Zero)
(phi (nzinj R1 (i1 (nzpro R1 x H1))))[=](nzinj R2 (i2 (nzpro R2 (phi x) H2))).
*)
-inline cic:/CoRN/reals/R_morphism/fun_pres_Lim.con.
+inline "cic:/CoRN/reals/R_morphism/fun_pres_Lim.con".
(* UNEXPORTED
End morphism_details.
*)
(* UNEXPORTED
End morphism_details.
*)
-inline cic:/CoRN/reals/R_morphism/Homomorphism.ind.
+inline "cic:/CoRN/reals/R_morphism/Homomorphism.ind".
+
+coercion "cic:/matita/CoRN-Decl/reals/R_morphism/map.con" 0 (* compounds *).
(* This might be useful later...
Definition Homo_as_CSetoid_fun:=
(* This might be useful later...
Definition Homo_as_CSetoid_fun:=
-inline cic:/CoRN/reals/R_morphism/map_strext_unfolded.con.
+inline "cic:/CoRN/reals/R_morphism/map_strext_unfolded.con".
-inline cic:/CoRN/reals/R_morphism/map_wd_unfolded.con.
+inline "cic:/CoRN/reals/R_morphism/map_wd_unfolded.con".
-inline cic:/CoRN/reals/R_morphism/map_pres_less_unfolded.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_less_unfolded.con".
-inline cic:/CoRN/reals/R_morphism/map_pres_plus_unfolded.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_plus_unfolded.con".
-inline cic:/CoRN/reals/R_morphism/map_pres_mult_unfolded.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_mult_unfolded.con".
(* Now we start to derive some useful properties of a Homomorphism *)
(* Now we start to derive some useful properties of a Homomorphism *)
-inline cic:/CoRN/reals/R_morphism/map_pres_zero.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_zero.con".
-inline cic:/CoRN/reals/R_morphism/map_pres_zero_unfolded.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_zero_unfolded.con".
-inline cic:/CoRN/reals/R_morphism/map_pres_minus.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_minus.con".
-inline cic:/CoRN/reals/R_morphism/map_pres_minus_unfolded.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_minus_unfolded.con".
-inline cic:/CoRN/reals/R_morphism/map_pres_apartness.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_apartness.con".
(* Merely a useful special case *)
(* Merely a useful special case *)
-inline cic:/CoRN/reals/R_morphism/map_pres_ap_zero.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_ap_zero.con".
-inline cic:/CoRN/reals/R_morphism/map_pres_one.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_one.con".
-inline cic:/CoRN/reals/R_morphism/map_pres_one_unfolded.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_one_unfolded.con".
(* I will not use the following lemma *)
(* I will not use the following lemma *)
-inline cic:/CoRN/reals/R_morphism/map_pres_inv_unfolded.con.
+inline "cic:/CoRN/reals/R_morphism/map_pres_inv_unfolded.con".
(* UNEXPORTED
End morphism.
(* UNEXPORTED
End morphism.
-inline cic:/CoRN/reals/R_morphism/R1.var.
+inline "cic:/CoRN/reals/R_morphism/R1.var".
-inline cic:/CoRN/reals/R_morphism/R2.var.
+inline "cic:/CoRN/reals/R_morphism/R2.var".
-inline cic:/CoRN/reals/R_morphism/R3.var.
+inline "cic:/CoRN/reals/R_morphism/R3.var".
-inline cic:/CoRN/reals/R_morphism/f.var.
+inline "cic:/CoRN/reals/R_morphism/f.var".
-inline cic:/CoRN/reals/R_morphism/g.var.
+inline "cic:/CoRN/reals/R_morphism/g.var".
-inline cic:/CoRN/reals/R_morphism/compose.con.
+inline "cic:/CoRN/reals/R_morphism/compose.con".
-inline cic:/CoRN/reals/R_morphism/compose_strext.con.
+inline "cic:/CoRN/reals/R_morphism/compose_strext.con".
-inline cic:/CoRN/reals/R_morphism/compose_pres_less.con.
+inline "cic:/CoRN/reals/R_morphism/compose_pres_less.con".
-inline cic:/CoRN/reals/R_morphism/compose_pres_plus.con.
+inline "cic:/CoRN/reals/R_morphism/compose_pres_plus.con".
-inline cic:/CoRN/reals/R_morphism/compose_pres_mult.con.
+inline "cic:/CoRN/reals/R_morphism/compose_pres_mult.con".
-inline cic:/CoRN/reals/R_morphism/compose_pres_Lim.con.
+inline "cic:/CoRN/reals/R_morphism/compose_pres_Lim.con".
-inline cic:/CoRN/reals/R_morphism/Compose.con.
+inline "cic:/CoRN/reals/R_morphism/Compose.con".
(* UNEXPORTED
End composition.
(* UNEXPORTED
End composition.
-inline cic:/CoRN/reals/R_morphism/R1.var.
+inline "cic:/CoRN/reals/R_morphism/R1.var".
-inline cic:/CoRN/reals/R_morphism/R2.var.
+inline "cic:/CoRN/reals/R_morphism/R2.var".
(* UNEXPORTED
Section identity_map.
*)
(* UNEXPORTED
Section identity_map.
*)
-inline cic:/CoRN/reals/R_morphism/R3.var.
+inline "cic:/CoRN/reals/R_morphism/R3.var".
-inline cic:/CoRN/reals/R_morphism/f.var.
+inline "cic:/CoRN/reals/R_morphism/f.var".
-inline cic:/CoRN/reals/R_morphism/map_is_id.con.
+inline "cic:/CoRN/reals/R_morphism/map_is_id.con".
(* UNEXPORTED
End identity_map.
*)
(* UNEXPORTED
End identity_map.
*)
-inline cic:/CoRN/reals/R_morphism/Isomorphism.ind.
+inline "cic:/CoRN/reals/R_morphism/Isomorphism.ind".
(* UNEXPORTED
End isomorphism.
(* UNEXPORTED
End isomorphism.
Section surjective_map.
*)
Section surjective_map.
*)
-inline cic:/CoRN/reals/R_morphism/R1.var.
+inline "cic:/CoRN/reals/R_morphism/R1.var".
-inline cic:/CoRN/reals/R_morphism/R2.var.
+inline "cic:/CoRN/reals/R_morphism/R2.var".
-inline cic:/CoRN/reals/R_morphism/f.var.
+inline "cic:/CoRN/reals/R_morphism/f.var".
-inline cic:/CoRN/reals/R_morphism/map_is_surjective.con.
+inline "cic:/CoRN/reals/R_morphism/map_is_surjective.con".
(* UNEXPORTED
End surjective_map.
(* UNEXPORTED
End surjective_map.
Section simplification.
*)
Section simplification.
*)
-inline cic:/CoRN/reals/R_morphism/R1.var.
+inline "cic:/CoRN/reals/R_morphism/R1.var".
-inline cic:/CoRN/reals/R_morphism/R2.var.
+inline "cic:/CoRN/reals/R_morphism/R2.var".
-inline cic:/CoRN/reals/R_morphism/f.var.
+inline "cic:/CoRN/reals/R_morphism/f.var".
-inline cic:/CoRN/reals/R_morphism/H1.var.
+inline "cic:/CoRN/reals/R_morphism/H1.var".
-inline cic:/CoRN/reals/R_morphism/f_well_def.con.
+inline "cic:/CoRN/reals/R_morphism/f_well_def.con".
(* UNEXPORTED
Section with_less.
*)
(* UNEXPORTED
Section with_less.
*)
-inline cic:/CoRN/reals/R_morphism/H2.var.
+inline "cic:/CoRN/reals/R_morphism/H2.var".
-inline cic:/CoRN/reals/R_morphism/less_pres_f.con.
+inline "cic:/CoRN/reals/R_morphism/less_pres_f.con".
-inline cic:/CoRN/reals/R_morphism/leEq_pres_f.con.
+inline "cic:/CoRN/reals/R_morphism/leEq_pres_f.con".
-inline cic:/CoRN/reals/R_morphism/f_pres_leEq.con.
+inline "cic:/CoRN/reals/R_morphism/f_pres_leEq.con".
-inline cic:/CoRN/reals/R_morphism/f_pres_apartness.con.
+inline "cic:/CoRN/reals/R_morphism/f_pres_apartness.con".
(* UNEXPORTED
End with_less.
(* UNEXPORTED
End with_less.
-inline cic:/CoRN/reals/R_morphism/H3.var.
+inline "cic:/CoRN/reals/R_morphism/H3.var".
-inline cic:/CoRN/reals/R_morphism/f_pres_Zero.con.
+inline "cic:/CoRN/reals/R_morphism/f_pres_Zero.con".
-inline cic:/CoRN/reals/R_morphism/f_pres_minus.con.
+inline "cic:/CoRN/reals/R_morphism/f_pres_minus.con".
-inline cic:/CoRN/reals/R_morphism/f_pres_min.con.
+inline "cic:/CoRN/reals/R_morphism/f_pres_min.con".
(* UNEXPORTED
End with_plus.
(* UNEXPORTED
End with_plus.
Section with_plus_less.
*)
Section with_plus_less.
*)
-inline cic:/CoRN/reals/R_morphism/H2.var.
+inline "cic:/CoRN/reals/R_morphism/H2.var".
-inline cic:/CoRN/reals/R_morphism/H3.var.
+inline "cic:/CoRN/reals/R_morphism/H3.var".
-inline cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con.
+inline "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con".
(* UNEXPORTED
Section surjectivity_helps.
*)
(* UNEXPORTED
Section surjectivity_helps.
*)
-inline cic:/CoRN/reals/R_morphism/f_surj.var.
+inline "cic:/CoRN/reals/R_morphism/f_surj.var".
-inline cic:/CoRN/reals/R_morphism/f_pres_Lim.con.
+inline "cic:/CoRN/reals/R_morphism/f_pres_Lim.con".
(* UNEXPORTED
End surjectivity_helps.
(* UNEXPORTED
End surjectivity_helps.
Section with_mult_plus_less.
*)
Section with_mult_plus_less.
*)
-inline cic:/CoRN/reals/R_morphism/H4.var.
+inline "cic:/CoRN/reals/R_morphism/H4.var".
-inline cic:/CoRN/reals/R_morphism/f_pres_one.con.
+inline "cic:/CoRN/reals/R_morphism/f_pres_one.con".
-inline cic:/CoRN/reals/R_morphism/f_pres_inv.con.
+inline "cic:/CoRN/reals/R_morphism/f_pres_inv.con".
-inline cic:/CoRN/reals/R_morphism/simplified_Homomorphism.con.
+inline "cic:/CoRN/reals/R_morphism/simplified_Homomorphism.con".
(* UNEXPORTED
End with_mult_plus_less.
(* UNEXPORTED
End with_mult_plus_less.
set "baseuri" "cic:/matita/CoRN-Decl/reals/RealFuncts".
set "baseuri" "cic:/matita/CoRN-Decl/reals/RealFuncts".
(* $Id: RealFuncts.v,v 1.4 2004/04/07 15:08:10 lcf Exp $ *)
(* $Id: RealFuncts.v,v 1.4 2004/04/07 15:08:10 lcf Exp $ *)
+include "reals/CReals1.ma".
(*#* * Continuity of Functions on Reals
*)
(*#* * Continuity of Functions on Reals
*)
-inline cic:/CoRN/reals/RealFuncts/f.var.
+inline "cic:/CoRN/reals/RealFuncts/f.var".
-inline cic:/CoRN/reals/RealFuncts/f2.var.
+inline "cic:/CoRN/reals/RealFuncts/f2.var".
(*#*
Let [f] be a unary setoid operation on [IR] and
(*#*
Let [f] be a unary setoid operation on [IR] and
$\emptyset$#∅# for [a [>] b]).
*)
$\emptyset$#∅# for [a [>] b]).
*)
-inline cic:/CoRN/reals/RealFuncts/Intclr.con.
+inline "cic:/CoRN/reals/RealFuncts/Intclr.con".
-inline cic:/CoRN/reals/RealFuncts/Intolr.con.
+inline "cic:/CoRN/reals/RealFuncts/Intolr.con".
-inline cic:/CoRN/reals/RealFuncts/Intol.con.
+inline "cic:/CoRN/reals/RealFuncts/Intol.con".
-inline cic:/CoRN/reals/RealFuncts/Intcl.con.
+inline "cic:/CoRN/reals/RealFuncts/Intcl.con".
-inline cic:/CoRN/reals/RealFuncts/Intcr.con.
+inline "cic:/CoRN/reals/RealFuncts/Intcr.con".
(*#* The limit of [f(x)] as [x] goes to [p = l], for both unary and binary
functions:
(*#* The limit of [f(x)] as [x] goes to [p = l], for both unary and binary
functions:
-inline cic:/CoRN/reals/RealFuncts/funLim.con.
+inline "cic:/CoRN/reals/RealFuncts/funLim.con".
(*#* The definition of limit of [f] in [p] using Cauchy sequences. *)
(*#* The definition of limit of [f] in [p] using Cauchy sequences. *)
-inline cic:/CoRN/reals/RealFuncts/funLim_Cauchy.con.
+inline "cic:/CoRN/reals/RealFuncts/funLim_Cauchy.con".
(*#* The first definition implies the second one. *)
(*#* The first definition implies the second one. *)
-inline cic:/CoRN/reals/RealFuncts/funLim2.con.
+inline "cic:/CoRN/reals/RealFuncts/funLim2.con".
(*#* The function [f] is continuous at [p] if the limit of [f(x)] as
[x] goes to [p] is [f(p)]. This is the [eps [/] delta] definition.
We also give the definition with limits of Cauchy sequences.
*)
(*#* The function [f] is continuous at [p] if the limit of [f(x)] as
[x] goes to [p] is [f(p)]. This is the [eps [/] delta] definition.
We also give the definition with limits of Cauchy sequences.
*)
-inline cic:/CoRN/reals/RealFuncts/continAt.con.
+inline "cic:/CoRN/reals/RealFuncts/continAt.con".
-inline cic:/CoRN/reals/RealFuncts/continAtCauchy.con.
+inline "cic:/CoRN/reals/RealFuncts/continAtCauchy.con".
-inline cic:/CoRN/reals/RealFuncts/continAt2.con.
+inline "cic:/CoRN/reals/RealFuncts/continAt2.con".
(*
Ax_iom continAt_prop1 :(p:IR)(continAt p)->(continAtCauchy p).
*)
(*
Ax_iom continAt_prop1 :(p:IR)(continAt p)->(continAtCauchy p).
*)
-inline cic:/CoRN/reals/RealFuncts/contin.con.
+inline "cic:/CoRN/reals/RealFuncts/contin.con".
-inline cic:/CoRN/reals/RealFuncts/continCauchy.con.
+inline "cic:/CoRN/reals/RealFuncts/continCauchy.con".
-inline cic:/CoRN/reals/RealFuncts/contin2.con.
+inline "cic:/CoRN/reals/RealFuncts/contin2.con".
(*#*
Continuous on a closed, resp.%\% open, resp.%\% left open, resp.%\% left closed
interval *)
(*#*
Continuous on a closed, resp.%\% open, resp.%\% left open, resp.%\% left closed
interval *)
-inline cic:/CoRN/reals/RealFuncts/continOnc.con.
+inline "cic:/CoRN/reals/RealFuncts/continOnc.con".
-inline cic:/CoRN/reals/RealFuncts/continOno.con.
+inline "cic:/CoRN/reals/RealFuncts/continOno.con".
-inline cic:/CoRN/reals/RealFuncts/continOnol.con.
+inline "cic:/CoRN/reals/RealFuncts/continOnol.con".
-inline cic:/CoRN/reals/RealFuncts/continOncl.con.
+inline "cic:/CoRN/reals/RealFuncts/continOncl.con".
(*
Section Sequence_and_function_limits.
(*
Section Sequence_and_function_limits.
set "baseuri" "cic:/matita/CoRN-Decl/reals/RealLists".
set "baseuri" "cic:/matita/CoRN-Decl/reals/RealLists".
(* $Id: RealLists.v,v 1.4 2004/04/23 10:01:05 lcf Exp $ *)
(* $Id: RealLists.v,v 1.4 2004/04/23 10:01:05 lcf Exp $ *)
+include "reals/CReals1.ma".
(* UNEXPORTED
Section Lists.
(* UNEXPORTED
Section Lists.
We start by defining maximum and minimum of lists of reals and two membership predicates. The value of these functions for the empty list is arbitrarily set to 0, but it will be irrelevant, as we will never work with empty lists.
*)
We start by defining maximum and minimum of lists of reals and two membership predicates. The value of these functions for the empty list is arbitrarily set to 0, but it will be irrelevant, as we will never work with empty lists.
*)
-inline cic:/CoRN/reals/RealLists/maxlist.con.
+inline "cic:/CoRN/reals/RealLists/maxlist.con".
-inline cic:/CoRN/reals/RealLists/minlist.con.
+inline "cic:/CoRN/reals/RealLists/minlist.con".
-inline cic:/CoRN/reals/RealLists/member.con.
+inline "cic:/CoRN/reals/RealLists/member.con".
(*#*
Sometimes the length of the list has to be restricted; the next definition provides an easy way to do that. *)
(*#*
Sometimes the length of the list has to be restricted; the next definition provides an easy way to do that. *)
-inline cic:/CoRN/reals/RealLists/length_leEq.con.
+inline "cic:/CoRN/reals/RealLists/length_leEq.con".
(*#* Length is preserved by mapping. *)
(*#* Length is preserved by mapping. *)
Implicit Arguments map [A B].
*)
Implicit Arguments map [A B].
*)
-inline cic:/CoRN/reals/RealLists/map_pres_length.con.
+inline "cic:/CoRN/reals/RealLists/map_pres_length.con".
(*#*
Often we want to map partial functions through a list; this next operator provides a way to do that, and is proved to be correct. *)
(*#*
Often we want to map partial functions through a list; this next operator provides a way to do that, and is proved to be correct. *)
Implicit Arguments cons [A].
*)
Implicit Arguments cons [A].
*)
-inline cic:/CoRN/reals/RealLists/map2.con.
+inline "cic:/CoRN/reals/RealLists/map2.con".
-inline cic:/CoRN/reals/RealLists/map2_wd.con.
+inline "cic:/CoRN/reals/RealLists/map2_wd.con".
-inline cic:/CoRN/reals/RealLists/map2_pres_member.con.
+inline "cic:/CoRN/reals/RealLists/map2_pres_member.con".
(*#*
As [maxlist] and [minlist] are generalizations of [Max] and [Min] to finite sets of real numbers, they have the expected properties: *)
(*#*
As [maxlist] and [minlist] are generalizations of [Max] and [Min] to finite sets of real numbers, they have the expected properties: *)
-inline cic:/CoRN/reals/RealLists/maxlist_greater.con.
+inline "cic:/CoRN/reals/RealLists/maxlist_greater.con".
-inline cic:/CoRN/reals/RealLists/maxlist_aux.con.
+inline "cic:/CoRN/reals/RealLists/maxlist_aux.con".
-inline cic:/CoRN/reals/RealLists/maxlist_leEq_eps.con.
+inline "cic:/CoRN/reals/RealLists/maxlist_leEq_eps.con".
-inline cic:/CoRN/reals/RealLists/maxlist_less.con.
+inline "cic:/CoRN/reals/RealLists/maxlist_less.con".
-inline cic:/CoRN/reals/RealLists/maxlist_leEq.con.
+inline "cic:/CoRN/reals/RealLists/maxlist_leEq.con".
-inline cic:/CoRN/reals/RealLists/minlist_smaller.con.
+inline "cic:/CoRN/reals/RealLists/minlist_smaller.con".
-inline cic:/CoRN/reals/RealLists/minlist_aux.con.
+inline "cic:/CoRN/reals/RealLists/minlist_aux.con".
-inline cic:/CoRN/reals/RealLists/minlist_leEq_eps.con.
+inline "cic:/CoRN/reals/RealLists/minlist_leEq_eps.con".
-inline cic:/CoRN/reals/RealLists/less_minlist.con.
+inline "cic:/CoRN/reals/RealLists/less_minlist.con".
-inline cic:/CoRN/reals/RealLists/leEq_minlist.con.
+inline "cic:/CoRN/reals/RealLists/leEq_minlist.con".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Series".
set "baseuri" "cic:/matita/CoRN-Decl/reals/Series".
(* $Id: Series.v,v 1.6 2004/04/23 10:01:05 lcf Exp $ *)
(*#* printing seq_part_sum %\ensuremath{\sum^n}% #∑<sup>n</sup># *)
(* $Id: Series.v,v 1.6 2004/04/23 10:01:05 lcf Exp $ *)
(*#* printing seq_part_sum %\ensuremath{\sum^n}% #∑<sup>n</sup># *)
(*#* printing pi %\ensuremath{\pi}% #π *)
(*#* printing pi %\ensuremath{\pi}% #π *)
-(* INCLUDE
-CSumsReals
-*)
+include "reals/CSumsReals.ma".
+include "reals/NRootIR.ma".
(* UNEXPORTED
Section Definitions.
(* UNEXPORTED
Section Definitions.
-inline cic:/CoRN/reals/Series/x.var.
+inline "cic:/CoRN/reals/Series/x.var".
-inline cic:/CoRN/reals/Series/seq_part_sum.con.
+inline "cic:/CoRN/reals/Series/seq_part_sum.con".
(*#*
For subsequent purposes it will be very useful to be able to write the
(*#*
For subsequent purposes it will be very useful to be able to write the
sums as a sum of elements of the original sequence.
*)
sums as a sum of elements of the original sequence.
*)
-inline cic:/CoRN/reals/Series/seq_part_sum_n.con.
+inline "cic:/CoRN/reals/Series/seq_part_sum_n.con".
(*#* A series is convergent iff its sequence of partial Sums is a
Cauchy sequence. To each convergent series we can assign a Sum.
*)
(*#* A series is convergent iff its sequence of partial Sums is a
Cauchy sequence. To each convergent series we can assign a Sum.
*)
-inline cic:/CoRN/reals/Series/convergent.con.
+inline "cic:/CoRN/reals/Series/convergent.con".
-inline cic:/CoRN/reals/Series/series_sum.con.
+inline "cic:/CoRN/reals/Series/series_sum.con".
(*#* Divergence can be characterized in a positive way, which will sometimes
be useful. We thus define divergence of sequences and series and prove the
(*#* Divergence can be characterized in a positive way, which will sometimes
be useful. We thus define divergence of sequences and series and prove the
considered either as a sequence or as a series.
*)
considered either as a sequence or as a series.
*)
-inline cic:/CoRN/reals/Series/divergent_seq.con.
+inline "cic:/CoRN/reals/Series/divergent_seq.con".
-inline cic:/CoRN/reals/Series/divergent.con.
+inline "cic:/CoRN/reals/Series/divergent.con".
-inline cic:/CoRN/reals/Series/conv_imp_not_div.con.
+inline "cic:/CoRN/reals/Series/conv_imp_not_div.con".
-inline cic:/CoRN/reals/Series/div_imp_not_conv.con.
+inline "cic:/CoRN/reals/Series/div_imp_not_conv.con".
-inline cic:/CoRN/reals/Series/convergent_imp_not_divergent.con.
+inline "cic:/CoRN/reals/Series/convergent_imp_not_divergent.con".
-inline cic:/CoRN/reals/Series/divergent_imp_not_convergent.con.
+inline "cic:/CoRN/reals/Series/divergent_imp_not_convergent.con".
(*#* Finally we have the well known fact that every convergent series converges
to zero as a sequence.
*)
(*#* Finally we have the well known fact that every convergent series converges
to zero as a sequence.
*)
-inline cic:/CoRN/reals/Series/series_seq_Lim.con.
+inline "cic:/CoRN/reals/Series/series_seq_Lim.con".
-inline cic:/CoRN/reals/Series/series_seq_Lim'.con.
+inline "cic:/CoRN/reals/Series/series_seq_Lim'.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
Section More_Definitions.
*)
Section More_Definitions.
*)
-inline cic:/CoRN/reals/Series/x.var.
+inline "cic:/CoRN/reals/Series/x.var".
(*#* We also define absolute convergence. *)
(*#* We also define absolute convergence. *)
-inline cic:/CoRN/reals/Series/abs_convergent.con.
+inline "cic:/CoRN/reals/Series/abs_convergent.con".
(* UNEXPORTED
End More_Definitions.
(* UNEXPORTED
End More_Definitions.
Power series are an important special case.
*)
Power series are an important special case.
*)
-inline cic:/CoRN/reals/Series/power_series.con.
+inline "cic:/CoRN/reals/Series/power_series.con".
(*#*
Specially important is the case when [c] is a positive real number
(*#*
Specially important is the case when [c] is a positive real number
-inline cic:/CoRN/reals/Series/c.var.
+inline "cic:/CoRN/reals/Series/c.var".
-inline cic:/CoRN/reals/Series/H0c.var.
+inline "cic:/CoRN/reals/Series/H0c.var".
-inline cic:/CoRN/reals/Series/Hc1.var.
+inline "cic:/CoRN/reals/Series/Hc1.var".
-inline cic:/CoRN/reals/Series/c_exp_Lim.con.
+inline "cic:/CoRN/reals/Series/c_exp_Lim.con".
-inline cic:/CoRN/reals/Series/power_series_Lim1.con.
+inline "cic:/CoRN/reals/Series/power_series_Lim1.con".
-inline cic:/CoRN/reals/Series/power_series_conv.con.
+inline "cic:/CoRN/reals/Series/power_series_conv.con".
-inline cic:/CoRN/reals/Series/power_series_sum.con.
+inline "cic:/CoRN/reals/Series/power_series_sum.con".
(* UNEXPORTED
End Power_Series.
(* UNEXPORTED
End Power_Series.
the series that is zero everywhere.
*)
the series that is zero everywhere.
*)
-inline cic:/CoRN/reals/Series/conv_zero_series.con.
+inline "cic:/CoRN/reals/Series/conv_zero_series.con".
-inline cic:/CoRN/reals/Series/series_sum_zero.con.
+inline "cic:/CoRN/reals/Series/series_sum_zero.con".
(*#* Next we consider extensionality, as well as the sum and difference
of two convergent series.
(*#* Next we consider extensionality, as well as the sum and difference
of two convergent series.
-inline cic:/CoRN/reals/Series/x.var.
+inline "cic:/CoRN/reals/Series/x.var".
-inline cic:/CoRN/reals/Series/y.var.
+inline "cic:/CoRN/reals/Series/y.var".
-inline cic:/CoRN/reals/Series/convX.var.
+inline "cic:/CoRN/reals/Series/convX.var".
-inline cic:/CoRN/reals/Series/convY.var.
+inline "cic:/CoRN/reals/Series/convY.var".
-inline cic:/CoRN/reals/Series/convergent_wd.con.
+inline "cic:/CoRN/reals/Series/convergent_wd.con".
-inline cic:/CoRN/reals/Series/series_sum_wd.con.
+inline "cic:/CoRN/reals/Series/series_sum_wd.con".
-inline cic:/CoRN/reals/Series/conv_series_plus.con.
+inline "cic:/CoRN/reals/Series/conv_series_plus.con".
-inline cic:/CoRN/reals/Series/series_sum_plus.con.
+inline "cic:/CoRN/reals/Series/series_sum_plus.con".
-inline cic:/CoRN/reals/Series/conv_series_minus.con.
+inline "cic:/CoRN/reals/Series/conv_series_minus.con".
-inline cic:/CoRN/reals/Series/series_sum_minus.con.
+inline "cic:/CoRN/reals/Series/series_sum_minus.con".
(*#* Multiplication by a scalar [c] is also permitted. *)
(*#* Multiplication by a scalar [c] is also permitted. *)
-inline cic:/CoRN/reals/Series/c.var.
+inline "cic:/CoRN/reals/Series/c.var".
-inline cic:/CoRN/reals/Series/conv_series_mult_scal.con.
+inline "cic:/CoRN/reals/Series/conv_series_mult_scal.con".
-inline cic:/CoRN/reals/Series/series_sum_mult_scal.con.
+inline "cic:/CoRN/reals/Series/series_sum_mult_scal.con".
(* UNEXPORTED
End Operations.
(* UNEXPORTED
End Operations.
Section More_Operations.
*)
Section More_Operations.
*)
-inline cic:/CoRN/reals/Series/x.var.
+inline "cic:/CoRN/reals/Series/x.var".
-inline cic:/CoRN/reals/Series/convX.var.
+inline "cic:/CoRN/reals/Series/convX.var".
(*#* As a corollary, we get the series of the inverses. *)
(*#* As a corollary, we get the series of the inverses. *)
-inline cic:/CoRN/reals/Series/conv_series_inv.con.
+inline "cic:/CoRN/reals/Series/conv_series_inv.con".
-inline cic:/CoRN/reals/Series/series_sum_inv.con.
+inline "cic:/CoRN/reals/Series/series_sum_inv.con".
(* UNEXPORTED
End More_Operations.
(* UNEXPORTED
End More_Operations.
Let [x,y : nat->IR] be equal after some natural number.
*)
Let [x,y : nat->IR] be equal after some natural number.
*)
-inline cic:/CoRN/reals/Series/x.var.
+inline "cic:/CoRN/reals/Series/x.var".
-inline cic:/CoRN/reals/Series/y.var.
+inline "cic:/CoRN/reals/Series/y.var".
-inline cic:/CoRN/reals/Series/aew_eq.con.
+inline "cic:/CoRN/reals/Series/aew_eq.con".
-inline cic:/CoRN/reals/Series/aew_equal.var.
+inline "cic:/CoRN/reals/Series/aew_equal.var".
-inline cic:/CoRN/reals/Series/aew_Cauchy.con.
+inline "cic:/CoRN/reals/Series/aew_Cauchy.con".
-inline cic:/CoRN/reals/Series/aew_Cauchy2.con.
+inline "cic:/CoRN/reals/Series/aew_Cauchy2.con".
-inline cic:/CoRN/reals/Series/aew_series_conv.con.
+inline "cic:/CoRN/reals/Series/aew_series_conv.con".
(* UNEXPORTED
End Almost_Everywhere.
(* UNEXPORTED
End Almost_Everywhere.
(*#* Suppose furthermore that [x,y] are Cauchy sequences. *)
(*#* Suppose furthermore that [x,y] are Cauchy sequences. *)
-inline cic:/CoRN/reals/Series/x.var.
+inline "cic:/CoRN/reals/Series/x.var".
-inline cic:/CoRN/reals/Series/y.var.
+inline "cic:/CoRN/reals/Series/y.var".
-inline cic:/CoRN/reals/Series/aew_equal.var.
+inline "cic:/CoRN/reals/Series/aew_equal.var".
-inline cic:/CoRN/reals/Series/aew_Lim.con.
+inline "cic:/CoRN/reals/Series/aew_Lim.con".
(* UNEXPORTED
End Cauchy_Almost_Everywhere.
(* UNEXPORTED
End Cauchy_Almost_Everywhere.
-inline cic:/CoRN/reals/Series/x.var.
+inline "cic:/CoRN/reals/Series/x.var".
(*#* We include the comparison test for series, both in a strong and in a less
general (but simpler) form.
*)
(*#* We include the comparison test for series, both in a strong and in a less
general (but simpler) form.
*)
-inline cic:/CoRN/reals/Series/str_comparison.con.
+inline "cic:/CoRN/reals/Series/str_comparison.con".
-inline cic:/CoRN/reals/Series/comparison.con.
+inline "cic:/CoRN/reals/Series/comparison.con".
(*#* As a corollary, we get that every absolutely convergent series converges. *)
(*#* As a corollary, we get that every absolutely convergent series converges. *)
-inline cic:/CoRN/reals/Series/abs_imp_conv.con.
+inline "cic:/CoRN/reals/Series/abs_imp_conv.con".
(*#* Next we have the ratio test, both as a positive and negative result. *)
(*#* Next we have the ratio test, both as a positive and negative result. *)
-inline cic:/CoRN/reals/Series/divergent_crit.con.
+inline "cic:/CoRN/reals/Series/divergent_crit.con".
-inline cic:/CoRN/reals/Series/tail_series.con.
+inline "cic:/CoRN/reals/Series/tail_series.con".
-inline cic:/CoRN/reals/Series/join_series.con.
+inline "cic:/CoRN/reals/Series/join_series.con".
(* UNEXPORTED
End Convergence_Criteria.
(* UNEXPORTED
End Convergence_Criteria.
-inline cic:/CoRN/reals/Series/x.var.
+inline "cic:/CoRN/reals/Series/x.var".
-inline cic:/CoRN/reals/Series/ratio_test_conv.con.
+inline "cic:/CoRN/reals/Series/ratio_test_conv.con".
-inline cic:/CoRN/reals/Series/ratio_test_div.con.
+inline "cic:/CoRN/reals/Series/ratio_test_div.con".
(* UNEXPORTED
End More_CC.
(* UNEXPORTED
End More_CC.
decreasing convergent to 0.
*)
decreasing convergent to 0.
*)
-inline cic:/CoRN/reals/Series/x.var.
+inline "cic:/CoRN/reals/Series/x.var".
-inline cic:/CoRN/reals/Series/pos_x.var.
+inline "cic:/CoRN/reals/Series/pos_x.var".
-inline cic:/CoRN/reals/Series/Lim_x.var.
+inline "cic:/CoRN/reals/Series/Lim_x.var".
-inline cic:/CoRN/reals/Series/mon_x.var.
+inline "cic:/CoRN/reals/Series/mon_x.var".
-inline cic:/CoRN/reals/Series/y.con.
+inline "cic:/CoRN/reals/Series/y.con".
-inline cic:/CoRN/reals/Series/alternate_lemma1.con.
+inline "cic:/CoRN/reals/Series/alternate_lemma1.con".
-inline cic:/CoRN/reals/Series/alternate_lemma2.con.
+inline "cic:/CoRN/reals/Series/alternate_lemma2.con".
-inline cic:/CoRN/reals/Series/alternate_lemma3.con.
+inline "cic:/CoRN/reals/Series/alternate_lemma3.con".
-inline cic:/CoRN/reals/Series/alternate_lemma4.con.
+inline "cic:/CoRN/reals/Series/alternate_lemma4.con".
-inline cic:/CoRN/reals/Series/alternate_series_conv.con.
+inline "cic:/CoRN/reals/Series/alternate_series_conv.con".
(* UNEXPORTED
End Alternate_Series.
(* UNEXPORTED
End Alternate_Series.
and $e$#e#, both as sums of convergent series.
*)
and $e$#e#, both as sums of convergent series.
*)
-inline cic:/CoRN/reals/Series/e_series.con.
+inline "cic:/CoRN/reals/Series/e_series.con".
-inline cic:/CoRN/reals/Series/e_series_conv.con.
+inline "cic:/CoRN/reals/Series/e_series_conv.con".
-inline cic:/CoRN/reals/Series/E.con.
+inline "cic:/CoRN/reals/Series/E.con".
-inline cic:/CoRN/reals/Series/pi_series.con.
+inline "cic:/CoRN/reals/Series/pi_series.con".
-inline cic:/CoRN/reals/Series/pi_series_conv.con.
+inline "cic:/CoRN/reals/Series/pi_series_conv.con".
-inline cic:/CoRN/reals/Series/pi.con.
+inline "cic:/CoRN/reals/Series/pi.con".
(* UNEXPORTED
End Important_Numbers.
(* UNEXPORTED
End Important_Numbers.
set "baseuri" "cic:/matita/CoRN-Decl/reals/iso_CReals".
set "baseuri" "cic:/matita/CoRN-Decl/reals/iso_CReals".
(* begin hide *)
(* in this file the concrete canonical isomorphism -in te sense of
R_morphisms.v - between two arbitrary model of real numbers is built *)
(* begin hide *)
(* in this file the concrete canonical isomorphism -in te sense of
R_morphisms.v - between two arbitrary model of real numbers is built *)
+include "reals/Q_dense.ma".
-(* INCLUDE
-R_morphism
-*)
+include "reals/R_morphism.ma".
-inline cic:/CoRN/reals/iso_CReals/less_pres_Lim.con.
+inline "cic:/CoRN/reals/iso_CReals/less_pres_Lim.con".
-inline cic:/CoRN/reals/iso_CReals/Lim_pres_less.con.
+inline "cic:/CoRN/reals/iso_CReals/Lim_pres_less.con".
-inline cic:/CoRN/reals/iso_CReals/inj_seq_less.con.
+inline "cic:/CoRN/reals/iso_CReals/inj_seq_less.con".
-inline cic:/CoRN/reals/iso_CReals/less_inj_seq.con.
+inline "cic:/CoRN/reals/iso_CReals/less_inj_seq.con".
-inline cic:/CoRN/reals/iso_CReals/SeqLimit_unique.con.
+inline "cic:/CoRN/reals/iso_CReals/SeqLimit_unique.con".
-inline cic:/CoRN/reals/iso_CReals/Lim_well_def.con.
+inline "cic:/CoRN/reals/iso_CReals/Lim_well_def.con".
-inline cic:/CoRN/reals/iso_CReals/Lim_one_one.con.
+inline "cic:/CoRN/reals/iso_CReals/Lim_one_one.con".
-inline cic:/CoRN/reals/iso_CReals/inj_seq_well_def.con.
+inline "cic:/CoRN/reals/iso_CReals/inj_seq_well_def.con".
-inline cic:/CoRN/reals/iso_CReals/inj_Q_one_one.con.
+inline "cic:/CoRN/reals/iso_CReals/inj_Q_one_one.con".
-inline cic:/CoRN/reals/iso_CReals/Lim_pres_plus.con.
+inline "cic:/CoRN/reals/iso_CReals/Lim_pres_plus.con".
-inline cic:/CoRN/reals/iso_CReals/G_pres_plus.con.
+inline "cic:/CoRN/reals/iso_CReals/G_pres_plus.con".
(* This theorem can be avoided but it is interesting *)
(* This theorem can be avoided but it is interesting *)
-inline cic:/CoRN/reals/iso_CReals/nonarchemaedian_bound_for_Lim.con.
+inline "cic:/CoRN/reals/iso_CReals/nonarchemaedian_bound_for_Lim.con".
-inline cic:/CoRN/reals/iso_CReals/Lim_pres_mult.con.
+inline "cic:/CoRN/reals/iso_CReals/Lim_pres_mult.con".
-inline cic:/CoRN/reals/iso_CReals/G_pres_mult.con.
+inline "cic:/CoRN/reals/iso_CReals/G_pres_mult.con".
(* UNEXPORTED
Section Concrete_iso_between_Creals.
*)
(* UNEXPORTED
Section Concrete_iso_between_Creals.
*)
-inline cic:/CoRN/reals/iso_CReals/R1.var.
+inline "cic:/CoRN/reals/iso_CReals/R1.var".
-inline cic:/CoRN/reals/iso_CReals/R2.var.
+inline "cic:/CoRN/reals/iso_CReals/R2.var".
-inline cic:/CoRN/reals/iso_CReals/image_Cauchy12.con.
+inline "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con".
-inline cic:/CoRN/reals/iso_CReals/image_Cauchy21.con.
+inline "cic:/CoRN/reals/iso_CReals/image_Cauchy21.con".
-inline cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq12.con.
+inline "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq12.con".
-inline cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq21.con.
+inline "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq21.con".
-inline cic:/CoRN/reals/iso_CReals/f12.con.
+inline "cic:/CoRN/reals/iso_CReals/f12.con".
-inline cic:/CoRN/reals/iso_CReals/g21.con.
+inline "cic:/CoRN/reals/iso_CReals/g21.con".
(*#****** ISO FROM R1 TO R2 ********)
(*#****** ISO FROM R1 TO R2 ********)
-inline cic:/CoRN/reals/iso_CReals/f12_is_inverse_g21.con.
+inline "cic:/CoRN/reals/iso_CReals/f12_is_inverse_g21.con".
-inline cic:/CoRN/reals/iso_CReals/f12_is_surjective.con.
+inline "cic:/CoRN/reals/iso_CReals/f12_is_surjective.con".
-inline cic:/CoRN/reals/iso_CReals/f12_strong_ext.con.
+inline "cic:/CoRN/reals/iso_CReals/f12_strong_ext.con".
-inline cic:/CoRN/reals/iso_CReals/f12_pres_less.con.
+inline "cic:/CoRN/reals/iso_CReals/f12_pres_less.con".
-inline cic:/CoRN/reals/iso_CReals/f12_pres_plus.con.
+inline "cic:/CoRN/reals/iso_CReals/f12_pres_plus.con".
-inline cic:/CoRN/reals/iso_CReals/f12_pres_mult.con.
+inline "cic:/CoRN/reals/iso_CReals/f12_pres_mult.con".
(*#********* ISO FROM R2 TO R1 **********)
(*#********* ISO FROM R2 TO R1 **********)
-inline cic:/CoRN/reals/iso_CReals/g21_is_inverse_f12.con.
+inline "cic:/CoRN/reals/iso_CReals/g21_is_inverse_f12.con".
-inline cic:/CoRN/reals/iso_CReals/g21_is_surjective.con.
+inline "cic:/CoRN/reals/iso_CReals/g21_is_surjective.con".
-inline cic:/CoRN/reals/iso_CReals/g21_strong_ext.con.
+inline "cic:/CoRN/reals/iso_CReals/g21_strong_ext.con".
-inline cic:/CoRN/reals/iso_CReals/g21_pres_less.con.
+inline "cic:/CoRN/reals/iso_CReals/g21_pres_less.con".
-inline cic:/CoRN/reals/iso_CReals/g21_pres_plus.con.
+inline "cic:/CoRN/reals/iso_CReals/g21_pres_plus.con".
-inline cic:/CoRN/reals/iso_CReals/g21_pres_mult.con.
+inline "cic:/CoRN/reals/iso_CReals/g21_pres_mult.con".
(*#** Building Homomorphisms out of f12 and g21 ***)
(*#** Building Homomorphisms out of f12 and g21 ***)
-inline cic:/CoRN/reals/iso_CReals/f12_as_Homomorphism.con.
+inline "cic:/CoRN/reals/iso_CReals/f12_as_Homomorphism.con".
-inline cic:/CoRN/reals/iso_CReals/g21_as_Homomorphism.con.
+inline "cic:/CoRN/reals/iso_CReals/g21_as_Homomorphism.con".
-inline cic:/CoRN/reals/iso_CReals/f12_inverse_lft.con.
+inline "cic:/CoRN/reals/iso_CReals/f12_inverse_lft.con".
-inline cic:/CoRN/reals/iso_CReals/g21_inverse_rht.con.
+inline "cic:/CoRN/reals/iso_CReals/g21_inverse_rht.con".
-inline cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con.
+inline "cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con".
(* UNEXPORTED
End Concrete_iso_between_Creals.
(* UNEXPORTED
End Concrete_iso_between_Creals.
set "baseuri" "cic:/matita/CoRN-Decl/tactics/AlgReflection".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/AlgReflection".
(* $Id: AlgReflection.v,v 1.2 2004/03/26 16:07:03 lcf Exp $ *)
(* begin hide *)
(* $Id: AlgReflection.v,v 1.2 2004/03/26 16:07:03 lcf Exp $ *)
(* begin hide *)
+include "algebra/CLogic.ma".
(* UNEXPORTED
Section Syntactic_Expressions.
*)
(* UNEXPORTED
Section Syntactic_Expressions.
*)
-inline cic:/CoRN/tactics/AlgReflection/varindex.con.
+inline "cic:/CoRN/tactics/AlgReflection/varindex.con".
-inline cic:/CoRN/tactics/AlgReflection/pfunindex.con.
+inline "cic:/CoRN/tactics/AlgReflection/pfunindex.con".
-inline cic:/CoRN/tactics/AlgReflection/unopindex.con.
+inline "cic:/CoRN/tactics/AlgReflection/unopindex.con".
-inline cic:/CoRN/tactics/AlgReflection/binopindex.con.
+inline "cic:/CoRN/tactics/AlgReflection/binopindex.con".
-inline cic:/CoRN/tactics/AlgReflection/expr.ind.
+inline "cic:/CoRN/tactics/AlgReflection/expr.ind".
-inline cic:/CoRN/tactics/AlgReflection/expr_zero.con.
+inline "cic:/CoRN/tactics/AlgReflection/expr_zero.con".
-inline cic:/CoRN/tactics/AlgReflection/expr_one.con.
+inline "cic:/CoRN/tactics/AlgReflection/expr_one.con".
-inline cic:/CoRN/tactics/AlgReflection/expr_nat.con.
+inline "cic:/CoRN/tactics/AlgReflection/expr_nat.con".
-inline cic:/CoRN/tactics/AlgReflection/expr_inv.con.
+inline "cic:/CoRN/tactics/AlgReflection/expr_inv.con".
-inline cic:/CoRN/tactics/AlgReflection/expr_minus.con.
+inline "cic:/CoRN/tactics/AlgReflection/expr_minus.con".
-inline cic:/CoRN/tactics/AlgReflection/expr_power.con.
+inline "cic:/CoRN/tactics/AlgReflection/expr_power.con".
(* UNEXPORTED
End Syntactic_Expressions.
(* UNEXPORTED
End Syntactic_Expressions.
Section Normalization_Function.
*)
Section Normalization_Function.
*)
-inline cic:/CoRN/tactics/AlgReflection/eq_nat.con.
+inline "cic:/CoRN/tactics/AlgReflection/eq_nat.con".
-inline cic:/CoRN/tactics/AlgReflection/lt_nat.con.
+inline "cic:/CoRN/tactics/AlgReflection/lt_nat.con".
-inline cic:/CoRN/tactics/AlgReflection/le_nat.con.
+inline "cic:/CoRN/tactics/AlgReflection/le_nat.con".
-inline cic:/CoRN/tactics/AlgReflection/eq_int.con.
+inline "cic:/CoRN/tactics/AlgReflection/eq_int.con".
-inline cic:/CoRN/tactics/AlgReflection/lt_int.con.
+inline "cic:/CoRN/tactics/AlgReflection/lt_int.con".
-inline cic:/CoRN/tactics/AlgReflection/le_int.con.
+inline "cic:/CoRN/tactics/AlgReflection/le_int.con".
-inline cic:/CoRN/tactics/AlgReflection/eq_expr.con.
+inline "cic:/CoRN/tactics/AlgReflection/eq_expr.con".
-inline cic:/CoRN/tactics/AlgReflection/lt_expr.con.
+inline "cic:/CoRN/tactics/AlgReflection/lt_expr.con".
-inline cic:/CoRN/tactics/AlgReflection/le_expr.con.
+inline "cic:/CoRN/tactics/AlgReflection/le_expr.con".
-inline cic:/CoRN/tactics/AlgReflection/eq_monom.con.
+inline "cic:/CoRN/tactics/AlgReflection/eq_monom.con".
-inline cic:/CoRN/tactics/AlgReflection/lt_monom.con.
+inline "cic:/CoRN/tactics/AlgReflection/lt_monom.con".
-inline cic:/CoRN/tactics/AlgReflection/MI_mult.con.
+inline "cic:/CoRN/tactics/AlgReflection/MI_mult.con".
-inline cic:/CoRN/tactics/AlgReflection/MV_mult.con.
+inline "cic:/CoRN/tactics/AlgReflection/MV_mult.con".
-inline cic:/CoRN/tactics/AlgReflection/MM_mult.con.
+inline "cic:/CoRN/tactics/AlgReflection/MM_mult.con".
-inline cic:/CoRN/tactics/AlgReflection/MM_plus.con.
+inline "cic:/CoRN/tactics/AlgReflection/MM_plus.con".
-inline cic:/CoRN/tactics/AlgReflection/PM_plus.con.
+inline "cic:/CoRN/tactics/AlgReflection/PM_plus.con".
-inline cic:/CoRN/tactics/AlgReflection/PP_plus.con.
+inline "cic:/CoRN/tactics/AlgReflection/PP_plus.con".
-inline cic:/CoRN/tactics/AlgReflection/PM_mult.con.
+inline "cic:/CoRN/tactics/AlgReflection/PM_mult.con".
-inline cic:/CoRN/tactics/AlgReflection/PP_mult.con.
+inline "cic:/CoRN/tactics/AlgReflection/PP_mult.con".
-inline cic:/CoRN/tactics/AlgReflection/FF_plus.con.
+inline "cic:/CoRN/tactics/AlgReflection/FF_plus.con".
-inline cic:/CoRN/tactics/AlgReflection/FF_mult.con.
+inline "cic:/CoRN/tactics/AlgReflection/FF_mult.con".
-inline cic:/CoRN/tactics/AlgReflection/FF_div.con.
+inline "cic:/CoRN/tactics/AlgReflection/FF_div.con".
-inline cic:/CoRN/tactics/AlgReflection/NormR.con.
+inline "cic:/CoRN/tactics/AlgReflection/NormR.con".
-inline cic:/CoRN/tactics/AlgReflection/NormG.con.
+inline "cic:/CoRN/tactics/AlgReflection/NormG.con".
-inline cic:/CoRN/tactics/AlgReflection/NormF.con.
+inline "cic:/CoRN/tactics/AlgReflection/NormF.con".
-inline cic:/CoRN/tactics/AlgReflection/expr_is_zero.con.
+inline "cic:/CoRN/tactics/AlgReflection/expr_is_zero.con".
(* UNEXPORTED
End Normalization_Function.
(* UNEXPORTED
End Normalization_Function.
Section Correctness_Results.
*)
Section Correctness_Results.
*)
-inline cic:/CoRN/tactics/AlgReflection/eq_nat_corr.con.
+inline "cic:/CoRN/tactics/AlgReflection/eq_nat_corr.con".
-inline cic:/CoRN/tactics/AlgReflection/eq_int_corr.con.
+inline "cic:/CoRN/tactics/AlgReflection/eq_int_corr.con".
-inline cic:/CoRN/tactics/AlgReflection/eq_expr_corr.con.
+inline "cic:/CoRN/tactics/AlgReflection/eq_expr_corr.con".
(* UNEXPORTED
End Correctness_Results.
(* UNEXPORTED
End Correctness_Results.
set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics1".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics1".
(* begin hide *)
(* UNEXPORTED
(* begin hide *)
(* UNEXPORTED
set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics2".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics2".
(* $Id: DiffTactics2.v,v 1.1.1.1 2004/02/05 16:25:45 lionelm Exp $ *)
(* begin hide *)
(* $Id: DiffTactics2.v,v 1.1.1.1 2004/02/05 16:25:45 lionelm Exp $ *)
(* begin hide *)
-(* INCLUDE
-Differentiability
-*)
+include "ftc/Differentiability.ma".
(* UNEXPORTED
Section Automatizing_Continuity.
*)
(* UNEXPORTED
Section Automatizing_Continuity.
*)
-inline cic:/CoRN/tactics/DiffTactics2/a.var.
+inline "cic:/CoRN/tactics/DiffTactics2/a.var".
-inline cic:/CoRN/tactics/DiffTactics2/b.var.
+inline "cic:/CoRN/tactics/DiffTactics2/b.var".
-inline cic:/CoRN/tactics/DiffTactics2/cont_function.ind.
+inline "cic:/CoRN/tactics/DiffTactics2/cont_function.ind".
-inline cic:/CoRN/tactics/DiffTactics2/cont_to_pfunct.con.
+inline "cic:/CoRN/tactics/DiffTactics2/cont_to_pfunct.con".
-inline cic:/CoRN/tactics/DiffTactics2/continuous_cont.con.
+inline "cic:/CoRN/tactics/DiffTactics2/continuous_cont.con".
(* UNEXPORTED
End Automatizing_Continuity.
(* UNEXPORTED
End Automatizing_Continuity.
Section Automatizing_Derivatives.
*)
Section Automatizing_Derivatives.
*)
-inline cic:/CoRN/tactics/DiffTactics2/a.var.
+inline "cic:/CoRN/tactics/DiffTactics2/a.var".
-inline cic:/CoRN/tactics/DiffTactics2/b.var.
+inline "cic:/CoRN/tactics/DiffTactics2/b.var".
-inline cic:/CoRN/tactics/DiffTactics2/deriv_function.ind.
+inline "cic:/CoRN/tactics/DiffTactics2/deriv_function.ind".
-inline cic:/CoRN/tactics/DiffTactics2/deriv_to_pfunct.con.
+inline "cic:/CoRN/tactics/DiffTactics2/deriv_to_pfunct.con".
-inline cic:/CoRN/tactics/DiffTactics2/deriv_deriv.con.
+inline "cic:/CoRN/tactics/DiffTactics2/deriv_deriv.con".
-inline cic:/CoRN/tactics/DiffTactics2/deriv_restr.con.
+inline "cic:/CoRN/tactics/DiffTactics2/deriv_restr.con".
-inline cic:/CoRN/tactics/DiffTactics2/diffble_restr.con.
+inline "cic:/CoRN/tactics/DiffTactics2/diffble_restr.con".
(* UNEXPORTED
End Automatizing_Derivatives.
(* UNEXPORTED
End Automatizing_Derivatives.
set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics3".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics3".
(* $Id: DiffTactics3.v,v 1.1.1.1 2004/02/05 16:25:44 lionelm Exp $ *)
(* begin hide *)
(* $Id: DiffTactics3.v,v 1.1.1.1 2004/02/05 16:25:44 lionelm Exp $ *)
(* begin hide *)
-(* INCLUDE
-MoreFunSeries
-*)
+include "ftc/MoreFunSeries.ma".
-(* INCLUDE
-Composition
-*)
+include "ftc/Composition.ma".
-(* INCLUDE
-DiffTactics2
-*)
+include "tactics/DiffTactics2.ma".
(* UNEXPORTED
Ltac Deriv_substR :=
(* UNEXPORTED
Ltac Deriv_substR :=
-inline cic:/CoRN/tactics/DiffTactics3/symbPF.ind.
+inline "cic:/CoRN/tactics/DiffTactics3/symbPF.ind".
(*
| ssum0 : nat->(nat->symbPF)->symbPF
(*
| ssum0 : nat->(nat->symbPF)->symbPF
| ssum : nat->nat->(nat->symbPF)->symbPF
*)
| ssum : nat->nat->(nat->symbPF)->symbPF
*)
-inline cic:/CoRN/tactics/DiffTactics3/symb_to_PartIR.con.
+inline "cic:/CoRN/tactics/DiffTactics3/symb_to_PartIR.con".
-inline cic:/CoRN/tactics/DiffTactics3/symbPF_deriv.con.
+inline "cic:/CoRN/tactics/DiffTactics3/symbPF_deriv.con".
(* UNEXPORTED
Ltac PartIR_to_symbPF f :=
(* UNEXPORTED
Ltac PartIR_to_symbPF f :=
set "baseuri" "cic:/matita/CoRN-Decl/tactics/FieldReflection".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/FieldReflection".
(* $Id: FieldReflection.v,v 1.4 2004/04/23 10:01:06 lcf Exp $ *)
(* begin hide *)
(* $Id: FieldReflection.v,v 1.4 2004/04/23 10:01:06 lcf Exp $ *)
(* begin hide *)
+include "algebra/CFields.ma".
-(* INCLUDE
-AlgReflection
-*)
+include "tactics/AlgReflection.ma".
(* UNEXPORTED
Section Field_Interpretation_Function.
*)
(* UNEXPORTED
Section Field_Interpretation_Function.
*)
-inline cic:/CoRN/tactics/FieldReflection/F.var.
+inline "cic:/CoRN/tactics/FieldReflection/F.var".
-inline cic:/CoRN/tactics/FieldReflection/val.var.
+inline "cic:/CoRN/tactics/FieldReflection/val.var".
-inline cic:/CoRN/tactics/FieldReflection/unop.var.
+inline "cic:/CoRN/tactics/FieldReflection/unop.var".
-inline cic:/CoRN/tactics/FieldReflection/binop.var.
+inline "cic:/CoRN/tactics/FieldReflection/binop.var".
-inline cic:/CoRN/tactics/FieldReflection/pfun.var.
+inline "cic:/CoRN/tactics/FieldReflection/pfun.var".
-inline cic:/CoRN/tactics/FieldReflection/interpF.ind.
+inline "cic:/CoRN/tactics/FieldReflection/interpF.ind".
-inline cic:/CoRN/tactics/FieldReflection/wfF.con.
+inline "cic:/CoRN/tactics/FieldReflection/wfF.con".
-inline cic:/CoRN/tactics/FieldReflection/xexprF.ind.
+inline "cic:/CoRN/tactics/FieldReflection/xexprF.ind".
-inline cic:/CoRN/tactics/FieldReflection/xforgetF.con.
+inline "cic:/CoRN/tactics/FieldReflection/xforgetF.con".
-inline cic:/CoRN/tactics/FieldReflection/xinterpF.con.
+inline "cic:/CoRN/tactics/FieldReflection/xinterpF.con".
-inline cic:/CoRN/tactics/FieldReflection/xexprF2interpF.con.
+inline "cic:/CoRN/tactics/FieldReflection/xexprF2interpF.con".
-inline cic:/CoRN/tactics/FieldReflection/xexprF_diagram_commutes.con.
+inline "cic:/CoRN/tactics/FieldReflection/xexprF_diagram_commutes.con".
-inline cic:/CoRN/tactics/FieldReflection/xexprF2wfF.con.
+inline "cic:/CoRN/tactics/FieldReflection/xexprF2wfF.con".
-inline cic:/CoRN/tactics/FieldReflection/fexprF.ind.
+inline "cic:/CoRN/tactics/FieldReflection/fexprF.ind".
-inline cic:/CoRN/tactics/FieldReflection/fexprF_var.con.
+inline "cic:/CoRN/tactics/FieldReflection/fexprF_var.con".
-inline cic:/CoRN/tactics/FieldReflection/fexprF_int.con.
+inline "cic:/CoRN/tactics/FieldReflection/fexprF_int.con".
-inline cic:/CoRN/tactics/FieldReflection/fexprF_plus.con.
+inline "cic:/CoRN/tactics/FieldReflection/fexprF_plus.con".
-inline cic:/CoRN/tactics/FieldReflection/fexprF_mult.con.
+inline "cic:/CoRN/tactics/FieldReflection/fexprF_mult.con".
-inline cic:/CoRN/tactics/FieldReflection/fforgetF.con.
+inline "cic:/CoRN/tactics/FieldReflection/fforgetF.con".
-inline cic:/CoRN/tactics/FieldReflection/fexprF2interpF.con.
+inline "cic:/CoRN/tactics/FieldReflection/fexprF2interpF.con".
-inline cic:/CoRN/tactics/FieldReflection/fexprF2wfF.con.
+inline "cic:/CoRN/tactics/FieldReflection/fexprF2wfF.con".
-(* INCLUDE
-Opaque_algebra
-*)
+include "tactics/Opaque_algebra.ma".
-inline cic:/CoRN/tactics/FieldReflection/refl_interpF.con.
+inline "cic:/CoRN/tactics/FieldReflection/refl_interpF.con".
-inline cic:/CoRN/tactics/FieldReflection/interpF_wd.con.
+inline "cic:/CoRN/tactics/FieldReflection/interpF_wd.con".
(* UNEXPORTED
End Field_Interpretation_Function.
(* UNEXPORTED
End Field_Interpretation_Function.
Section Field_NormCorrect.
*)
Section Field_NormCorrect.
*)
-inline cic:/CoRN/tactics/FieldReflection/F.var.
+inline "cic:/CoRN/tactics/FieldReflection/F.var".
-inline cic:/CoRN/tactics/FieldReflection/val.var.
+inline "cic:/CoRN/tactics/FieldReflection/val.var".
-inline cic:/CoRN/tactics/FieldReflection/unop.var.
+inline "cic:/CoRN/tactics/FieldReflection/unop.var".
-inline cic:/CoRN/tactics/FieldReflection/binop.var.
+inline "cic:/CoRN/tactics/FieldReflection/binop.var".
-inline cic:/CoRN/tactics/FieldReflection/pfun.var.
+inline "cic:/CoRN/tactics/FieldReflection/pfun.var".
-inline cic:/CoRN/tactics/FieldReflection/MI_mult_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/MI_mult_corr_F.con".
(* UNEXPORTED
Transparent Zmult.
(* UNEXPORTED
Transparent Zmult.
-inline cic:/CoRN/tactics/FieldReflection/MV_mult_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/MV_mult_corr_F.con".
(* UNEXPORTED
Transparent MI_mult.
(* UNEXPORTED
Transparent MI_mult.
Opaque MV_mult MI_mult.
*)
Opaque MV_mult MI_mult.
*)
-inline cic:/CoRN/tactics/FieldReflection/MM_mult_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/MM_mult_corr_F.con".
(* UNEXPORTED
Transparent MV_mult MI_mult.
(* UNEXPORTED
Transparent MV_mult MI_mult.
-inline cic:/CoRN/tactics/FieldReflection/MM_plus_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/MM_plus_corr_F.con".
(* UNEXPORTED
Transparent MV_mult.
(* UNEXPORTED
Transparent MV_mult.
-inline cic:/CoRN/tactics/FieldReflection/PM_plus_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/PM_plus_corr_F.con".
(* UNEXPORTED
Transparent MM_plus.
(* UNEXPORTED
Transparent MM_plus.
-inline cic:/CoRN/tactics/FieldReflection/PP_plus_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/PP_plus_corr_F.con".
(* UNEXPORTED
Transparent PM_plus.
(* UNEXPORTED
Transparent PM_plus.
Opaque PM_plus MM_mult MI_mult.
*)
Opaque PM_plus MM_mult MI_mult.
*)
-inline cic:/CoRN/tactics/FieldReflection/PM_mult_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/PM_mult_corr_F.con".
(* UNEXPORTED
Opaque PM_mult.
*)
(* UNEXPORTED
Opaque PM_mult.
*)
-inline cic:/CoRN/tactics/FieldReflection/PP_mult_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/PP_mult_corr_F.con".
(* UNEXPORTED
Transparent PP_plus PM_mult PP_mult PM_plus MI_mult.
*)
(* UNEXPORTED
Transparent PP_plus PM_mult PP_mult PM_plus MI_mult.
*)
-inline cic:/CoRN/tactics/FieldReflection/FF_plus_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/FF_plus_corr_F.con".
-inline cic:/CoRN/tactics/FieldReflection/FF_mult_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/FF_mult_corr_F.con".
(* UNEXPORTED
Transparent FF_div.
*)
(* UNEXPORTED
Transparent FF_div.
*)
-inline cic:/CoRN/tactics/FieldReflection/FF_div_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/FF_div_corr_F.con".
-inline cic:/CoRN/tactics/FieldReflection/NormF_corr.con.
+inline "cic:/CoRN/tactics/FieldReflection/NormF_corr.con".
-inline cic:/CoRN/tactics/FieldReflection/Norm_wfF.con.
+inline "cic:/CoRN/tactics/FieldReflection/Norm_wfF.con".
-inline cic:/CoRN/tactics/FieldReflection/expr_is_zero_corr_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/expr_is_zero_corr_F.con".
-inline cic:/CoRN/tactics/FieldReflection/Tactic_lemma_zero_F.con.
+inline "cic:/CoRN/tactics/FieldReflection/Tactic_lemma_zero_F.con".
-inline cic:/CoRN/tactics/FieldReflection/Tactic_lemmaF.con.
+inline "cic:/CoRN/tactics/FieldReflection/Tactic_lemmaF.con".
(* UNEXPORTED
End Field_NormCorrect.
(* UNEXPORTED
End Field_NormCorrect.
set "baseuri" "cic:/matita/CoRN-Decl/tactics/GroupReflection".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/GroupReflection".
(* $Id: GroupReflection.v,v 1.3 2004/04/23 10:01:06 lcf Exp $ *)
(* begin hide *)
(* $Id: GroupReflection.v,v 1.3 2004/04/23 10:01:06 lcf Exp $ *)
(* begin hide *)
-(* INCLUDE
-CAbGroups
-*)
+include "algebra/CAbGroups.ma".
-(* INCLUDE
-AlgReflection
-*)
+include "tactics/AlgReflection.ma".
(* UNEXPORTED
Section Group_Interpretation_Function.
*)
(* UNEXPORTED
Section Group_Interpretation_Function.
*)
-inline cic:/CoRN/tactics/GroupReflection/G.var.
+inline "cic:/CoRN/tactics/GroupReflection/G.var".
-inline cic:/CoRN/tactics/GroupReflection/val.var.
+inline "cic:/CoRN/tactics/GroupReflection/val.var".
-inline cic:/CoRN/tactics/GroupReflection/unop.var.
+inline "cic:/CoRN/tactics/GroupReflection/unop.var".
-inline cic:/CoRN/tactics/GroupReflection/binop.var.
+inline "cic:/CoRN/tactics/GroupReflection/binop.var".
-inline cic:/CoRN/tactics/GroupReflection/pfun.var.
+inline "cic:/CoRN/tactics/GroupReflection/pfun.var".
-inline cic:/CoRN/tactics/GroupReflection/interpG.ind.
+inline "cic:/CoRN/tactics/GroupReflection/interpG.ind".
-inline cic:/CoRN/tactics/GroupReflection/wfG.con.
+inline "cic:/CoRN/tactics/GroupReflection/wfG.con".
-inline cic:/CoRN/tactics/GroupReflection/xexprG.ind.
+inline "cic:/CoRN/tactics/GroupReflection/xexprG.ind".
-inline cic:/CoRN/tactics/GroupReflection/xforgetG.con.
+inline "cic:/CoRN/tactics/GroupReflection/xforgetG.con".
-inline cic:/CoRN/tactics/GroupReflection/xinterpG.con.
+inline "cic:/CoRN/tactics/GroupReflection/xinterpG.con".
-inline cic:/CoRN/tactics/GroupReflection/xexprG2interpG.con.
+inline "cic:/CoRN/tactics/GroupReflection/xexprG2interpG.con".
-inline cic:/CoRN/tactics/GroupReflection/xexprG_diagram_commutes.con.
+inline "cic:/CoRN/tactics/GroupReflection/xexprG_diagram_commutes.con".
-inline cic:/CoRN/tactics/GroupReflection/xexprG2wfG.con.
+inline "cic:/CoRN/tactics/GroupReflection/xexprG2wfG.con".
-inline cic:/CoRN/tactics/GroupReflection/fexprG.ind.
+inline "cic:/CoRN/tactics/GroupReflection/fexprG.ind".
-inline cic:/CoRN/tactics/GroupReflection/fexprG_var.con.
+inline "cic:/CoRN/tactics/GroupReflection/fexprG_var.con".
-inline cic:/CoRN/tactics/GroupReflection/fexprG_zero.con.
+inline "cic:/CoRN/tactics/GroupReflection/fexprG_zero.con".
-inline cic:/CoRN/tactics/GroupReflection/fexprG_plus.con.
+inline "cic:/CoRN/tactics/GroupReflection/fexprG_plus.con".
-inline cic:/CoRN/tactics/GroupReflection/fexprG_mult_int.con.
+inline "cic:/CoRN/tactics/GroupReflection/fexprG_mult_int.con".
-inline cic:/CoRN/tactics/GroupReflection/fforgetG.con.
+inline "cic:/CoRN/tactics/GroupReflection/fforgetG.con".
-inline cic:/CoRN/tactics/GroupReflection/fexprG2interp.con.
+inline "cic:/CoRN/tactics/GroupReflection/fexprG2interp.con".
-inline cic:/CoRN/tactics/GroupReflection/fexprG2wf.con.
+inline "cic:/CoRN/tactics/GroupReflection/fexprG2wf.con".
(* UNEXPORTED
Opaque csg_crr.
(* UNEXPORTED
Opaque csg_crr.
-inline cic:/CoRN/tactics/GroupReflection/refl_interpG.con.
+inline "cic:/CoRN/tactics/GroupReflection/refl_interpG.con".
-inline cic:/CoRN/tactics/GroupReflection/interpG_wd.con.
+inline "cic:/CoRN/tactics/GroupReflection/interpG_wd.con".
(* UNEXPORTED
End Group_Interpretation_Function.
(* UNEXPORTED
End Group_Interpretation_Function.
Section Group_NormCorrect.
*)
Section Group_NormCorrect.
*)
-inline cic:/CoRN/tactics/GroupReflection/G.var.
+inline "cic:/CoRN/tactics/GroupReflection/G.var".
-inline cic:/CoRN/tactics/GroupReflection/val.var.
+inline "cic:/CoRN/tactics/GroupReflection/val.var".
-inline cic:/CoRN/tactics/GroupReflection/unop.var.
+inline "cic:/CoRN/tactics/GroupReflection/unop.var".
-inline cic:/CoRN/tactics/GroupReflection/binop.var.
+inline "cic:/CoRN/tactics/GroupReflection/binop.var".
-inline cic:/CoRN/tactics/GroupReflection/pfun.var.
+inline "cic:/CoRN/tactics/GroupReflection/pfun.var".
P: sorted on M, all M's not an I
*)
P: sorted on M, all M's not an I
*)
-inline cic:/CoRN/tactics/GroupReflection/MI_mult_comm_int.con.
+inline "cic:/CoRN/tactics/GroupReflection/MI_mult_comm_int.con".
(* UNEXPORTED
Opaque Zmult.
*)
(* UNEXPORTED
Opaque Zmult.
*)
-inline cic:/CoRN/tactics/GroupReflection/MI_mult_corr_G.con.
+inline "cic:/CoRN/tactics/GroupReflection/MI_mult_corr_G.con".
(* UNEXPORTED
Transparent Zmult.
(* UNEXPORTED
Transparent Zmult.
-inline cic:/CoRN/tactics/GroupReflection/MV_mult_corr_G.con.
+inline "cic:/CoRN/tactics/GroupReflection/MV_mult_corr_G.con".
(* UNEXPORTED
Opaque MV_mult.
*)
(* UNEXPORTED
Opaque MV_mult.
*)
-inline cic:/CoRN/tactics/GroupReflection/MM_mult_corr_G.con.
+inline "cic:/CoRN/tactics/GroupReflection/MM_mult_corr_G.con".
(* UNEXPORTED
Transparent MV_mult MI_mult.
(* UNEXPORTED
Transparent MV_mult MI_mult.
-inline cic:/CoRN/tactics/GroupReflection/MM_plus_corr_G.con.
+inline "cic:/CoRN/tactics/GroupReflection/MM_plus_corr_G.con".
(* UNEXPORTED
Transparent MV_mult.
(* UNEXPORTED
Transparent MV_mult.
-inline cic:/CoRN/tactics/GroupReflection/PM_plus_corr_G.con.
+inline "cic:/CoRN/tactics/GroupReflection/PM_plus_corr_G.con".
(* UNEXPORTED
Transparent MM_plus.
(* UNEXPORTED
Transparent MM_plus.
-inline cic:/CoRN/tactics/GroupReflection/PP_plus_corr_G.con.
+inline "cic:/CoRN/tactics/GroupReflection/PP_plus_corr_G.con".
(* UNEXPORTED
Transparent PM_plus.
(* UNEXPORTED
Transparent PM_plus.
Opaque PM_plus MM_mult MI_mult.
*)
Opaque PM_plus MM_mult MI_mult.
*)
-inline cic:/CoRN/tactics/GroupReflection/PM_mult_corr_G.con.
+inline "cic:/CoRN/tactics/GroupReflection/PM_mult_corr_G.con".
(* UNEXPORTED
Opaque PM_mult.
*)
(* UNEXPORTED
Opaque PM_mult.
*)
-inline cic:/CoRN/tactics/GroupReflection/PP_mult_corr_G.con.
+inline "cic:/CoRN/tactics/GroupReflection/PP_mult_corr_G.con".
-inline cic:/CoRN/tactics/GroupReflection/NormG_corr_G.con.
+inline "cic:/CoRN/tactics/GroupReflection/NormG_corr_G.con".
-inline cic:/CoRN/tactics/GroupReflection/Tactic_lemmaG.con.
+inline "cic:/CoRN/tactics/GroupReflection/Tactic_lemmaG.con".
(* UNEXPORTED
End Group_NormCorrect.
(* UNEXPORTED
End Group_NormCorrect.
set "baseuri" "cic:/matita/CoRN-Decl/tactics/Opaque_algebra".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/Opaque_algebra".
(* $Id: Opaque_algebra.v,v 1.1 2004/02/11 10:56:57 lcf Exp $ *)
(* Opaque cs_crr. *)
(* $Id: Opaque_algebra.v,v 1.1 2004/02/11 10:56:57 lcf Exp $ *)
(* Opaque cs_crr. *)
set "baseuri" "cic:/matita/CoRN-Decl/tactics/RingReflection".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/RingReflection".
(* $Id: RingReflection.v,v 1.4 2004/04/23 10:01:06 lcf Exp $ *)
(* begin hide *)
(* $Id: RingReflection.v,v 1.4 2004/04/23 10:01:06 lcf Exp $ *)
(* begin hide *)
+include "algebra/CRings.ma".
-(* INCLUDE
-AlgReflection
-*)
+include "tactics/AlgReflection.ma".
(* UNEXPORTED
Section Ring_Interpretation_Function.
*)
(* UNEXPORTED
Section Ring_Interpretation_Function.
*)
-inline cic:/CoRN/tactics/RingReflection/R.var.
+inline "cic:/CoRN/tactics/RingReflection/R.var".
-inline cic:/CoRN/tactics/RingReflection/val.var.
+inline "cic:/CoRN/tactics/RingReflection/val.var".
-inline cic:/CoRN/tactics/RingReflection/unop.var.
+inline "cic:/CoRN/tactics/RingReflection/unop.var".
-inline cic:/CoRN/tactics/RingReflection/binop.var.
+inline "cic:/CoRN/tactics/RingReflection/binop.var".
-inline cic:/CoRN/tactics/RingReflection/pfun.var.
+inline "cic:/CoRN/tactics/RingReflection/pfun.var".
-inline cic:/CoRN/tactics/RingReflection/interpR.ind.
+inline "cic:/CoRN/tactics/RingReflection/interpR.ind".
-inline cic:/CoRN/tactics/RingReflection/wfR.con.
+inline "cic:/CoRN/tactics/RingReflection/wfR.con".
-inline cic:/CoRN/tactics/RingReflection/xexprR.ind.
+inline "cic:/CoRN/tactics/RingReflection/xexprR.ind".
-inline cic:/CoRN/tactics/RingReflection/xforgetR.con.
+inline "cic:/CoRN/tactics/RingReflection/xforgetR.con".
-inline cic:/CoRN/tactics/RingReflection/xinterpR.con.
+inline "cic:/CoRN/tactics/RingReflection/xinterpR.con".
-inline cic:/CoRN/tactics/RingReflection/xexprR2interpR.con.
+inline "cic:/CoRN/tactics/RingReflection/xexprR2interpR.con".
-inline cic:/CoRN/tactics/RingReflection/xexprR_diagram_commutes.con.
+inline "cic:/CoRN/tactics/RingReflection/xexprR_diagram_commutes.con".
-inline cic:/CoRN/tactics/RingReflection/xexprR2wfR.con.
+inline "cic:/CoRN/tactics/RingReflection/xexprR2wfR.con".
-inline cic:/CoRN/tactics/RingReflection/fexprR.ind.
+inline "cic:/CoRN/tactics/RingReflection/fexprR.ind".
-inline cic:/CoRN/tactics/RingReflection/fexprR_var.con.
+inline "cic:/CoRN/tactics/RingReflection/fexprR_var.con".
-inline cic:/CoRN/tactics/RingReflection/fexprR_int.con.
+inline "cic:/CoRN/tactics/RingReflection/fexprR_int.con".
-inline cic:/CoRN/tactics/RingReflection/fexprR_plus.con.
+inline "cic:/CoRN/tactics/RingReflection/fexprR_plus.con".
-inline cic:/CoRN/tactics/RingReflection/fexprR_mult.con.
+inline "cic:/CoRN/tactics/RingReflection/fexprR_mult.con".
-inline cic:/CoRN/tactics/RingReflection/fforgetR.con.
+inline "cic:/CoRN/tactics/RingReflection/fforgetR.con".
-inline cic:/CoRN/tactics/RingReflection/fexprR2interp.con.
+inline "cic:/CoRN/tactics/RingReflection/fexprR2interp.con".
-inline cic:/CoRN/tactics/RingReflection/fexprR2wf.con.
+inline "cic:/CoRN/tactics/RingReflection/fexprR2wf.con".
(* UNEXPORTED
Opaque csg_crr.
(* UNEXPORTED
Opaque csg_crr.
-inline cic:/CoRN/tactics/RingReflection/refl_interpR.con.
+inline "cic:/CoRN/tactics/RingReflection/refl_interpR.con".
-inline cic:/CoRN/tactics/RingReflection/interpR_wd.con.
+inline "cic:/CoRN/tactics/RingReflection/interpR_wd.con".
(* UNEXPORTED
End Ring_Interpretation_Function.
(* UNEXPORTED
End Ring_Interpretation_Function.
Section Ring_NormCorrect.
*)
Section Ring_NormCorrect.
*)
-inline cic:/CoRN/tactics/RingReflection/R.var.
+inline "cic:/CoRN/tactics/RingReflection/R.var".
-inline cic:/CoRN/tactics/RingReflection/val.var.
+inline "cic:/CoRN/tactics/RingReflection/val.var".
-inline cic:/CoRN/tactics/RingReflection/unop.var.
+inline "cic:/CoRN/tactics/RingReflection/unop.var".
-inline cic:/CoRN/tactics/RingReflection/binop.var.
+inline "cic:/CoRN/tactics/RingReflection/binop.var".
-inline cic:/CoRN/tactics/RingReflection/pfun.var.
+inline "cic:/CoRN/tactics/RingReflection/pfun.var".
-inline cic:/CoRN/tactics/RingReflection/MI_mult_corr_R.con.
+inline "cic:/CoRN/tactics/RingReflection/MI_mult_corr_R.con".
(* UNEXPORTED
Transparent Zmult.
(* UNEXPORTED
Transparent Zmult.
-inline cic:/CoRN/tactics/RingReflection/MV_mult_corr_R.con.
+inline "cic:/CoRN/tactics/RingReflection/MV_mult_corr_R.con".
(* UNEXPORTED
Transparent MI_mult.
(* UNEXPORTED
Transparent MI_mult.
Opaque MV_mult MI_mult.
*)
Opaque MV_mult MI_mult.
*)
-inline cic:/CoRN/tactics/RingReflection/MM_mult_corr_R.con.
+inline "cic:/CoRN/tactics/RingReflection/MM_mult_corr_R.con".
(* UNEXPORTED
Transparent MV_mult MI_mult.
(* UNEXPORTED
Transparent MV_mult MI_mult.
-inline cic:/CoRN/tactics/RingReflection/MM_plus_corr_R.con.
+inline "cic:/CoRN/tactics/RingReflection/MM_plus_corr_R.con".
(* UNEXPORTED
Transparent MV_mult.
(* UNEXPORTED
Transparent MV_mult.
-inline cic:/CoRN/tactics/RingReflection/PM_plus_corr_R.con.
+inline "cic:/CoRN/tactics/RingReflection/PM_plus_corr_R.con".
(* UNEXPORTED
Transparent MM_plus.
(* UNEXPORTED
Transparent MM_plus.
-inline cic:/CoRN/tactics/RingReflection/PP_plus_corr_R.con.
+inline "cic:/CoRN/tactics/RingReflection/PP_plus_corr_R.con".
(* UNEXPORTED
Transparent PM_plus.
(* UNEXPORTED
Transparent PM_plus.
Opaque PM_plus MM_mult MI_mult.
*)
Opaque PM_plus MM_mult MI_mult.
*)
-inline cic:/CoRN/tactics/RingReflection/PM_mult_corr_R.con.
+inline "cic:/CoRN/tactics/RingReflection/PM_mult_corr_R.con".
(* UNEXPORTED
Opaque PM_mult.
*)
(* UNEXPORTED
Opaque PM_mult.
*)
-inline cic:/CoRN/tactics/RingReflection/PP_mult_corr_R.con.
+inline "cic:/CoRN/tactics/RingReflection/PP_mult_corr_R.con".
(*
Transparent PP_plus PM_mult PP_mult PM_plus MI_mult.
(*
Transparent PP_plus PM_mult PP_mult PM_plus MI_mult.
-inline cic:/CoRN/tactics/RingReflection/NormR_corr.con.
+inline "cic:/CoRN/tactics/RingReflection/NormR_corr.con".
-inline cic:/CoRN/tactics/RingReflection/Tactic_lemmaR.con.
+inline "cic:/CoRN/tactics/RingReflection/Tactic_lemmaR.con".
(* UNEXPORTED
End Ring_NormCorrect.
(* UNEXPORTED
End Ring_NormCorrect.
set "baseuri" "cic:/matita/CoRN-Decl/tactics/Step".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/Step".
(* begin hide *)
(* UNEXPORTED
(* begin hide *)
(* UNEXPORTED
set "baseuri" "cic:/matita/CoRN-Decl/tactics/Transparent_algebra".
set "baseuri" "cic:/matita/CoRN-Decl/tactics/Transparent_algebra".
(* $Id: Transparent_algebra.v,v 1.1 2004/02/11 10:56:58 lcf Exp $ *)
(* UNEXPORTED
(* $Id: Transparent_algebra.v,v 1.1 2004/02/11 10:56:58 lcf Exp $ *)
(* UNEXPORTED
set "baseuri" "cic:/matita/CoRN-Decl/transc/Exponential".
set "baseuri" "cic:/matita/CoRN-Decl/transc/Exponential".
(* $Id: Exponential.v,v 1.7 2004/04/23 10:01:07 lcf Exp $ *)
(* $Id: Exponential.v,v 1.7 2004/04/23 10:01:07 lcf Exp $ *)
-(* INCLUDE
-TaylorSeries
-*)
+include "transc/TaylorSeries.ma".
(* UNEXPORTED
Opaque Min Max.
(* UNEXPORTED
Opaque Min Max.
Exponential is strongly extensional and well defined.
*)
Exponential is strongly extensional and well defined.
*)
-inline cic:/CoRN/transc/Exponential/Exp_strext.con.
+inline "cic:/CoRN/transc/Exponential/Exp_strext.con".
-inline cic:/CoRN/transc/Exponential/Exp_wd.con.
+inline "cic:/CoRN/transc/Exponential/Exp_wd.con".
(* UNEXPORTED
Hint Resolve Exp_wd: algebra.
*)
(* UNEXPORTED
Hint Resolve Exp_wd: algebra.
*)
-inline cic:/CoRN/transc/Exponential/Exp_zero.con.
+inline "cic:/CoRN/transc/Exponential/Exp_zero.con".
(*#* $e^1=e$#e<sup>1</sup>=e#, where [e] was defined a long time ago.
*)
(*#* $e^1=e$#e<sup>1</sup>=e#, where [e] was defined a long time ago.
*)
-inline cic:/CoRN/transc/Exponential/Exp_one.con.
+inline "cic:/CoRN/transc/Exponential/Exp_one.con".
(* UNEXPORTED
Hint Resolve Exp_zero Exp_one: algebra.
(* UNEXPORTED
Hint Resolve Exp_zero Exp_one: algebra.
The exponential function is its own derivative, and continuous.
*)
The exponential function is its own derivative, and continuous.
*)
-inline cic:/CoRN/transc/Exponential/Derivative_Exp.con.
+inline "cic:/CoRN/transc/Exponential/Derivative_Exp.con".
(* UNEXPORTED
Hint Resolve Derivative_Exp: derivate.
*)
(* UNEXPORTED
Hint Resolve Derivative_Exp: derivate.
*)
-inline cic:/CoRN/transc/Exponential/Continuous_Exp.con.
+inline "cic:/CoRN/transc/Exponential/Continuous_Exp.con".
(* UNEXPORTED
Hint Resolve Continuous_Exp: continuous.
(* UNEXPORTED
Hint Resolve Continuous_Exp: continuous.
Negative numbers are projected into the interval [[0,1]].
*)
Negative numbers are projected into the interval [[0,1]].
*)
-inline cic:/CoRN/transc/Exponential/One_less_Exp.con.
+inline "cic:/CoRN/transc/Exponential/One_less_Exp.con".
-inline cic:/CoRN/transc/Exponential/One_leEq_Exp.con.
+inline "cic:/CoRN/transc/Exponential/One_leEq_Exp.con".
-inline cic:/CoRN/transc/Exponential/Exp_pos'.con.
+inline "cic:/CoRN/transc/Exponential/Exp_pos'.con".
(*#*
Exponential is the unique function which evaluates to 1 at 0 and is
its own derivative.
*)
(*#*
Exponential is the unique function which evaluates to 1 at 0 and is
its own derivative.
*)
-inline cic:/CoRN/transc/Exponential/Exp_unique_lemma.con.
+inline "cic:/CoRN/transc/Exponential/Exp_unique_lemma.con".
-inline cic:/CoRN/transc/Exponential/Exp_bnd.con.
+inline "cic:/CoRN/transc/Exponential/Exp_bnd.con".
(* UNEXPORTED
Opaque Expon.
(* UNEXPORTED
Opaque Expon.
-inline cic:/CoRN/transc/Exponential/Exp_unique.con.
+inline "cic:/CoRN/transc/Exponential/Exp_unique.con".
(* UNEXPORTED
Opaque Expon.
*)
(* UNEXPORTED
Opaque Expon.
*)
-inline cic:/CoRN/transc/Exponential/Exp_plus_pos.con.
+inline "cic:/CoRN/transc/Exponential/Exp_plus_pos.con".
(*#* The usual rules for computing the exponential of a sum. *)
(*#* The usual rules for computing the exponential of a sum. *)
-inline cic:/CoRN/transc/Exponential/Exp_plus.con.
+inline "cic:/CoRN/transc/Exponential/Exp_plus.con".
(* UNEXPORTED
Hint Resolve Exp_plus: algebra.
*)
(* UNEXPORTED
Hint Resolve Exp_plus: algebra.
*)
-inline cic:/CoRN/transc/Exponential/Exp_plus'.con.
+inline "cic:/CoRN/transc/Exponential/Exp_plus'.con".
-inline cic:/CoRN/transc/Exponential/Exp_inv_char.con.
+inline "cic:/CoRN/transc/Exponential/Exp_inv_char.con".
(* UNEXPORTED
Hint Resolve Exp_inv_char: algebra.
(* UNEXPORTED
Hint Resolve Exp_inv_char: algebra.
-inline cic:/CoRN/transc/Exponential/Exp_pos.con.
+inline "cic:/CoRN/transc/Exponential/Exp_pos.con".
-inline cic:/CoRN/transc/Exponential/Exp_ap_zero.con.
+inline "cic:/CoRN/transc/Exponential/Exp_ap_zero.con".
(*#*
And the rules for the exponential of differences.
*)
(*#*
And the rules for the exponential of differences.
*)
-inline cic:/CoRN/transc/Exponential/Exp_inv.con.
+inline "cic:/CoRN/transc/Exponential/Exp_inv.con".
(* UNEXPORTED
Hint Resolve Exp_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve Exp_inv: algebra.
*)
-inline cic:/CoRN/transc/Exponential/Exp_minus.con.
+inline "cic:/CoRN/transc/Exponential/Exp_minus.con".
(* UNEXPORTED
Hint Resolve Exp_minus: algebra.
*)
(* UNEXPORTED
Hint Resolve Exp_minus: algebra.
*)
-inline cic:/CoRN/transc/Exponential/Exp_inv'.con.
+inline "cic:/CoRN/transc/Exponential/Exp_inv'.con".
-inline cic:/CoRN/transc/Exponential/Exp_minus'.con.
+inline "cic:/CoRN/transc/Exponential/Exp_minus'.con".
(*#* Exponential is a monotonous function. *)
(*#* Exponential is a monotonous function. *)
-inline cic:/CoRN/transc/Exponential/Exp_less_One.con.
+inline "cic:/CoRN/transc/Exponential/Exp_less_One.con".
-inline cic:/CoRN/transc/Exponential/Exp_leEq_One.con.
+inline "cic:/CoRN/transc/Exponential/Exp_leEq_One.con".
-inline cic:/CoRN/transc/Exponential/Exp_resp_less.con.
+inline "cic:/CoRN/transc/Exponential/Exp_resp_less.con".
-inline cic:/CoRN/transc/Exponential/Exp_resp_leEq.con.
+inline "cic:/CoRN/transc/Exponential/Exp_resp_leEq.con".
(*#* **Properties of Logarithm
The logarithm is a continuous function with derivative [One[/]x].
*)
(*#* **Properties of Logarithm
The logarithm is a continuous function with derivative [One[/]x].
*)
-inline cic:/CoRN/transc/Exponential/Derivative_Log.con.
+inline "cic:/CoRN/transc/Exponential/Derivative_Log.con".
(* UNEXPORTED
Hint Resolve Derivative_Log: derivate.
*)
(* UNEXPORTED
Hint Resolve Derivative_Log: derivate.
*)
-inline cic:/CoRN/transc/Exponential/Continuous_Log.con.
+inline "cic:/CoRN/transc/Exponential/Continuous_Log.con".
(* UNEXPORTED
Hint Resolve Continuous_Log: continuous.
(* UNEXPORTED
Hint Resolve Continuous_Log: continuous.
(*#* Logarithm of [One]. *)
(*#* Logarithm of [One]. *)
-inline cic:/CoRN/transc/Exponential/Log_one.con.
+inline "cic:/CoRN/transc/Exponential/Log_one.con".
(* UNEXPORTED
Hint Resolve Log_one: algebra.
(* UNEXPORTED
Hint Resolve Log_one: algebra.
(*#* The logarithm is (strongly) extensional. *)
(*#* The logarithm is (strongly) extensional. *)
-inline cic:/CoRN/transc/Exponential/Log_strext.con.
+inline "cic:/CoRN/transc/Exponential/Log_strext.con".
-inline cic:/CoRN/transc/Exponential/Log_wd.con.
+inline "cic:/CoRN/transc/Exponential/Log_wd.con".
(* UNEXPORTED
Hint Resolve Log_wd: algebra.
(* UNEXPORTED
Hint Resolve Log_wd: algebra.
Transparent Logarithm.
*)
Transparent Logarithm.
*)
-inline cic:/CoRN/transc/Exponential/Log_mult.con.
+inline "cic:/CoRN/transc/Exponential/Log_mult.con".
(* UNEXPORTED
Hint Resolve Log_mult: algebra.
*)
(* UNEXPORTED
Hint Resolve Log_mult: algebra.
*)
-inline cic:/CoRN/transc/Exponential/Log_mult'.con.
+inline "cic:/CoRN/transc/Exponential/Log_mult'.con".
(*#* A characterization of the domain of the logarithm. *)
(*#* A characterization of the domain of the logarithm. *)
-inline cic:/CoRN/transc/Exponential/Log_domain.con.
+inline "cic:/CoRN/transc/Exponential/Log_domain.con".
(* UNEXPORTED
Opaque Expon Logarithm.
(* UNEXPORTED
Opaque Expon Logarithm.
numerical and as a functional equation.
*)
numerical and as a functional equation.
*)
-inline cic:/CoRN/transc/Exponential/Log_Exp_inv.con.
+inline "cic:/CoRN/transc/Exponential/Log_Exp_inv.con".
-inline cic:/CoRN/transc/Exponential/Log_Exp.con.
+inline "cic:/CoRN/transc/Exponential/Log_Exp.con".
(* UNEXPORTED
Transparent Logarithm.
(* UNEXPORTED
Transparent Logarithm.
Hint Resolve Log_Exp: algebra.
*)
Hint Resolve Log_Exp: algebra.
*)
-inline cic:/CoRN/transc/Exponential/Exp_Log_lemma.con.
+inline "cic:/CoRN/transc/Exponential/Exp_Log_lemma.con".
(*#* The converse expression. *)
(*#* The converse expression. *)
-inline cic:/CoRN/transc/Exponential/Exp_Log.con.
+inline "cic:/CoRN/transc/Exponential/Exp_Log.con".
(* UNEXPORTED
Hint Resolve Exp_Log: algebra.
(* UNEXPORTED
Hint Resolve Exp_Log: algebra.
(*#* Exponential and logarithm are injective. *)
(*#* Exponential and logarithm are injective. *)
-inline cic:/CoRN/transc/Exponential/Exp_cancel.con.
+inline "cic:/CoRN/transc/Exponential/Exp_cancel.con".
-inline cic:/CoRN/transc/Exponential/Log_cancel.con.
+inline "cic:/CoRN/transc/Exponential/Log_cancel.con".
(* UNEXPORTED
Opaque Logarithm.
(* UNEXPORTED
Opaque Logarithm.
(*#* And the final characterization as inverse functions. *)
(*#* And the final characterization as inverse functions. *)
-inline cic:/CoRN/transc/Exponential/Exp_Log_inv.con.
+inline "cic:/CoRN/transc/Exponential/Exp_Log_inv.con".
-inline cic:/CoRN/transc/Exponential/Log_E.con.
+inline "cic:/CoRN/transc/Exponential/Log_E.con".
(* UNEXPORTED
Hint Resolve Log_E: algebra.
(* UNEXPORTED
Hint Resolve Log_E: algebra.
(*#* Several rules regarding inequalities. *)
(*#* Several rules regarding inequalities. *)
-inline cic:/CoRN/transc/Exponential/Log_cancel_less.con.
+inline "cic:/CoRN/transc/Exponential/Log_cancel_less.con".
-inline cic:/CoRN/transc/Exponential/Log_cancel_leEq.con.
+inline "cic:/CoRN/transc/Exponential/Log_cancel_leEq.con".
-inline cic:/CoRN/transc/Exponential/Log_resp_less.con.
+inline "cic:/CoRN/transc/Exponential/Log_resp_less.con".
-inline cic:/CoRN/transc/Exponential/Log_resp_leEq.con.
+inline "cic:/CoRN/transc/Exponential/Log_resp_leEq.con".
-inline cic:/CoRN/transc/Exponential/Exp_cancel_less.con.
+inline "cic:/CoRN/transc/Exponential/Exp_cancel_less.con".
-inline cic:/CoRN/transc/Exponential/Exp_cancel_leEq.con.
+inline "cic:/CoRN/transc/Exponential/Exp_cancel_leEq.con".
-inline cic:/CoRN/transc/Exponential/Log_less_Zero.con.
+inline "cic:/CoRN/transc/Exponential/Log_less_Zero.con".
-inline cic:/CoRN/transc/Exponential/Log_leEq_Zero.con.
+inline "cic:/CoRN/transc/Exponential/Log_leEq_Zero.con".
-inline cic:/CoRN/transc/Exponential/Zero_less_Log.con.
+inline "cic:/CoRN/transc/Exponential/Zero_less_Log.con".
-inline cic:/CoRN/transc/Exponential/Zero_leEq_Log.con.
+inline "cic:/CoRN/transc/Exponential/Zero_leEq_Log.con".
(*#* Finally, rules for logarithm of quotients. *)
(*#* Finally, rules for logarithm of quotients. *)
-inline cic:/CoRN/transc/Exponential/Log_recip_char.con.
+inline "cic:/CoRN/transc/Exponential/Log_recip_char.con".
-inline cic:/CoRN/transc/Exponential/Log_recip.con.
+inline "cic:/CoRN/transc/Exponential/Log_recip.con".
(* UNEXPORTED
Hint Resolve Log_recip: algebra.
*)
(* UNEXPORTED
Hint Resolve Log_recip: algebra.
*)
-inline cic:/CoRN/transc/Exponential/Log_recip'.con.
+inline "cic:/CoRN/transc/Exponential/Log_recip'.con".
-inline cic:/CoRN/transc/Exponential/Log_div.con.
+inline "cic:/CoRN/transc/Exponential/Log_div.con".
(* UNEXPORTED
Hint Resolve Log_div: algebra.
*)
(* UNEXPORTED
Hint Resolve Log_div: algebra.
*)
-inline cic:/CoRN/transc/Exponential/Log_div'.con.
+inline "cic:/CoRN/transc/Exponential/Log_div'.con".
set "baseuri" "cic:/matita/CoRN-Decl/transc/InvTrigonom".
set "baseuri" "cic:/matita/CoRN-Decl/transc/InvTrigonom".
(* $Id: InvTrigonom.v,v 1.9 2004/04/23 10:01:07 lcf Exp $ *)
(* $Id: InvTrigonom.v,v 1.9 2004/04/23 10:01:07 lcf Exp $ *)
-(* INCLUDE
-RealPowers
-*)
+include "transc/RealPowers.ma".
+include "transc/TrigMon.ma".
-(* INCLUDE
-StrongIVT
-*)
+include "ftc/StrongIVT.ma".
(*#* printing ArcSin %\ensuremath{\arcsin}% *)
(*#* printing ArcSin %\ensuremath{\arcsin}% *)
Opaque Sine Cosine Expon Logarithm.
*)
Opaque Sine Cosine Expon Logarithm.
*)
-inline cic:/CoRN/transc/InvTrigonom/ArcSin_def_lemma.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcSin_def_lemma.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcSin_def_zero.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcSin_def_zero.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcSin.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcSin.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcSin_domain.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcSin_domain.con".
-inline cic:/CoRN/transc/InvTrigonom/Continuous_ArcSin.con.
+inline "cic:/CoRN/transc/InvTrigonom/Continuous_ArcSin.con".
-inline cic:/CoRN/transc/InvTrigonom/Derivative_ArcSin.con.
+inline "cic:/CoRN/transc/InvTrigonom/Derivative_ArcSin.con".
(* UNEXPORTED
Hint Resolve Derivative_ArcSin: derivate.
(* UNEXPORTED
Hint Resolve Derivative_ArcSin: derivate.
-inline cic:/CoRN/transc/InvTrigonom/ArcCos.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcCos.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcCos_domain.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcCos_domain.con".
-inline cic:/CoRN/transc/InvTrigonom/Continuous_ArcCos.con.
+inline "cic:/CoRN/transc/InvTrigonom/Continuous_ArcCos.con".
-inline cic:/CoRN/transc/InvTrigonom/Derivative_ArcCos.con.
+inline "cic:/CoRN/transc/InvTrigonom/Derivative_ArcCos.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcTan_def_lemma.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcTan_def_lemma.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcTang.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcTang.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcTan_domain.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcTan_domain.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcTan.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcTan.con".
-inline cic:/CoRN/transc/InvTrigonom/Continuous_ArcTan.con.
+inline "cic:/CoRN/transc/InvTrigonom/Continuous_ArcTan.con".
-inline cic:/CoRN/transc/InvTrigonom/Derivative_ArcTan.con.
+inline "cic:/CoRN/transc/InvTrigonom/Derivative_ArcTan.con".
(* UNEXPORTED
Hint Resolve Derivative_ArcCos Derivative_ArcTan: derivate.
(* UNEXPORTED
Hint Resolve Derivative_ArcCos Derivative_ArcTan: derivate.
-inline cic:/CoRN/transc/InvTrigonom/maps_Sin.con.
+inline "cic:/CoRN/transc/InvTrigonom/maps_Sin.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcSin_Sin_inv.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin_inv.con".
(* UNEXPORTED
Opaque ArcSin.
*)
(* UNEXPORTED
Opaque ArcSin.
*)
-inline cic:/CoRN/transc/InvTrigonom/ArcSin_Sin.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin.con".
(* UNEXPORTED
Transparent ArcSin.
*)
(* UNEXPORTED
Transparent ArcSin.
*)
-inline cic:/CoRN/transc/InvTrigonom/ArcSin_range.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcSin_range.con".
(* UNEXPORTED
Transparent ArcSin.
*)
(* UNEXPORTED
Transparent ArcSin.
*)
-inline cic:/CoRN/transc/InvTrigonom/Sin_ArcSin.con.
+inline "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin.con".
-inline cic:/CoRN/transc/InvTrigonom/Sin_ArcSin_inv.con.
+inline "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin_inv.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcSin_resp_leEq.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcSin_resp_leEq.con".
(*#* ***Cosine and Arcosine
*)
(*#* ***Cosine and Arcosine
*)
-inline cic:/CoRN/transc/InvTrigonom/ArcCos_Cos.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos.con".
-inline cic:/CoRN/transc/InvTrigonom/Cos_ArcCos.con.
+inline "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcCos_Cos_inv.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos_inv.con".
-inline cic:/CoRN/transc/InvTrigonom/Cos_ArcCos_inv.con.
+inline "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos_inv.con".
(* UNEXPORTED
Opaque ArcSin.
*)
(* UNEXPORTED
Opaque ArcSin.
*)
-inline cic:/CoRN/transc/InvTrigonom/ArcCos_resp_leEq.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcCos_resp_leEq.con".
(*#* ***Tangent and Arctangent
*)
(*#* ***Tangent and Arctangent
*)
-inline cic:/CoRN/transc/InvTrigonom/maps_Tan.con.
+inline "cic:/CoRN/transc/InvTrigonom/maps_Tan.con".
(* UNEXPORTED
Opaque Tang.
*)
(* UNEXPORTED
Opaque Tang.
*)
-inline cic:/CoRN/transc/InvTrigonom/ArcTan_Tan_inv.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan_inv.con".
(* UNEXPORTED
Transparent Tang.
(* UNEXPORTED
Transparent Tang.
-inline cic:/CoRN/transc/InvTrigonom/ArcTan_Tan.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan.con".
(* UNEXPORTED
Opaque iprop.
(* UNEXPORTED
Opaque iprop.
-inline cic:/CoRN/transc/InvTrigonom/Tan_ilim.con.
+inline "cic:/CoRN/transc/InvTrigonom/Tan_ilim.con".
(* UNEXPORTED
Opaque Min.
(* UNEXPORTED
Opaque Min.
-inline cic:/CoRN/transc/InvTrigonom/x.var.
+inline "cic:/CoRN/transc/InvTrigonom/x.var".
-inline cic:/CoRN/transc/InvTrigonom/min.con.
+inline "cic:/CoRN/transc/InvTrigonom/min.con".
-inline cic:/CoRN/transc/InvTrigonom/max.con.
+inline "cic:/CoRN/transc/InvTrigonom/max.con".
-inline cic:/CoRN/transc/InvTrigonom/min1.con.
+inline "cic:/CoRN/transc/InvTrigonom/min1.con".
-inline cic:/CoRN/transc/InvTrigonom/min2.con.
+inline "cic:/CoRN/transc/InvTrigonom/min2.con".
-inline cic:/CoRN/transc/InvTrigonom/min3.con.
+inline "cic:/CoRN/transc/InvTrigonom/min3.con".
-inline cic:/CoRN/transc/InvTrigonom/min4.con.
+inline "cic:/CoRN/transc/InvTrigonom/min4.con".
-inline cic:/CoRN/transc/InvTrigonom/max1.con.
+inline "cic:/CoRN/transc/InvTrigonom/max1.con".
-inline cic:/CoRN/transc/InvTrigonom/max2.con.
+inline "cic:/CoRN/transc/InvTrigonom/max2.con".
-inline cic:/CoRN/transc/InvTrigonom/max3.con.
+inline "cic:/CoRN/transc/InvTrigonom/max3.con".
-inline cic:/CoRN/transc/InvTrigonom/max4.con.
+inline "cic:/CoRN/transc/InvTrigonom/max4.con".
-inline cic:/CoRN/transc/InvTrigonom/min5.con.
+inline "cic:/CoRN/transc/InvTrigonom/min5.con".
-inline cic:/CoRN/transc/InvTrigonom/min6.con.
+inline "cic:/CoRN/transc/InvTrigonom/min6.con".
-inline cic:/CoRN/transc/InvTrigonom/max5.con.
+inline "cic:/CoRN/transc/InvTrigonom/max5.con".
-inline cic:/CoRN/transc/InvTrigonom/max6.con.
+inline "cic:/CoRN/transc/InvTrigonom/max6.con".
-inline cic:/CoRN/transc/InvTrigonom/a.con.
+inline "cic:/CoRN/transc/InvTrigonom/a.con".
-inline cic:/CoRN/transc/InvTrigonom/a1.con.
+inline "cic:/CoRN/transc/InvTrigonom/a1.con".
-inline cic:/CoRN/transc/InvTrigonom/a2.con.
+inline "cic:/CoRN/transc/InvTrigonom/a2.con".
-inline cic:/CoRN/transc/InvTrigonom/a3.con.
+inline "cic:/CoRN/transc/InvTrigonom/a3.con".
-inline cic:/CoRN/transc/InvTrigonom/a4.con.
+inline "cic:/CoRN/transc/InvTrigonom/a4.con".
-inline cic:/CoRN/transc/InvTrigonom/a5.con.
+inline "cic:/CoRN/transc/InvTrigonom/a5.con".
-inline cic:/CoRN/transc/InvTrigonom/b.con.
+inline "cic:/CoRN/transc/InvTrigonom/b.con".
-inline cic:/CoRN/transc/InvTrigonom/b1.con.
+inline "cic:/CoRN/transc/InvTrigonom/b1.con".
-inline cic:/CoRN/transc/InvTrigonom/b2.con.
+inline "cic:/CoRN/transc/InvTrigonom/b2.con".
-inline cic:/CoRN/transc/InvTrigonom/b3.con.
+inline "cic:/CoRN/transc/InvTrigonom/b3.con".
-inline cic:/CoRN/transc/InvTrigonom/b4.con.
+inline "cic:/CoRN/transc/InvTrigonom/b4.con".
-inline cic:/CoRN/transc/InvTrigonom/b5.con.
+inline "cic:/CoRN/transc/InvTrigonom/b5.con".
-inline cic:/CoRN/transc/InvTrigonom/ab.con.
+inline "cic:/CoRN/transc/InvTrigonom/ab.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con".
-inline cic:/CoRN/transc/InvTrigonom/ArcTan_range.con.
+inline "cic:/CoRN/transc/InvTrigonom/ArcTan_range.con".
(* UNEXPORTED
End ArcTan_Range.
(* UNEXPORTED
End ArcTan_Range.
-inline cic:/CoRN/transc/InvTrigonom/Tan_ArcTan.con.
+inline "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan.con".
(* UNEXPORTED
Opaque ArcTang.
*)
(* UNEXPORTED
Opaque ArcTang.
*)
-inline cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con.
+inline "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con".
(* UNEXPORTED
End Inverses.
(* UNEXPORTED
End Inverses.
set "baseuri" "cic:/matita/CoRN-Decl/transc/Pi".
set "baseuri" "cic:/matita/CoRN-Decl/transc/Pi".
+include "CoRN.ma".
+
+include "transc/SinCos.ma".
(* UNEXPORTED
Section Properties_of_Pi.
(* UNEXPORTED
Section Properties_of_Pi.
[Pi] is defined as twice the first positive zero of the cosine. In order to do this, we follow the construction described in Bishop 1969, section 7.
*)
[Pi] is defined as twice the first positive zero of the cosine. In order to do this, we follow the construction described in Bishop 1969, section 7.
*)
-inline cic:/CoRN/transc/Pi/pi_seq.con.
+inline "cic:/CoRN/transc/Pi/pi_seq.con".
(* UNEXPORTED
Opaque Cosine.
(* UNEXPORTED
Opaque Cosine.
-inline cic:/CoRN/transc/Pi/pi_seq_lemma.con.
+inline "cic:/CoRN/transc/Pi/pi_seq_lemma.con".
sequence is strictly increasing.
*)
sequence is strictly increasing.
*)
-inline cic:/CoRN/transc/Pi/pi_seq_nonneg.con.
+inline "cic:/CoRN/transc/Pi/pi_seq_nonneg.con".
-inline cic:/CoRN/transc/Pi/cos_pi_seq_pos.con.
+inline "cic:/CoRN/transc/Pi/cos_pi_seq_pos.con".
-inline cic:/CoRN/transc/Pi/pi_seq_incr.con.
+inline "cic:/CoRN/transc/Pi/pi_seq_incr.con".
(*#* Trivial---but useful---consequences. *)
(*#* Trivial---but useful---consequences. *)
-inline cic:/CoRN/transc/Pi/sin_pi_seq_mon.con.
+inline "cic:/CoRN/transc/Pi/sin_pi_seq_mon.con".
-inline cic:/CoRN/transc/Pi/sin_pi_seq_nonneg.con.
+inline "cic:/CoRN/transc/Pi/sin_pi_seq_nonneg.con".
-inline cic:/CoRN/transc/Pi/sin_pi_seq_gt_one.con.
+inline "cic:/CoRN/transc/Pi/sin_pi_seq_gt_one.con".
-inline cic:/CoRN/transc/Pi/cos_pi_seq_mon.con.
+inline "cic:/CoRN/transc/Pi/cos_pi_seq_mon.con".
-inline cic:/CoRN/transc/Pi/pi_seq_gt_one.con.
+inline "cic:/CoRN/transc/Pi/pi_seq_gt_one.con".
(* UNEXPORTED
Opaque Sine Cosine.
*)
(* UNEXPORTED
Opaque Sine Cosine.
*)
-inline cic:/CoRN/transc/Pi/pi_seq_bnd.con.
+inline "cic:/CoRN/transc/Pi/pi_seq_bnd.con".
-inline cic:/CoRN/transc/Pi/pi_seq_bnd'.con.
+inline "cic:/CoRN/transc/Pi/pi_seq_bnd'.con".
-inline cic:/CoRN/transc/Pi/pi_seq_bnd''.con.
+inline "cic:/CoRN/transc/Pi/pi_seq_bnd''.con".
(* end hide *)
(*#* An auxiliary result. *)
(* end hide *)
(*#* An auxiliary result. *)
-inline cic:/CoRN/transc/Pi/Sin_One_pos.con.
+inline "cic:/CoRN/transc/Pi/Sin_One_pos.con".
(*#* We can now prove that this is a Cauchy sequence. We define [Pi] as
twice its limit.
*)
(*#* We can now prove that this is a Cauchy sequence. We define [Pi] as
twice its limit.
*)
-inline cic:/CoRN/transc/Pi/pi_seq_Cauchy.con.
+inline "cic:/CoRN/transc/Pi/pi_seq_Cauchy.con".
-inline cic:/CoRN/transc/Pi/Pi.con.
+inline "cic:/CoRN/transc/Pi/Pi.con".
(*#*
For $x\in[0,\frac{\pi}2)$#x∈[0,π/2)#, [(Cos x) [>] 0];
$\cos(\frac{pi}2)=0$#cos(π/2)=0#.
*)
(*#*
For $x\in[0,\frac{\pi}2)$#x∈[0,π/2)#, [(Cos x) [>] 0];
$\cos(\frac{pi}2)=0$#cos(π/2)=0#.
*)
-inline cic:/CoRN/transc/Pi/pos_cos.con.
+inline "cic:/CoRN/transc/Pi/pos_cos.con".
-inline cic:/CoRN/transc/Pi/Cos_HalfPi.con.
+inline "cic:/CoRN/transc/Pi/Cos_HalfPi.con".
(*#* Convergence to [Pi [/] Two] is increasing; therefore, [Pi] is positive. *)
(*#* Convergence to [Pi [/] Two] is increasing; therefore, [Pi] is positive. *)
-inline cic:/CoRN/transc/Pi/HalfPi_gt_pi_seq.con.
+inline "cic:/CoRN/transc/Pi/HalfPi_gt_pi_seq.con".
-inline cic:/CoRN/transc/Pi/pos_Pi.con.
+inline "cic:/CoRN/transc/Pi/pos_Pi.con".
(* UNEXPORTED
End Properties_of_Pi.
(* UNEXPORTED
End Properties_of_Pi.
[PiSolve] will prove any of these inequalities.
*)
[PiSolve] will prove any of these inequalities.
*)
-inline cic:/CoRN/transc/Pi/pos_HalfPi.con.
+inline "cic:/CoRN/transc/Pi/pos_HalfPi.con".
-inline cic:/CoRN/transc/Pi/pos_QuarterPi.con.
+inline "cic:/CoRN/transc/Pi/pos_QuarterPi.con".
-inline cic:/CoRN/transc/Pi/QuarterPi_less_HalfPi.con.
+inline "cic:/CoRN/transc/Pi/QuarterPi_less_HalfPi.con".
-inline cic:/CoRN/transc/Pi/HalfPi_less_Pi.con.
+inline "cic:/CoRN/transc/Pi/HalfPi_less_Pi.con".
-inline cic:/CoRN/transc/Pi/QuarterPi_less_Pi.con.
+inline "cic:/CoRN/transc/Pi/QuarterPi_less_Pi.con".
-inline cic:/CoRN/transc/Pi/neg_invPi.con.
+inline "cic:/CoRN/transc/Pi/neg_invPi.con".
-inline cic:/CoRN/transc/Pi/neg_invHalfPi.con.
+inline "cic:/CoRN/transc/Pi/neg_invHalfPi.con".
-inline cic:/CoRN/transc/Pi/neg_invQuarterPi.con.
+inline "cic:/CoRN/transc/Pi/neg_invQuarterPi.con".
-inline cic:/CoRN/transc/Pi/invHalfPi_less_invQuarterPi.con.
+inline "cic:/CoRN/transc/Pi/invHalfPi_less_invQuarterPi.con".
-inline cic:/CoRN/transc/Pi/invPi_less_invHalfPi.con.
+inline "cic:/CoRN/transc/Pi/invPi_less_invHalfPi.con".
-inline cic:/CoRN/transc/Pi/invPi_less_invQuarterPi.con.
+inline "cic:/CoRN/transc/Pi/invPi_less_invQuarterPi.con".
-inline cic:/CoRN/transc/Pi/invPi_less_Pi.con.
+inline "cic:/CoRN/transc/Pi/invPi_less_Pi.con".
-inline cic:/CoRN/transc/Pi/invPi_less_HalfPi.con.
+inline "cic:/CoRN/transc/Pi/invPi_less_HalfPi.con".
-inline cic:/CoRN/transc/Pi/invPi_less_QuarterPi.con.
+inline "cic:/CoRN/transc/Pi/invPi_less_QuarterPi.con".
-inline cic:/CoRN/transc/Pi/invHalfPi_less_Pi.con.
+inline "cic:/CoRN/transc/Pi/invHalfPi_less_Pi.con".
-inline cic:/CoRN/transc/Pi/invHalfPi_less_HalfPi.con.
+inline "cic:/CoRN/transc/Pi/invHalfPi_less_HalfPi.con".
-inline cic:/CoRN/transc/Pi/invHalfPi_less_QuarterPi.con.
+inline "cic:/CoRN/transc/Pi/invHalfPi_less_QuarterPi.con".
-inline cic:/CoRN/transc/Pi/invQuarterPi_less_Pi.con.
+inline "cic:/CoRN/transc/Pi/invQuarterPi_less_Pi.con".
-inline cic:/CoRN/transc/Pi/invQuarterPi_less_HalfPi.con.
+inline "cic:/CoRN/transc/Pi/invQuarterPi_less_HalfPi.con".
-inline cic:/CoRN/transc/Pi/invQuarterPi_less_QuarterPi.con.
+inline "cic:/CoRN/transc/Pi/invQuarterPi_less_QuarterPi.con".
(* UNEXPORTED
End Pi_and_Order.
(* UNEXPORTED
End Pi_and_Order.
-inline cic:/CoRN/transc/Pi/Cos_double.con.
+inline "cic:/CoRN/transc/Pi/Cos_double.con".
-inline cic:/CoRN/transc/Pi/Sin_double.con.
+inline "cic:/CoRN/transc/Pi/Sin_double.con".
-inline cic:/CoRN/transc/Pi/Tan_double.con.
+inline "cic:/CoRN/transc/Pi/Tan_double.con".
-inline cic:/CoRN/transc/Pi/sqrt_lemma.con.
+inline "cic:/CoRN/transc/Pi/sqrt_lemma.con".
(* end hide *)
(*#* Value of trigonometric functions at [Pi[/]Four]. *)
(* end hide *)
(*#* Value of trigonometric functions at [Pi[/]Four]. *)
-inline cic:/CoRN/transc/Pi/Cos_QuarterPi.con.
+inline "cic:/CoRN/transc/Pi/Cos_QuarterPi.con".
-inline cic:/CoRN/transc/Pi/Sin_QuarterPi.con.
+inline "cic:/CoRN/transc/Pi/Sin_QuarterPi.con".
(* UNEXPORTED
Hint Resolve Sin_QuarterPi Cos_QuarterPi: algebra.
(* UNEXPORTED
Hint Resolve Sin_QuarterPi Cos_QuarterPi: algebra.
-inline cic:/CoRN/transc/Pi/Tan_QuarterPi.con.
+inline "cic:/CoRN/transc/Pi/Tan_QuarterPi.con".
(*#* Shifting sine and cosine by [Pi[/]Two] and [Pi]. *)
(*#* Shifting sine and cosine by [Pi[/]Two] and [Pi]. *)
-inline cic:/CoRN/transc/Pi/Sin_HalfPi.con.
+inline "cic:/CoRN/transc/Pi/Sin_HalfPi.con".
(* UNEXPORTED
Hint Resolve Sin_HalfPi: algebra.
*)
(* UNEXPORTED
Hint Resolve Sin_HalfPi: algebra.
*)
-inline cic:/CoRN/transc/Pi/Sin_plus_HalfPi.con.
+inline "cic:/CoRN/transc/Pi/Sin_plus_HalfPi.con".
-inline cic:/CoRN/transc/Pi/Sin_HalfPi_minus.con.
+inline "cic:/CoRN/transc/Pi/Sin_HalfPi_minus.con".
-inline cic:/CoRN/transc/Pi/Cos_plus_HalfPi.con.
+inline "cic:/CoRN/transc/Pi/Cos_plus_HalfPi.con".
-inline cic:/CoRN/transc/Pi/Cos_HalfPi_minus.con.
+inline "cic:/CoRN/transc/Pi/Cos_HalfPi_minus.con".
-inline cic:/CoRN/transc/Pi/Sin_Pi.con.
+inline "cic:/CoRN/transc/Pi/Sin_Pi.con".
-inline cic:/CoRN/transc/Pi/Cos_Pi.con.
+inline "cic:/CoRN/transc/Pi/Cos_Pi.con".
-inline cic:/CoRN/transc/Pi/Sin_plus_Pi.con.
+inline "cic:/CoRN/transc/Pi/Sin_plus_Pi.con".
-inline cic:/CoRN/transc/Pi/Cos_plus_Pi.con.
+inline "cic:/CoRN/transc/Pi/Cos_plus_Pi.con".
(* UNEXPORTED
Hint Resolve Sin_plus_Pi Cos_plus_Pi: algebra.
(* UNEXPORTED
Hint Resolve Sin_plus_Pi Cos_plus_Pi: algebra.
(*#* Sine and cosine have period [Two Pi], tangent has period [Pi]. *)
(*#* Sine and cosine have period [Two Pi], tangent has period [Pi]. *)
-inline cic:/CoRN/transc/Pi/Sin_periodic.con.
+inline "cic:/CoRN/transc/Pi/Sin_periodic.con".
-inline cic:/CoRN/transc/Pi/Cos_periodic.con.
+inline "cic:/CoRN/transc/Pi/Cos_periodic.con".
-inline cic:/CoRN/transc/Pi/Tan_periodic.con.
+inline "cic:/CoRN/transc/Pi/Tan_periodic.con".
(* UNEXPORTED
End Sin_And_Cos.
(* UNEXPORTED
End Sin_And_Cos.
set "baseuri" "cic:/matita/CoRN-Decl/transc/PowerSeries".
set "baseuri" "cic:/matita/CoRN-Decl/transc/PowerSeries".
(* $Id: PowerSeries.v,v 1.8 2004/04/23 10:01:08 lcf Exp $ *)
(*#* printing Exp %\ensuremath{\exp}% *)
(* $Id: PowerSeries.v,v 1.8 2004/04/23 10:01:08 lcf Exp $ *)
(*#* printing Exp %\ensuremath{\exp}% *)
(*#* printing Tan %\ensuremath{\tan}% *)
(*#* printing Tan %\ensuremath{\tan}% *)
(*#* *More on Power Series
(*#* *More on Power Series
-inline cic:/CoRN/transc/PowerSeries/J.var.
+inline "cic:/CoRN/transc/PowerSeries/J.var".
-inline cic:/CoRN/transc/PowerSeries/x0.var.
+inline "cic:/CoRN/transc/PowerSeries/x0.var".
-inline cic:/CoRN/transc/PowerSeries/Hx0.var.
+inline "cic:/CoRN/transc/PowerSeries/Hx0.var".
-inline cic:/CoRN/transc/PowerSeries/a.var.
+inline "cic:/CoRN/transc/PowerSeries/a.var".
-inline cic:/CoRN/transc/PowerSeries/FPowerSeries.con.
+inline "cic:/CoRN/transc/PowerSeries/FPowerSeries.con".
(*#*
The most important convergence criterium specifically for power series
(*#*
The most important convergence criterium specifically for power series
-inline cic:/CoRN/transc/PowerSeries/Ha.var.
+inline "cic:/CoRN/transc/PowerSeries/Ha.var".
-inline cic:/CoRN/transc/PowerSeries/r.con.
+inline "cic:/CoRN/transc/PowerSeries/r.con".
-inline cic:/CoRN/transc/PowerSeries/Hr.con.
+inline "cic:/CoRN/transc/PowerSeries/Hr.con".
-inline cic:/CoRN/transc/PowerSeries/Dirichlet_crit.con.
+inline "cic:/CoRN/transc/PowerSeries/Dirichlet_crit.con".
(*#*
When defining a function using its Taylor series as a motivation, the following operator can be of use.
*)
(*#*
When defining a function using its Taylor series as a motivation, the following operator can be of use.
*)
-inline cic:/CoRN/transc/PowerSeries/FPowerSeries'.con.
+inline "cic:/CoRN/transc/PowerSeries/FPowerSeries'.con".
(*#*
This function is also continuous and has a good convergence ratio.
*)
(*#*
This function is also continuous and has a good convergence ratio.
*)
-inline cic:/CoRN/transc/PowerSeries/FPowerSeries'_cont.con.
+inline "cic:/CoRN/transc/PowerSeries/FPowerSeries'_cont.con".
-inline cic:/CoRN/transc/PowerSeries/included_FPowerSeries'.con.
+inline "cic:/CoRN/transc/PowerSeries/included_FPowerSeries'.con".
-inline cic:/CoRN/transc/PowerSeries/Ha'.var.
+inline "cic:/CoRN/transc/PowerSeries/Ha'.var".
-inline cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv'.con.
+inline "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv'.con".
-inline cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv.con.
+inline "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv.con".
(* UNEXPORTED
End Power_Series.
(* UNEXPORTED
End Power_Series.
-inline cic:/CoRN/transc/PowerSeries/x0.var.
+inline "cic:/CoRN/transc/PowerSeries/x0.var".
-inline cic:/CoRN/transc/PowerSeries/a.var.
+inline "cic:/CoRN/transc/PowerSeries/a.var".
-inline cic:/CoRN/transc/PowerSeries/F.con.
+inline "cic:/CoRN/transc/PowerSeries/F.con".
-inline cic:/CoRN/transc/PowerSeries/G.con.
+inline "cic:/CoRN/transc/PowerSeries/G.con".
(* end hide *)
(* begin show *)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/transc/PowerSeries/Hf.var.
+inline "cic:/CoRN/transc/PowerSeries/Hf.var".
-inline cic:/CoRN/transc/PowerSeries/Hf'.var.
+inline "cic:/CoRN/transc/PowerSeries/Hf'.var".
-inline cic:/CoRN/transc/PowerSeries/Hg.var.
+inline "cic:/CoRN/transc/PowerSeries/Hg.var".
(* end show *)
(*#* We get a comparison test for power series. *)
(* end show *)
(*#* We get a comparison test for power series. *)
-inline cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con.
+inline "cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con".
(*#* And a rule for differentiation. *)
(*#* And a rule for differentiation. *)
-inline cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con.
+inline "cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con".
(* UNEXPORTED
End More_on_PowerSeries.
(* UNEXPORTED
End More_on_PowerSeries.
quotient of sine over cosine.
*)
quotient of sine over cosine.
*)
-inline cic:/CoRN/transc/PowerSeries/Exp_ps.con.
+inline "cic:/CoRN/transc/PowerSeries/Exp_ps.con".
-inline cic:/CoRN/transc/PowerSeries/sin_seq.con.
+inline "cic:/CoRN/transc/PowerSeries/sin_seq.con".
-inline cic:/CoRN/transc/PowerSeries/sin_ps.con.
+inline "cic:/CoRN/transc/PowerSeries/sin_ps.con".
-inline cic:/CoRN/transc/PowerSeries/cos_seq.con.
+inline "cic:/CoRN/transc/PowerSeries/cos_seq.con".
-inline cic:/CoRN/transc/PowerSeries/cos_ps.con.
+inline "cic:/CoRN/transc/PowerSeries/cos_ps.con".
-inline cic:/CoRN/transc/PowerSeries/Exp_conv'.con.
+inline "cic:/CoRN/transc/PowerSeries/Exp_conv'.con".
-inline cic:/CoRN/transc/PowerSeries/Exp_conv.con.
+inline "cic:/CoRN/transc/PowerSeries/Exp_conv.con".
-inline cic:/CoRN/transc/PowerSeries/sin_conv.con.
+inline "cic:/CoRN/transc/PowerSeries/sin_conv.con".
-inline cic:/CoRN/transc/PowerSeries/cos_conv.con.
+inline "cic:/CoRN/transc/PowerSeries/cos_conv.con".
-inline cic:/CoRN/transc/PowerSeries/Expon.con.
+inline "cic:/CoRN/transc/PowerSeries/Expon.con".
-inline cic:/CoRN/transc/PowerSeries/Sine.con.
+inline "cic:/CoRN/transc/PowerSeries/Sine.con".
-inline cic:/CoRN/transc/PowerSeries/Cosine.con.
+inline "cic:/CoRN/transc/PowerSeries/Cosine.con".
-inline cic:/CoRN/transc/PowerSeries/Tang.con.
+inline "cic:/CoRN/transc/PowerSeries/Tang.con".
(*#*
Some auxiliary domain results.
*)
(*#*
Some auxiliary domain results.
*)
-inline cic:/CoRN/transc/PowerSeries/Exp_domain.con.
+inline "cic:/CoRN/transc/PowerSeries/Exp_domain.con".
-inline cic:/CoRN/transc/PowerSeries/sin_domain.con.
+inline "cic:/CoRN/transc/PowerSeries/sin_domain.con".
-inline cic:/CoRN/transc/PowerSeries/cos_domain.con.
+inline "cic:/CoRN/transc/PowerSeries/cos_domain.con".
-inline cic:/CoRN/transc/PowerSeries/included_Exp.con.
+inline "cic:/CoRN/transc/PowerSeries/included_Exp.con".
-inline cic:/CoRN/transc/PowerSeries/included_Sin.con.
+inline "cic:/CoRN/transc/PowerSeries/included_Sin.con".
-inline cic:/CoRN/transc/PowerSeries/included_Cos.con.
+inline "cic:/CoRN/transc/PowerSeries/included_Cos.con".
(*#*
Definition of the logarithm.
*)
(*#*
Definition of the logarithm.
*)
-inline cic:/CoRN/transc/PowerSeries/log_defn_lemma.con.
+inline "cic:/CoRN/transc/PowerSeries/log_defn_lemma.con".
-inline cic:/CoRN/transc/PowerSeries/Logarithm.con.
+inline "cic:/CoRN/transc/PowerSeries/Logarithm.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
As most of these functions are total, it makes sense to treat them as setoid functions on the reals. In the case of logarithm and tangent, this is not possible; however, we still define some abbreviations for aesthetical reasons.
*)
As most of these functions are total, it makes sense to treat them as setoid functions on the reals. In the case of logarithm and tangent, this is not possible; however, we still define some abbreviations for aesthetical reasons.
*)
-inline cic:/CoRN/transc/PowerSeries/Exp.con.
+inline "cic:/CoRN/transc/PowerSeries/Exp.con".
-inline cic:/CoRN/transc/PowerSeries/Sin.con.
+inline "cic:/CoRN/transc/PowerSeries/Sin.con".
-inline cic:/CoRN/transc/PowerSeries/Cos.con.
+inline "cic:/CoRN/transc/PowerSeries/Cos.con".
-inline cic:/CoRN/transc/PowerSeries/Log.con.
+inline "cic:/CoRN/transc/PowerSeries/Log.con".
-inline cic:/CoRN/transc/PowerSeries/Tan.con.
+inline "cic:/CoRN/transc/PowerSeries/Tan.con".
set "baseuri" "cic:/matita/CoRN-Decl/transc/RealPowers".
set "baseuri" "cic:/matita/CoRN-Decl/transc/RealPowers".
(* $Id: RealPowers.v,v 1.5 2004/04/23 10:01:08 lcf Exp $ *)
(*#* printing [!] %\ensuremath{\hat{\ }}% #^# *)
(*#* printing {!} %\ensuremath{\hat{\ }}% #^# *)
(* $Id: RealPowers.v,v 1.5 2004/04/23 10:01:08 lcf Exp $ *)
(*#* printing [!] %\ensuremath{\hat{\ }}% #^# *)
(*#* printing {!} %\ensuremath{\hat{\ }}% #^# *)
-(* INCLUDE
-Exponential
-*)
+include "transc/Exponential.ma".
(* UNEXPORTED
Opaque Expon.
(* UNEXPORTED
Opaque Expon.
[x [>] 0], inspired by the rules for manipulating these expressions.
*)
[x [>] 0], inspired by the rules for manipulating these expressions.
*)
-inline cic:/CoRN/transc/RealPowers/power.con.
+inline "cic:/CoRN/transc/RealPowers/power.con".
(*#*
This definition yields a well defined, strongly extensional function
(*#*
This definition yields a well defined, strongly extensional function
coincides with the exponential function.
*)
coincides with the exponential function.
*)
-inline cic:/CoRN/transc/RealPowers/power_wd.con.
+inline "cic:/CoRN/transc/RealPowers/power_wd.con".
-inline cic:/CoRN/transc/RealPowers/power_strext.con.
+inline "cic:/CoRN/transc/RealPowers/power_strext.con".
-inline cic:/CoRN/transc/RealPowers/power_plus.con.
+inline "cic:/CoRN/transc/RealPowers/power_plus.con".
-inline cic:/CoRN/transc/RealPowers/power_inv.con.
+inline "cic:/CoRN/transc/RealPowers/power_inv.con".
(* UNEXPORTED
Hint Resolve power_wd power_plus power_inv: algebra.
*)
(* UNEXPORTED
Hint Resolve power_wd power_plus power_inv: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_minus.con.
+inline "cic:/CoRN/transc/RealPowers/power_minus.con".
-inline cic:/CoRN/transc/RealPowers/power_nat.con.
+inline "cic:/CoRN/transc/RealPowers/power_nat.con".
(* UNEXPORTED
Hint Resolve power_minus power_nat: algebra.
*)
(* UNEXPORTED
Hint Resolve power_minus power_nat: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_zero.con.
+inline "cic:/CoRN/transc/RealPowers/power_zero.con".
-inline cic:/CoRN/transc/RealPowers/power_one.con.
+inline "cic:/CoRN/transc/RealPowers/power_one.con".
(* UNEXPORTED
Hint Resolve power_zero power_one: algebra.
(* UNEXPORTED
Hint Resolve power_zero power_one: algebra.
-inline cic:/CoRN/transc/RealPowers/power_int.con.
+inline "cic:/CoRN/transc/RealPowers/power_int.con".
(* UNEXPORTED
Hint Resolve power_int: algebra.
*)
(* UNEXPORTED
Hint Resolve power_int: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/Exp_power.con.
+inline "cic:/CoRN/transc/RealPowers/Exp_power.con".
-inline cic:/CoRN/transc/RealPowers/mult_power.con.
+inline "cic:/CoRN/transc/RealPowers/mult_power.con".
-inline cic:/CoRN/transc/RealPowers/recip_power.con.
+inline "cic:/CoRN/transc/RealPowers/recip_power.con".
(* UNEXPORTED
Hint Resolve Exp_power mult_power recip_power: algebra.
*)
(* UNEXPORTED
Hint Resolve Exp_power mult_power recip_power: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/div_power.con.
+inline "cic:/CoRN/transc/RealPowers/div_power.con".
(* UNEXPORTED
Hint Resolve div_power: algebra.
*)
(* UNEXPORTED
Hint Resolve div_power: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_ap_zero.con.
+inline "cic:/CoRN/transc/RealPowers/power_ap_zero.con".
-inline cic:/CoRN/transc/RealPowers/power_mult.con.
+inline "cic:/CoRN/transc/RealPowers/power_mult.con".
-inline cic:/CoRN/transc/RealPowers/power_pos.con.
+inline "cic:/CoRN/transc/RealPowers/power_pos.con".
(* UNEXPORTED
Hint Resolve power_mult: algebra.
*)
(* UNEXPORTED
Hint Resolve power_mult: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_recip.con.
+inline "cic:/CoRN/transc/RealPowers/power_recip.con".
(* UNEXPORTED
Hint Resolve power_recip: algebra.
*)
(* UNEXPORTED
Hint Resolve power_recip: algebra.
*)
-inline cic:/CoRN/transc/RealPowers/power_div.con.
+inline "cic:/CoRN/transc/RealPowers/power_div.con".
(* UNEXPORTED
Hint Resolve power_div: algebra.
(* UNEXPORTED
Hint Resolve power_div: algebra.
-inline cic:/CoRN/transc/RealPowers/J.var.
+inline "cic:/CoRN/transc/RealPowers/J.var".
-inline cic:/CoRN/transc/RealPowers/F.var.
+inline "cic:/CoRN/transc/RealPowers/F.var".
-inline cic:/CoRN/transc/RealPowers/G.var.
+inline "cic:/CoRN/transc/RealPowers/G.var".
-inline cic:/CoRN/transc/RealPowers/FPower.con.
+inline "cic:/CoRN/transc/RealPowers/FPower.con".
-inline cic:/CoRN/transc/RealPowers/FPower_domain.con.
+inline "cic:/CoRN/transc/RealPowers/FPower_domain.con".
-inline cic:/CoRN/transc/RealPowers/Continuous_power.con.
+inline "cic:/CoRN/transc/RealPowers/Continuous_power.con".
(* UNEXPORTED
End Power_Function.
(* UNEXPORTED
End Power_Function.
(*#* From global continuity we can obviously get local continuity: *)
(*#* From global continuity we can obviously get local continuity: *)
-inline cic:/CoRN/transc/RealPowers/continuous_I_power.con.
+inline "cic:/CoRN/transc/RealPowers/continuous_I_power.con".
(*#* The rule for differentiation is a must. *)
(*#* The rule for differentiation is a must. *)
-inline cic:/CoRN/transc/RealPowers/Derivative_power.con.
+inline "cic:/CoRN/transc/RealPowers/Derivative_power.con".
-inline cic:/CoRN/transc/RealPowers/Diffble_power.con.
+inline "cic:/CoRN/transc/RealPowers/Diffble_power.con".
(* UNEXPORTED
End More_on_Power_Function.
(* UNEXPORTED
End More_on_Power_Function.
set "baseuri" "cic:/matita/CoRN-Decl/transc/SinCos".
set "baseuri" "cic:/matita/CoRN-Decl/transc/SinCos".
(* $Id: SinCos.v,v 1.6 2004/04/23 10:01:08 lcf Exp $ *)
(* $Id: SinCos.v,v 1.6 2004/04/23 10:01:08 lcf Exp $ *)
-(* INCLUDE
-Trigonometric
-*)
+include "transc/Trigonometric.ma".
(* UNEXPORTED
Section Sum_and_so_on.
(* UNEXPORTED
Section Sum_and_so_on.
-inline cic:/CoRN/transc/SinCos/F.con.
+inline "cic:/CoRN/transc/SinCos/F.con".
-inline cic:/CoRN/transc/SinCos/G.con.
+inline "cic:/CoRN/transc/SinCos/G.con".
-inline cic:/CoRN/transc/SinCos/F'.con.
+inline "cic:/CoRN/transc/SinCos/F'.con".
-inline cic:/CoRN/transc/SinCos/G'.con.
+inline "cic:/CoRN/transc/SinCos/G'.con".
-inline cic:/CoRN/transc/SinCos/Sin_plus.con.
+inline "cic:/CoRN/transc/SinCos/Sin_plus.con".
-inline cic:/CoRN/transc/SinCos/Cos_plus.con.
+inline "cic:/CoRN/transc/SinCos/Cos_plus.con".
(* UNEXPORTED
Opaque Sine Cosine.
(* UNEXPORTED
Opaque Sine Cosine.
(*#* As a corollary we get the rule for the tangent of the sum. *)
(*#* As a corollary we get the rule for the tangent of the sum. *)
-inline cic:/CoRN/transc/SinCos/Tan_plus.con.
+inline "cic:/CoRN/transc/SinCos/Tan_plus.con".
(* UNEXPORTED
Transparent Sine Cosine.
(* UNEXPORTED
Transparent Sine Cosine.
(*#* Sine, cosine and tangent of [[--]x]. *)
(*#* Sine, cosine and tangent of [[--]x]. *)
-inline cic:/CoRN/transc/SinCos/Cos_inv.con.
+inline "cic:/CoRN/transc/SinCos/Cos_inv.con".
-inline cic:/CoRN/transc/SinCos/Sin_inv.con.
+inline "cic:/CoRN/transc/SinCos/Sin_inv.con".
(* UNEXPORTED
Opaque Sine Cosine.
(* UNEXPORTED
Opaque Sine Cosine.
Hint Resolve Cos_inv Sin_inv: algebra.
*)
Hint Resolve Cos_inv Sin_inv: algebra.
*)
-inline cic:/CoRN/transc/SinCos/Tan_inv.con.
+inline "cic:/CoRN/transc/SinCos/Tan_inv.con".
(* UNEXPORTED
Transparent Sine Cosine.
(* UNEXPORTED
Transparent Sine Cosine.
Hint Resolve Cos_zero: algebra.
*)
Hint Resolve Cos_zero: algebra.
*)
-inline cic:/CoRN/transc/SinCos/FFT.con.
+inline "cic:/CoRN/transc/SinCos/FFT.con".
(* UNEXPORTED
Opaque Sine Cosine.
(* UNEXPORTED
Opaque Sine Cosine.
Hint Resolve FFT: algebra.
*)
Hint Resolve FFT: algebra.
*)
-inline cic:/CoRN/transc/SinCos/FFT'.con.
+inline "cic:/CoRN/transc/SinCos/FFT'.con".
(* UNEXPORTED
End Sum_and_so_on.
(* UNEXPORTED
End Sum_and_so_on.
Sine, cosine and tangent are strongly extensional and well defined.
*)
Sine, cosine and tangent are strongly extensional and well defined.
*)
-inline cic:/CoRN/transc/SinCos/Sin_strext.con.
+inline "cic:/CoRN/transc/SinCos/Sin_strext.con".
-inline cic:/CoRN/transc/SinCos/Cos_strext.con.
+inline "cic:/CoRN/transc/SinCos/Cos_strext.con".
-inline cic:/CoRN/transc/SinCos/Tan_strext.con.
+inline "cic:/CoRN/transc/SinCos/Tan_strext.con".
-inline cic:/CoRN/transc/SinCos/Sin_wd.con.
+inline "cic:/CoRN/transc/SinCos/Sin_wd.con".
-inline cic:/CoRN/transc/SinCos/Cos_wd.con.
+inline "cic:/CoRN/transc/SinCos/Cos_wd.con".
-inline cic:/CoRN/transc/SinCos/Tan_wd.con.
+inline "cic:/CoRN/transc/SinCos/Tan_wd.con".
(*#*
The sine and cosine produce values in [[-1,1]].
*)
(*#*
The sine and cosine produce values in [[-1,1]].
*)
-inline cic:/CoRN/transc/SinCos/AbsIR_Sin_leEq_One.con.
+inline "cic:/CoRN/transc/SinCos/AbsIR_Sin_leEq_One.con".
-inline cic:/CoRN/transc/SinCos/AbsIR_Cos_leEq_One.con.
+inline "cic:/CoRN/transc/SinCos/AbsIR_Cos_leEq_One.con".
-inline cic:/CoRN/transc/SinCos/Sin_leEq_One.con.
+inline "cic:/CoRN/transc/SinCos/Sin_leEq_One.con".
-inline cic:/CoRN/transc/SinCos/Cos_leEq_One.con.
+inline "cic:/CoRN/transc/SinCos/Cos_leEq_One.con".
(*#*
If the cosine is positive then the sine is in [(-1,1)].
*)
(*#*
If the cosine is positive then the sine is in [(-1,1)].
*)
-inline cic:/CoRN/transc/SinCos/Sin_less_One.con.
+inline "cic:/CoRN/transc/SinCos/Sin_less_One.con".
-inline cic:/CoRN/transc/SinCos/AbsIR_Sin_less_One.con.
+inline "cic:/CoRN/transc/SinCos/AbsIR_Sin_less_One.con".
(* UNEXPORTED
End Basic_Properties.
(* UNEXPORTED
End Basic_Properties.
set "baseuri" "cic:/matita/CoRN-Decl/transc/TaylorSeries".
set "baseuri" "cic:/matita/CoRN-Decl/transc/TaylorSeries".
(* $Id: TaylorSeries.v,v 1.7 2004/04/23 10:01:08 lcf Exp $ *)
(* $Id: TaylorSeries.v,v 1.7 2004/04/23 10:01:08 lcf Exp $ *)
-(* INCLUDE
-PowerSeries
-*)
+include "transc/PowerSeries.ma".
+include "ftc/Taylor.ma".
-inline cic:/CoRN/transc/TaylorSeries/J.var.
+inline "cic:/CoRN/transc/TaylorSeries/J.var".
-inline cic:/CoRN/transc/TaylorSeries/pJ.var.
+inline "cic:/CoRN/transc/TaylorSeries/pJ.var".
-inline cic:/CoRN/transc/TaylorSeries/F.var.
+inline "cic:/CoRN/transc/TaylorSeries/F.var".
-inline cic:/CoRN/transc/TaylorSeries/diffF.var.
+inline "cic:/CoRN/transc/TaylorSeries/diffF.var".
-inline cic:/CoRN/transc/TaylorSeries/a.var.
+inline "cic:/CoRN/transc/TaylorSeries/a.var".
-inline cic:/CoRN/transc/TaylorSeries/Ha.var.
+inline "cic:/CoRN/transc/TaylorSeries/Ha.var".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con".
(*#*
%\begin{convention}% Assume also that [f] is the sequence of
(*#*
%\begin{convention}% Assume also that [f] is the sequence of
-inline cic:/CoRN/transc/TaylorSeries/f.var.
+inline "cic:/CoRN/transc/TaylorSeries/f.var".
-inline cic:/CoRN/transc/TaylorSeries/derF.var.
+inline "cic:/CoRN/transc/TaylorSeries/derF.var".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series.con".
(* UNEXPORTED
Opaque N_Deriv.
(* UNEXPORTED
Opaque N_Deriv.
(*#* Characterizations of the Taylor remainder. *)
(*#* Characterizations of the Taylor remainder. *)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Rem_char.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Rem_char.con".
-inline cic:/CoRN/transc/TaylorSeries/abs_Taylor_Rem_char.con.
+inline "cic:/CoRN/transc/TaylorSeries/abs_Taylor_Rem_char.con".
(* UNEXPORTED
End Definitions.
(* UNEXPORTED
End Definitions.
-inline cic:/CoRN/transc/TaylorSeries/H.var.
+inline "cic:/CoRN/transc/TaylorSeries/H.var".
-inline cic:/CoRN/transc/TaylorSeries/F.var.
+inline "cic:/CoRN/transc/TaylorSeries/F.var".
-inline cic:/CoRN/transc/TaylorSeries/a.var.
+inline "cic:/CoRN/transc/TaylorSeries/a.var".
-inline cic:/CoRN/transc/TaylorSeries/Ha.var.
+inline "cic:/CoRN/transc/TaylorSeries/Ha.var".
-inline cic:/CoRN/transc/TaylorSeries/f.var.
+inline "cic:/CoRN/transc/TaylorSeries/f.var".
-inline cic:/CoRN/transc/TaylorSeries/derF.var.
+inline "cic:/CoRN/transc/TaylorSeries/derF.var".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_lemma_cont.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_lemma_cont.con".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_bnd.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_bnd.con".
-inline cic:/CoRN/transc/TaylorSeries/bndf.var.
+inline "cic:/CoRN/transc/TaylorSeries/bndf.var".
-inline cic:/CoRN/transc/TaylorSeries/H1.con.
+inline "cic:/CoRN/transc/TaylorSeries/H1.con".
(* UNEXPORTED
Transparent nexp_op.
*)
(* UNEXPORTED
Transparent nexp_op.
*)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma1.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma1.con".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma2.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma2.con".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_IR.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_IR.con".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_majoration_lemma.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_majoration_lemma.con".
(* UNEXPORTED
Opaque N_Deriv fac.
*)
(* UNEXPORTED
Opaque N_Deriv fac.
*)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma3.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma3.con".
-inline cic:/CoRN/transc/TaylorSeries/Hf.var.
+inline "cic:/CoRN/transc/TaylorSeries/Hf.var".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_to_fun.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_to_fun.con".
(* UNEXPORTED
End Convergence_in_IR.
(* UNEXPORTED
End Convergence_in_IR.
give some helpful lemmas.
*)
give some helpful lemmas.
*)
-inline cic:/CoRN/transc/TaylorSeries/Taylor_bnd_trans.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_bnd_trans.con".
-inline cic:/CoRN/transc/TaylorSeries/convergence_lemma.con.
+inline "cic:/CoRN/transc/TaylorSeries/convergence_lemma.con".
-inline cic:/CoRN/transc/TaylorSeries/bnd_imp_Taylor_bnd.con.
+inline "cic:/CoRN/transc/TaylorSeries/bnd_imp_Taylor_bnd.con".
(*#*
Finally, a uniqueness criterium: two functions [F] and [G] are equal,
(*#*
Finally, a uniqueness criterium: two functions [F] and [G] are equal,
Taylor series converge to themselves.
*)
Taylor series converge to themselves.
*)
-inline cic:/CoRN/transc/TaylorSeries/F.var.
+inline "cic:/CoRN/transc/TaylorSeries/F.var".
-inline cic:/CoRN/transc/TaylorSeries/G.var.
+inline "cic:/CoRN/transc/TaylorSeries/G.var".
-inline cic:/CoRN/transc/TaylorSeries/a.var.
+inline "cic:/CoRN/transc/TaylorSeries/a.var".
-inline cic:/CoRN/transc/TaylorSeries/f.var.
+inline "cic:/CoRN/transc/TaylorSeries/f.var".
-inline cic:/CoRN/transc/TaylorSeries/g.var.
+inline "cic:/CoRN/transc/TaylorSeries/g.var".
-inline cic:/CoRN/transc/TaylorSeries/derF.var.
+inline "cic:/CoRN/transc/TaylorSeries/derF.var".
-inline cic:/CoRN/transc/TaylorSeries/derG.var.
+inline "cic:/CoRN/transc/TaylorSeries/derG.var".
-inline cic:/CoRN/transc/TaylorSeries/bndf.var.
+inline "cic:/CoRN/transc/TaylorSeries/bndf.var".
-inline cic:/CoRN/transc/TaylorSeries/bndg.var.
+inline "cic:/CoRN/transc/TaylorSeries/bndg.var".
-inline cic:/CoRN/transc/TaylorSeries/Heq.var.
+inline "cic:/CoRN/transc/TaylorSeries/Heq.var".
(* end show *)
(* begin hide *)
(* end show *)
(* begin hide *)
-inline cic:/CoRN/transc/TaylorSeries/Hf.con.
+inline "cic:/CoRN/transc/TaylorSeries/Hf.con".
-inline cic:/CoRN/transc/TaylorSeries/Taylor_unique_crit.con.
+inline "cic:/CoRN/transc/TaylorSeries/Taylor_unique_crit.con".
(* UNEXPORTED
End Other_Results.
(* UNEXPORTED
End Other_Results.
set "baseuri" "cic:/matita/CoRN-Decl/transc/TrigMon".
set "baseuri" "cic:/matita/CoRN-Decl/transc/TrigMon".
(* $Id: TrigMon.v,v 1.9 2004/04/23 10:01:08 lcf Exp $ *)
(* $Id: TrigMon.v,v 1.9 2004/04/23 10:01:08 lcf Exp $ *)
(* UNEXPORTED
Opaque Sine Cosine.
(* UNEXPORTED
Opaque Sine Cosine.
$(0,\pi)$#(0,π)# and tangent in $(0,\frac{\pi}2)$#0,π/2)#.
*)
$(0,\pi)$#(0,π)# and tangent in $(0,\frac{\pi}2)$#0,π/2)#.
*)
-inline cic:/CoRN/transc/TrigMon/Cos_pos.con.
+inline "cic:/CoRN/transc/TrigMon/Cos_pos.con".
-inline cic:/CoRN/transc/TrigMon/Sin_pos.con.
+inline "cic:/CoRN/transc/TrigMon/Sin_pos.con".
-inline cic:/CoRN/transc/TrigMon/Tan_pos.con.
+inline "cic:/CoRN/transc/TrigMon/Tan_pos.con".
-inline cic:/CoRN/transc/TrigMon/Cos_nonneg.con.
+inline "cic:/CoRN/transc/TrigMon/Cos_nonneg.con".
-inline cic:/CoRN/transc/TrigMon/Sin_nonneg.con.
+inline "cic:/CoRN/transc/TrigMon/Sin_nonneg.con".
-inline cic:/CoRN/transc/TrigMon/Abs_Sin_less_One.con.
+inline "cic:/CoRN/transc/TrigMon/Abs_Sin_less_One.con".
-inline cic:/CoRN/transc/TrigMon/Abs_Cos_less_One.con.
+inline "cic:/CoRN/transc/TrigMon/Abs_Cos_less_One.con".
(*#*
Sine is (strictly) increasing in [[ [--]Pi[/]Two,Pi[/]Two]]; cosine
is (strictly) decreasing in [[Zero,Pi]].
*)
(*#*
Sine is (strictly) increasing in [[ [--]Pi[/]Two,Pi[/]Two]]; cosine
is (strictly) decreasing in [[Zero,Pi]].
*)
-inline cic:/CoRN/transc/TrigMon/Sin_resp_leEq.con.
+inline "cic:/CoRN/transc/TrigMon/Sin_resp_leEq.con".
-inline cic:/CoRN/transc/TrigMon/Cos_resp_leEq.con.
+inline "cic:/CoRN/transc/TrigMon/Cos_resp_leEq.con".
-inline cic:/CoRN/transc/TrigMon/Cos_resp_less_aux.con.
+inline "cic:/CoRN/transc/TrigMon/Cos_resp_less_aux.con".
-inline cic:/CoRN/transc/TrigMon/Cos_resp_less_aux'.con.
+inline "cic:/CoRN/transc/TrigMon/Cos_resp_less_aux'.con".
-inline cic:/CoRN/transc/TrigMon/Cos_resp_less.con.
+inline "cic:/CoRN/transc/TrigMon/Cos_resp_less.con".
-inline cic:/CoRN/transc/TrigMon/Sin_resp_less.con.
+inline "cic:/CoRN/transc/TrigMon/Sin_resp_less.con".
(* UNEXPORTED
Section Tangent.
(* UNEXPORTED
Section Tangent.
monotonicity properties.
*)
monotonicity properties.
*)
-inline cic:/CoRN/transc/TrigMon/bnd_Cos.con.
+inline "cic:/CoRN/transc/TrigMon/bnd_Cos.con".
(* UNEXPORTED
Opaque Sine Cosine.
*)
(* UNEXPORTED
Opaque Sine Cosine.
*)
-inline cic:/CoRN/transc/TrigMon/Derivative_Tan_1.con.
+inline "cic:/CoRN/transc/TrigMon/Derivative_Tan_1.con".
-inline cic:/CoRN/transc/TrigMon/Derivative_Tan_2.con.
+inline "cic:/CoRN/transc/TrigMon/Derivative_Tan_2.con".
-inline cic:/CoRN/transc/TrigMon/Tan_resp_less.con.
+inline "cic:/CoRN/transc/TrigMon/Tan_resp_less.con".
-inline cic:/CoRN/transc/TrigMon/Tan_resp_leEq.con.
+inline "cic:/CoRN/transc/TrigMon/Tan_resp_leEq.con".
(* UNEXPORTED
End Tangent.
(* UNEXPORTED
End Tangent.
set "baseuri" "cic:/matita/CoRN-Decl/transc/Trigonometric".
set "baseuri" "cic:/matita/CoRN-Decl/transc/Trigonometric".
(* $Id: Trigonometric.v,v 1.5 2004/04/23 10:01:08 lcf Exp $ *)
(* $Id: Trigonometric.v,v 1.5 2004/04/23 10:01:08 lcf Exp $ *)
-(* INCLUDE
-TaylorSeries
-*)
+include "transc/TaylorSeries.ma".
(*#* *The Trigonometric Functions
(*#* *The Trigonometric Functions
(*#* First, we need a lemma on mappings. *)
(*#* First, we need a lemma on mappings. *)
-inline cic:/CoRN/transc/Trigonometric/maps_translation.con.
+inline "cic:/CoRN/transc/Trigonometric/maps_translation.con".
(* UNEXPORTED
End Lemmas.
(* UNEXPORTED
End Lemmas.
(*#* Sine, cosine and tangent at [Zero]. *)
(*#* Sine, cosine and tangent at [Zero]. *)
-inline cic:/CoRN/transc/Trigonometric/Sin_zero.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_zero.con".
-inline cic:/CoRN/transc/Trigonometric/Cos_zero.con.
+inline "cic:/CoRN/transc/Trigonometric/Cos_zero.con".
(* UNEXPORTED
Hint Resolve Sin_zero Cos_zero: algebra.
(* UNEXPORTED
Hint Resolve Sin_zero Cos_zero: algebra.
-inline cic:/CoRN/transc/Trigonometric/Tan_zero.con.
+inline "cic:/CoRN/transc/Trigonometric/Tan_zero.con".
(* UNEXPORTED
Transparent Sine Cosine.
(* UNEXPORTED
Transparent Sine Cosine.
Continuity of sine and cosine are trivial.
*)
Continuity of sine and cosine are trivial.
*)
-inline cic:/CoRN/transc/Trigonometric/Continuous_Sin.con.
+inline "cic:/CoRN/transc/Trigonometric/Continuous_Sin.con".
-inline cic:/CoRN/transc/Trigonometric/Continuous_Cos.con.
+inline "cic:/CoRN/transc/Trigonometric/Continuous_Cos.con".
(*#*
The rules for the derivative of the sine and cosine function; we begin by proving that their defining sequences can be expressed in terms of one another.
*)
(*#*
The rules for the derivative of the sine and cosine function; we begin by proving that their defining sequences can be expressed in terms of one another.
*)
-inline cic:/CoRN/transc/Trigonometric/cos_sin_seq.con.
+inline "cic:/CoRN/transc/Trigonometric/cos_sin_seq.con".
-inline cic:/CoRN/transc/Trigonometric/sin_cos_seq.con.
+inline "cic:/CoRN/transc/Trigonometric/sin_cos_seq.con".
-inline cic:/CoRN/transc/Trigonometric/Derivative_Sin.con.
+inline "cic:/CoRN/transc/Trigonometric/Derivative_Sin.con".
-inline cic:/CoRN/transc/Trigonometric/Derivative_Cos.con.
+inline "cic:/CoRN/transc/Trigonometric/Derivative_Cos.con".
(* UNEXPORTED
Hint Resolve Derivative_Sin Derivative_Cos: derivate.
(* UNEXPORTED
Hint Resolve Derivative_Sin Derivative_Cos: derivate.
-inline cic:/CoRN/transc/Trigonometric/F.con.
+inline "cic:/CoRN/transc/Trigonometric/F.con".
-inline cic:/CoRN/transc/Trigonometric/G.con.
+inline "cic:/CoRN/transc/Trigonometric/G.con".
-inline cic:/CoRN/transc/Trigonometric/F'.con.
+inline "cic:/CoRN/transc/Trigonometric/F'.con".
-inline cic:/CoRN/transc/Trigonometric/G'.con.
+inline "cic:/CoRN/transc/Trigonometric/G'.con".
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_lft.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_lft.con".
(* UNEXPORTED
Opaque FAbs.
(* UNEXPORTED
Opaque FAbs.
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_rht.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_rht.con".
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_eq.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_eq.con".
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_der_lft.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_der_lft.con".
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_der_rht.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_der_rht.con".
-inline cic:/CoRN/transc/Trigonometric/Sin_plus_fun.con.
+inline "cic:/CoRN/transc/Trigonometric/Sin_plus_fun.con".
(* UNEXPORTED
End Sine_of_Sum.
(* UNEXPORTED
End Sine_of_Sum.
-inline cic:/CoRN/transc/Trigonometric/Cos_plus_fun.con.
+inline "cic:/CoRN/transc/Trigonometric/Cos_plus_fun.con".
(* UNEXPORTED
End Sine_and_Cosine.
(* UNEXPORTED
End Sine_and_Cosine.