From: Ferruccio Guidi Date: Thu, 16 Nov 2006 14:45:39 +0000 (+0000) Subject: - transcript: now outputs includes and coercions correctly X-Git-Tag: 0.4.95@7852~803 X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=f104e234238586ac846881feb30e1b56a509cfd3;p=helm.git - transcript: now outputs includes and coercions correctly - GrafiteAstPp: coercion and inline pretty printing patched - CoRN-Decl: regenerated: starts to compile :) but inline is broken :( --- diff --git a/components/binaries/transcript/Makefile b/components/binaries/transcript/Makefile index 1252d345f..21dedfc0d 100644 --- a/components/binaries/transcript/Makefile +++ b/components/binaries/transcript/Makefile @@ -1,3 +1,5 @@ +include ../../../Makefile.defs + H=@ REQUIRES = unix str helm-grafite_parser @@ -8,6 +10,9 @@ CLEAN = v8Parser.ml v8Parser.mli v8Lexer.ml PACKAGES = CoRN +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) @@ -25,11 +30,11 @@ all: transcript .depend opt: transcript.opt $(EXTRAS) .depend.opt #echo -n -transcript: $(CMIS) $(CMOS) $(EXTRAS) +transcript: $(CMIS) $(CMOS) $(EXTRAS) $(LIBRARIES) @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 $@ $(CMXS) @@ -80,14 +85,22 @@ depend.opt: .depend.opt include ../../../Makefile.defs -ifeq ($(MAKECMDGOALS), opt) - include .depend.opt +ifeq ($(MAKECMDGOALS),) + include .depend endif ifeq ($(MAKECMDGOALS), all) include .depend endif -ifeq ($(MAKECMDGOALS),) +ifeq ($(MAKECMDGOALS), opt) + include .depend.opt +endif + +ifeq ($(MAKECMDGOALS), test) include .depend endif + +ifeq ($(MAKECMDGOALS), test.opt) + include .depend.opt +endif diff --git a/components/binaries/transcript/engine.ml b/components/binaries/transcript/engine.ml index e0d62a8cb..8908897dd 100644 --- a/components/binaries/transcript/engine.ml +++ b/components/binaries/transcript/engine.ml @@ -131,6 +131,9 @@ let set_baseuri st name = 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 @@ -145,17 +148,25 @@ let commit st name = 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 = - 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 - 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; @@ -170,7 +181,8 @@ let produce st = 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 diff --git a/components/binaries/transcript/grafite.ml b/components/binaries/transcript/grafite.ml index 374d3bda6..86a95270a 100644 --- a/components/binaries/transcript/grafite.ml +++ b/components/binaries/transcript/grafite.ml @@ -25,6 +25,7 @@ module T = Types +module UM = UriManager module NP = CicNotationPp module GP = GrafiteAstPp module G = GrafiteAst @@ -77,6 +78,9 @@ let set key value = 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)) @@ -84,11 +88,11 @@ let commit och items = 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.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 diff --git a/components/binaries/transcript/v8Parser.mly b/components/binaries/transcript/v8Parser.mly index 7fd69615d..61413e7fe 100644 --- a/components/binaries/transcript/v8Parser.mly +++ b/components/binaries/transcript/v8Parser.mly @@ -91,7 +91,6 @@ id: ID spcs { $1 ^ $2 }; coerc: COERC spcs { $1 ^ $2 }; - idents: | ident { [$1] } | ident idents { $1 :: $2 } @@ -189,8 +188,10 @@ | 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)] } ; fields: | field { $1 } @@ -256,7 +257,7 @@ | 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 diff --git a/components/grafite/grafiteAstPp.ml b/components/grafite/grafiteAstPp.ml index 13a4690dd..d064ef619 100644 --- a/components/grafite/grafiteAstPp.ml +++ b/components/grafite/grafiteAstPp.ml @@ -203,7 +203,7 @@ let pp_macro ~term_pp = (* 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" @@ -222,7 +222,7 @@ let pp_default what uris = (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 diff --git a/matita/contribs/CoRN-Decl/CoRN.ma b/matita/contribs/CoRN-Decl/CoRN.ma index 45e4664b5..fe83e449b 100644 --- a/matita/contribs/CoRN-Decl/CoRN.ma +++ b/matita/contribs/CoRN-Decl/CoRN.ma @@ -30,28 +30,8 @@ Notation Proj1 := (proj1 (B:=_)). Notation Proj2 := (proj2 (B:=_)). *) -(* COERCION -Z_of_nat -*) - -(* From algebra/CAbGroups *************************************************) - -(* COERCION -cag_crr -*) - -(* From algebra/CAbMonoids ************************************************) - -(* COERCION -cam_crr -*) - (* From algebra/CFields ***************************************************) -(* COERCION -cf_crr -*) - (* NOTATION Notation "x [/] y [//] Hy" := (cf_div x y Hy) (at level 80). *) @@ -66,10 +46,6 @@ Infix "{/}" := Fdiv (at level 41, no associativity). (* From algebra/CGroups ***************************************************) -(* COERCION -cg_crr -*) - (* NOTATION Notation "[--] x" := (cg_inv x) (at level 2, right associativity). *) @@ -121,10 +97,6 @@ Notation ProjT2 := (proj2_sigT _ _). (* From algebra/CMonoids **************************************************) -(* COERCION -cm_crr -*) - (* NOTATION Notation Zero := (cm_unit _). *) @@ -139,18 +111,8 @@ Notation ZeroR := (Zero:R). Notation AbsBig := (absBig _). *) -(* From algebra/COrdCauchy ************************************************) - -(* COERCION -CS_seq -*) - (* From algebra/COrdFields ************************************************) -(* COERCION -cof_crr -*) - (* NOTATION Infix "[<]" := cof_less (at level 70, no associativity). *) @@ -295,10 +257,6 @@ Notation Cpoly_cring := (cpoly_cring CR). (* From algebra/CRings ****************************************************) -(* COERCION -cr_crr -*) - (* NOTATION Notation One := (cr_one _). *) @@ -369,10 +327,6 @@ Infix "{^}" := Fnth (at level 30, right associativity). (* From algebra/CSemiGroups ***********************************************) -(* COERCION -csg_crr -*) - (* NOTATION Infix "[+]" := csg_op (at level 50, left associativity). *) @@ -387,18 +341,10 @@ Infix "{+}" := Fplus (at level 50, left associativity). Notation Conj := (conjP _). *) -(* COERCION -bpfpfun -*) - (* NOTATION Notation BDom := (bpfdom _ _). *) -(* COERCION -pfpfun -*) - (* NOTATION Notation Dom := (pfdom _). *) @@ -429,10 +375,6 @@ Notation Prj2 := (prj2 _ _ _ _). (* From algebra/CSetoids **************************************************) -(* COERCION -cs_crr -*) - (* NOTATION Infix "[=]" := cs_eq (at level 70, no associativity). *) @@ -445,52 +387,8 @@ Infix "[#]" := cs_ap (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 **********************************************) -(* COERCION -vs_vs -*) - (* NOTATION Infix "[']" := vs_op (at level 30, no associativity). *) @@ -511,22 +409,6 @@ Notation CCX := (cpoly_cring CC). 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 @@ -539,18 +421,6 @@ Notation "[-S-] F" := (Fprim F) (at level 20). Notation Integral := (integral _ _ Hab). *) -(* From ftc/MoreIntervals *************************************************) - -(* COERCION -iprop -*) - -(* From ftc/Partitions ****************************************************) - -(* COERCION -Pts -*) - (* From ftc/RefLemma ******************************************************) (* NOTATION @@ -625,18 +495,8 @@ Notation B := (Build_subcsetoid_crr IR _ _ TL_compact_b). Infix "**" := prodT (at level 20). *) -(* From metrics/CMetricSpaces *********************************************) - -(* COERCION -scms_crr -*) - (* From metrics/CPseudoMSpaces ********************************************) -(* COERCION -cms_crr -*) - (* NOTATION Infix "[-d]" := cms_d (at level 68, left associativity). *) @@ -673,20 +533,12 @@ Infix "{*Q}" := Qmult (no associativity, at level 80). 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). *) -(* COERCION -Zpos -*) - (* From reals/Bridges_LUB *************************************************) (* NOTATION @@ -695,24 +547,10 @@ Notation "( p , q )" := (pairT p q). (* From reals/CMetricFields ***********************************************) -(* COERCION -cmf_crr -*) - (* NOTATION Notation MAbs := (cmf_abs _). *) -(* COERCION -MCS_seq -*) - -(* From reals/CReals ******************************************************) - -(* COERCION -crl_crr -*) - (* From reals/CauchySeq ***************************************************) (* NOTATION @@ -753,26 +591,10 @@ Notation FRestr := (Frestr (compact_wd _ _ _)). (* From reals/Q_dense *****************************************************) -(* COERCION -pair_crr -*) - (* 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 @@ -801,13 +623,3 @@ Notation "x [!] y [//] Hy" := (power x y Hy) (at level 20). Notation "F {!} G" := (FPower F G) (at level 20). *) -(* From devel/loeb/per/lst2fun ********************************************) - -(* COERCION -F_crr -*) - -(* COERCION -to_nat -*) - diff --git a/matita/contribs/CoRN-Decl/algebra/Basics.ma b/matita/contribs/CoRN-Decl/algebra/Basics.ma index 8794b52cc..22f1f819a 100644 --- a/matita/contribs/CoRN-Decl/algebra/Basics.ma +++ b/matita/contribs/CoRN-Decl/algebra/Basics.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/Basics". +include "CoRN.ma". + (* $Id: Basics.v,v 1.7 2004/04/09 15:58:31 lcf Exp $ *) (*#* printing alpha %\ensuremath{\alpha}% #α# *) @@ -36,50 +38,32 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/Basics". (*#* printing Z %\ensuremath{\mathbb Z}% #Z# *) -(* 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. *) -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 *) -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. *) -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 *) @@ -125,9 +109,9 @@ Intros. Right. Reflexivity. Qed. *) -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". (* begin hide *) @@ -148,33 +132,35 @@ coercion. *) (* begin hide *) +coercion "cic:/matita/CoRN-Decl/algebra/Basics/Z_of_nat.con" 0 (* compounds *). + (* end hide *) -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". (* begin hide *) @@ -188,7 +174,7 @@ Unset Strict Implicit. (* end hide *) -inline cic:/CoRN/algebra/Basics/caseZ_diff.con. +inline "cic:/CoRN/algebra/Basics/caseZ_diff.con". (* begin hide *) @@ -202,37 +188,37 @@ Unset Implicit Arguments. (* end hide *) -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. *) -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 *) -inline cic:/CoRN/algebra/Basics/Acc.ind. +inline "cic:/CoRN/algebra/Basics/Acc.ind". (* UNEXPORTED End Well_foundedT. @@ -242,9 +228,9 @@ End Well_foundedT. Section AccT. *) -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". (* UNEXPORTED End AccT. @@ -258,29 +244,29 @@ Implicit Arguments Acc [A]. Section IndT. *) -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. *) -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. *) -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". (* UNEXPORTED End IndT. @@ -290,15 +276,15 @@ End IndT. Section InductionT. *) -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. @@ -308,7 +294,7 @@ End InductionT. Section InductionTT. *) -inline cic:/CoRN/algebra/Basics/lt_wf_rect.con. +inline "cic:/CoRN/algebra/Basics/lt_wf_rect.con". (* UNEXPORTED End InductionTT. diff --git a/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma b/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma index b137c572c..01031bca9 100644 --- a/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma +++ b/matita/contribs/CoRN-Decl/algebra/CAbGroups.ma @@ -16,9 +16,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CAbGroups". -(* INCLUDE -CGroups -*) +include "CoRN.ma". + +include "algebra/CGroups.ma". (* UNEXPORTED Section Abelian_Groups. @@ -29,26 +29,28 @@ Section Abelian_Groups. 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. *) -inline cic:/CoRN/algebra/CAbGroups/G.var. +inline "cic:/CoRN/algebra/CAbGroups/G.var". (*#* %\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. @@ -62,15 +64,15 @@ Section SubCAbGroups. ** 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}% @@ -79,11 +81,11 @@ that contains [Zero] and is closed under [[+]] and [[--]]. %\end{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. @@ -101,28 +103,28 @@ Section Various. 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}% *) -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. *) -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. @@ -161,11 +163,11 @@ as a left unit, and a unary setoid 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}% @@ -177,35 +179,35 @@ for [plus] and [(inv x)] is a right-inverse of [x] w.r.t.%\% [plus]. %\end{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. @@ -220,29 +222,29 @@ For reflection the following is needed; hopefully it is also useful. Section Group_Extras. *) -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. *) -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. @@ -260,27 +262,27 @@ auto with zarith. Qed. *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/CAbMonoids.ma b/matita/contribs/CoRN-Decl/algebra/CAbMonoids.ma index 8b671e37f..b7a5cda21 100644 --- a/matita/contribs/CoRN-Decl/algebra/CAbMonoids.ma +++ b/matita/contribs/CoRN-Decl/algebra/CAbMonoids.ma @@ -16,9 +16,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CAbMonoids". -(* INCLUDE -CMonoids -*) +include "CoRN.ma". + +include "algebra/CMonoids.ma". (* UNEXPORTED Section Abelian_Monoids. @@ -29,26 +29,28 @@ Section Abelian_Monoids. 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. *) -inline cic:/CoRN/algebra/CAbMonoids/M.var. +inline "cic:/CoRN/algebra/CAbMonoids/M.var". (*#* %\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. @@ -62,13 +64,13 @@ Section SubCAbMonoids. ** 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}% @@ -77,11 +79,11 @@ that contains [Zero] and is closed under [[+]] and [[--]]. %\end{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. diff --git a/matita/contribs/CoRN-Decl/algebra/CFields.ma b/matita/contribs/CoRN-Decl/algebra/CFields.ma index 606136603..05377cd11 100644 --- a/matita/contribs/CoRN-Decl/algebra/CFields.ma +++ b/matita/contribs/CoRN-Decl/algebra/CFields.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CFields". +include "CoRN.ma". + (* $Id: CFields.v,v 1.12 2004/04/23 10:00:52 lcf Exp $ *) (*#* printing [/] %\ensuremath{/}% #/# *) @@ -28,9 +30,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CFields". (*#* printing [/]?[//] %\ensuremath{/?\ddagger}% #/?‡# *) -(* INCLUDE -CRings -*) +include "algebra/CRings.ma". (* UNEXPORTED Transparent sym_eq. @@ -121,15 +121,17 @@ Transparent nexp_op. ** 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 *). (* End_SpecReals *) -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]. @@ -141,7 +143,7 @@ multiplication and the reciprocal. [x[/]y] is only defined if 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]. @@ -182,11 +184,11 @@ write [e[/] (Snring n)] and [e[/]TwoNZ], [e[/]ThreeNZ] and so on. Section Field_axioms. *) -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. @@ -201,17 +203,17 @@ Section Field_basics. %\end{convention}% *) -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. *) -inline cic:/CoRN/algebra/CFields/field_mult_inv_op.con. +inline "cic:/CoRN/algebra/CFields/field_mult_inv_op.con". (* UNEXPORTED End Field_basics. @@ -231,29 +233,29 @@ Section Field_multiplication. %\end{convention}% *) -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. @@ -263,9 +265,9 @@ End Field_multiplication. Section x_square. *) -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. @@ -285,17 +287,17 @@ Section Rcpcl_properties. %\end{convention}% *) -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. @@ -311,19 +313,19 @@ Section MultipGroup. %\end{convention}% *) -inline cic:/CoRN/algebra/CFields/F.var. +inline "cic:/CoRN/algebra/CFields/F.var". (*#* 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. @@ -344,40 +346,40 @@ In the names of lemmas, we denote [[/]] by [div], and %\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. *) -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. *) -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#. *) -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. *) -inline cic:/CoRN/algebra/CFields/div_wd.con. +inline "cic:/CoRN/algebra/CFields/div_wd.con". (* UNEXPORTED Hint Resolve div_wd: algebra_c. @@ -388,39 +390,39 @@ The next lemma says $\frac{\frac{x}{y}}{z} = \frac{x}{y\cdot z}$ #[(x/y)/z = x/(y.z)]# *) -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]# *) -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)]# *) -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. *) -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. @@ -442,15 +444,15 @@ Hint Resolve div_1 div_1' div_1'' div_wd x_div_x x_div_one div_div div_div2 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. @@ -474,17 +476,17 @@ Let [X] be a Field and [F,G:(PartFunct X)] have domains respectively %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) @@ -496,15 +498,15 @@ Section Part_Function_Recip. 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. @@ -518,15 +520,15 @@ Section Part_Function_Div. 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. @@ -537,17 +539,17 @@ End Part_Function_Div. %\end{convention}% *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/CGroups.ma b/matita/contribs/CoRN-Decl/algebra/CGroups.ma index d13953b41..76804f360 100644 --- a/matita/contribs/CoRN-Decl/algebra/CGroups.ma +++ b/matita/contribs/CoRN-Decl/algebra/CGroups.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CGroups". +include "CoRN.ma". + (* $Id: CGroups.v,v 1.9 2004/04/23 10:00:52 lcf Exp $ *) (*#* printing [-] %\ensuremath-% #−# *) @@ -26,9 +28,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CGroups". (*#* printing {--} %\ensuremath-% #−# *) -(* INCLUDE -CMonoids -*) +include "algebra/CMonoids.ma". (* Begin_SpecReals *) @@ -37,15 +37,17 @@ CMonoids ** 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]. *) -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 *). (* End_SpecReals *) @@ -55,7 +57,7 @@ inline cic:/CoRN/algebra/CGroups/CGroup.ind. Implicit Arguments cg_inv [c]. *) -inline cic:/CoRN/algebra/CGroups/cg_minus.con. +inline "cic:/CoRN/algebra/CGroups/cg_minus.con". (*#* %\begin{nameconvention}% @@ -80,9 +82,9 @@ Implicit Arguments cg_minus [G]. 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. @@ -99,76 +101,76 @@ General properties of groups. 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. *) -inline cic:/CoRN/algebra/CGroups/cg_inverse'.con. +inline "cic:/CoRN/algebra/CGroups/cg_inverse'.con". (* Hints for Auto *) -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. *) -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. *) -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. *) -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. *) -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. *) -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. *) -inline cic:/CoRN/algebra/CGroups/x_minus_x.con. +inline "cic:/CoRN/algebra/CGroups/x_minus_x.con". (*#* ** Sub-groups @@ -181,21 +183,21 @@ inline cic:/CoRN/algebra/CGroups/x_minus_x.con. Section SubCGroups. *) -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. @@ -231,15 +233,15 @@ Hint Resolve cg_minus_wd: algebra_c. 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. @@ -261,29 +263,29 @@ Specific properties of 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. @@ -312,17 +314,17 @@ by [P] and [Q]. %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) @@ -330,9 +332,9 @@ inline cic:/CoRN/algebra/CGroups/Q.con. 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. @@ -342,9 +344,9 @@ End Part_Function_Inv. 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. @@ -355,17 +357,17 @@ End Part_Function_Minus. %\end{convention}% *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/CLogic.ma b/matita/contribs/CoRN-Decl/algebra/CLogic.ma index 73f7f812a..a2be35c23 100644 --- a/matita/contribs/CoRN-Decl/algebra/CLogic.ma +++ b/matita/contribs/CoRN-Decl/algebra/CLogic.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CLogic". +include "CoRN.ma". + (* $Id: CLogic.v,v 1.10 2004/04/09 15:58:31 lcf Exp $ *) (*#* printing Not %\ensuremath\neg% #~# *) @@ -36,29 +38,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CLogic". (*#* 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 @@ -98,7 +78,7 @@ propositions, such as [(le m n)], we have to introduce a [CProp]-valued version. *) -inline cic:/CoRN/algebra/CLogic/CProp.con. +inline "cic:/CoRN/algebra/CLogic/CProp.con". (* UNEXPORTED Section Basics. @@ -109,53 +89,53 @@ Here we treat conversion from [Prop] to [CProp] and vice versa, 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.*) -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. @@ -177,9 +157,9 @@ End Basics. (* end hide *) -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". (* begin hide *) @@ -214,9 +194,9 @@ Section Choice. 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. @@ -230,9 +210,9 @@ Section Logical_Remarks. 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. @@ -249,19 +229,19 @@ Similar to Relations.v in Coq's standard library. %\end{convention}% *) -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. @@ -278,25 +258,25 @@ Analogous. %\end{convention}% *) -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. *) -inline cic:/CoRN/algebra/CLogic/eqs.ind. +inline "cic:/CoRN/algebra/CLogic/eqs.ind". (* UNEXPORTED Section le_odd. @@ -305,45 +285,45 @@ Section le_odd. (*#* ** 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. *) -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. @@ -356,17 +336,17 @@ Section Misc. (*#* **Miscellaneous *) -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". (* UNEXPORTED End Misc. @@ -381,9 +361,9 @@ write them in that form but we will single out the preservation of the setoid equality. *) -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]. @@ -403,14 +383,14 @@ We begin by proving that this case distinction is decidable. 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. *) -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. @@ -436,27 +416,27 @@ definitions. Giving a name to these results allows us to use them in 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. @@ -464,7 +444,7 @@ inline cic:/CoRN/algebra/CLogic/plus_pred_pred_plus.con. %\end{convention}% *) -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)] @@ -472,17 +452,17 @@ for every natural number [n] then [h] is monotonous. An analogous result 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: *) -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]. *) -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 @@ -491,9 +471,9 @@ natural number [n] there is an [i] such that [h(i) <= n<(n+1) <= h(i+1)]. 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. @@ -503,7 +483,7 @@ End Natural_Numbers. 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. @@ -517,23 +497,23 @@ for [CProp]- and [Prop]-valued predicates. We begin by presenting the 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. *) -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. @@ -547,13 +527,13 @@ Section Predicates_to_Prop. completeness's sake. *) -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. @@ -572,41 +552,41 @@ Tactic Notation "ElimCompare" constr(c) constr(d) := elim_compare c d. (* end hide *) -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. *) -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". diff --git a/matita/contribs/CoRN-Decl/algebra/CMonoids.ma b/matita/contribs/CoRN-Decl/algebra/CMonoids.ma index 2d93e1651..0b8b3ef64 100644 --- a/matita/contribs/CoRN-Decl/algebra/CMonoids.ma +++ b/matita/contribs/CoRN-Decl/algebra/CMonoids.ma @@ -16,13 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CMonoids". +include "CoRN.ma". + (* $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". (* Begin_SpecReals *) @@ -31,11 +31,11 @@ CSemiGroups ** Definition of monoids *) -inline cic:/CoRN/algebra/CMonoids/is_rht_unit.con. +inline "cic:/CoRN/algebra/CMonoids/is_rht_unit.con". (* End_SpecReals *) -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]. @@ -47,9 +47,11 @@ Implicit Arguments is_lft_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}% @@ -68,7 +70,7 @@ In lemmas we will continue to write [x [#] Zero], rather than e.g. for the setoid of non-zeros. *) -inline cic:/CoRN/algebra/CMonoids/nonZeroP.con. +inline "cic:/CoRN/algebra/CMonoids/nonZeroP.con". (* End_SpecReals *) @@ -86,13 +88,13 @@ Implicit Arguments nonZeroP [M]. 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. @@ -108,19 +110,19 @@ End CMonoid_axioms. 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. *) -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". (* Begin_SpecReals *) @@ -128,7 +130,7 @@ inline cic:/CoRN/algebra/CMonoids/cm_unit_unique_rht.con. 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". (* End_SpecReals *) @@ -143,17 +145,17 @@ Let [P] a predicate on [M] containing [Zero] and closed under [[+]]. Section SubCMonoids. *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/COrdAbs.ma b/matita/contribs/CoRN-Decl/algebra/COrdAbs.ma index b779a5716..3de0c3fd0 100644 --- a/matita/contribs/CoRN-Decl/algebra/COrdAbs.ma +++ b/matita/contribs/CoRN-Decl/algebra/COrdAbs.ma @@ -16,9 +16,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdAbs". -(* INCLUDE -COrdFields2 -*) +include "CoRN.ma". + +include "algebra/COrdFields2.ma". (*#* ** Properties of [AbsSmall] @@ -26,7 +26,7 @@ COrdFields2 (* Begin_SpecReals *) -inline cic:/CoRN/algebra/COrdAbs/AbsSmall.con. +inline "cic:/CoRN/algebra/COrdAbs/AbsSmall.con". (* UNEXPORTED Implicit Arguments AbsSmall [R]. @@ -43,15 +43,15 @@ Section AbsSmall_properties. %\end{convention}% *) -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. @@ -65,41 +65,41 @@ Declare Right Step AbsSmall_wdr_unfolded. (* end hide *) -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. @@ -115,9 +115,9 @@ Declare Right Step AbsSmall_wdr_unfolded. (*#* ** 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. @@ -128,15 +128,15 @@ Section absBig_wd_properties. %\end{convention}% *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/COrdCauchy.ma b/matita/contribs/CoRN-Decl/algebra/COrdCauchy.ma index 37ce37a22..5f5e5091c 100644 --- a/matita/contribs/CoRN-Decl/algebra/COrdCauchy.ma +++ b/matita/contribs/CoRN-Decl/algebra/COrdCauchy.ma @@ -16,9 +16,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdCauchy". -(* INCLUDE -COrdAbs -*) +include "CoRN.ma". + +include "algebra/COrdAbs.ma". (* Begin_SpecReals *) @@ -31,7 +31,7 @@ Section OrdField_Cauchy. %\end{convention}% *) -inline cic:/CoRN/algebra/COrdCauchy/R.var. +inline "cic:/CoRN/algebra/COrdCauchy/R.var". (* begin hide *) @@ -45,7 +45,7 @@ Unset Strict Implicit. (* end hide *) -inline cic:/CoRN/algebra/COrdCauchy/Cauchy_prop.con. +inline "cic:/CoRN/algebra/COrdCauchy/Cauchy_prop.con". (* begin hide *) @@ -68,9 +68,11 @@ Implicit arguments turned off, because Coq makes a mess of it in combination with the coercions *) -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". (* End_SpecReals *) @@ -84,28 +86,28 @@ hold). %\end{convention}% *) -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}% *) -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 @@ -119,19 +121,19 @@ Let [e] be a postive element of [R] and let [N:nat] be such that from %\end{convention}% *) -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. @@ -146,13 +148,13 @@ The following lemma does not require the sequence to be Cauchy, but it fits well here anyway. *) -inline cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con. +inline "cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con". (* UNEXPORTED Section Mult_AbsSmall. *) -inline cic:/CoRN/algebra/COrdCauchy/R.var. +inline "cic:/CoRN/algebra/COrdCauchy/R.var". (*#* ** [AbsSmall] revisited @@ -160,13 +162,13 @@ inline cic:/CoRN/algebra/COrdCauchy/R.var. %\end{convention}% *) -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. @@ -176,7 +178,7 @@ End Mult_AbsSmall. Section Mult_Continuous. *) -inline cic:/CoRN/algebra/COrdCauchy/R.var. +inline "cic:/CoRN/algebra/COrdCauchy/R.var". (*#* ** Multiplication is continuous @@ -184,15 +186,15 @@ inline cic:/CoRN/algebra/COrdCauchy/R.var. %\end{convention}% *) -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. *) -inline cic:/CoRN/algebra/COrdCauchy/plus_contin.con. +inline "cic:/CoRN/algebra/COrdCauchy/plus_contin.con". (* UNEXPORTED End Mult_Continuous. @@ -212,20 +214,20 @@ characterize them in some way. %\end{convention}% *) -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). *) -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 @@ -236,45 +238,45 @@ is monotonous iff [f(i) [<] f(i+1)] for every [i]. 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. *) -inline cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con. +inline "cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con". (* UNEXPORTED End Monotonous_functions. diff --git a/matita/contribs/CoRN-Decl/algebra/COrdFields.ma b/matita/contribs/CoRN-Decl/algebra/COrdFields.ma index 69382e44f..c68ec867d 100644 --- a/matita/contribs/CoRN-Decl/algebra/COrdFields.ma +++ b/matita/contribs/CoRN-Decl/algebra/COrdFields.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdFields". +include "CoRN.ma". + (* $Id: COrdFields.v,v 1.6 2004/04/23 10:00:52 lcf Exp $ *) (*#* printing [<] %\ensuremath<% #<# *) @@ -48,9 +50,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdFields". (*#* printing FortyEightNZ %\ensuremath{\mathbf{48}}% #48# *) -(* INCLUDE -FieldReflection -*) +include "tactics/FieldReflection.ma". (* ORDERED FIELDS *) @@ -61,7 +61,7 @@ FieldReflection (* Begin_SpecReals *) -inline cic:/CoRN/algebra/COrdFields/strictorder.ind. +inline "cic:/CoRN/algebra/COrdFields/strictorder.ind". (* UNEXPORTED Implicit Arguments strictorder [A]. @@ -79,9 +79,11 @@ Implicit Arguments so_trans [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}% @@ -94,7 +96,7 @@ is written as [pos]. Implicit Arguments cof_less [c]. *) -inline cic:/CoRN/algebra/COrdFields/greater.con. +inline "cic:/CoRN/algebra/COrdFields/greater.con". (* UNEXPORTED Implicit Arguments greater [F]. @@ -106,7 +108,7 @@ Implicit Arguments greater [F]. 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}% @@ -130,29 +132,29 @@ Let [F] be a field. %\end{convention}% *) -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. @@ -181,27 +183,27 @@ Let in the rest of this section (and all subsections) %\end{convention}% *) -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. *) -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 *) -inline cic:/CoRN/algebra/COrdFields/leEq_not_eq.con. +inline "cic:/CoRN/algebra/COrdFields/leEq_not_eq.con". (* UNEXPORTED End OrdField_basics. @@ -218,13 +220,13 @@ Section Basic_Properties_of_leEq. (*#* ** 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. @@ -234,19 +236,19 @@ Declare Left Step leEq_wdl. 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. @@ -274,39 +276,35 @@ and so on. These are elements of [NonZeros], so that we can write e.g.%\% [x[/]TwoNZ]. *) -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. @@ -320,35 +318,35 @@ In the names of lemmas, we denote the numbers 0,1,2,3,4 and so on, by %\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. @@ -360,37 +358,37 @@ Section More_than_four. (*#* *** 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. @@ -416,15 +414,15 @@ Section 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. *) -inline cic:/CoRN/algebra/COrdFields/char0_OrdField.con. +inline "cic:/CoRN/algebra/COrdFields/char0_OrdField.con". (* UNEXPORTED End consequences_of_infinity. @@ -442,7 +440,7 @@ Section Properties_of_Ordering. ** 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, @@ -461,23 +459,23 @@ Section addition. *) -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. *) -inline cic:/CoRN/algebra/COrdFields/minus_resp_less.con. +inline "cic:/CoRN/algebra/COrdFields/minus_resp_less.con". (* 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 @@ -487,9 +485,9 @@ Section~\ref{section:leEq-plus-minus}%. Cancellation laws *) -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". (*#* @@ -508,31 +506,31 @@ However, it is impractical to use these in 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. *) -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. @@ -557,26 +555,26 @@ We do this to keep it easy to use such lemmas. *) -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 *) -inline cic:/CoRN/algebra/COrdFields/mult_cancel_less.con. +inline "cic:/CoRN/algebra/COrdFields/mult_cancel_less.con". (*#* Laws for shifting @@ -585,30 +583,30 @@ Laws for shifting on plus and minus.% *) -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 *) -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). @@ -619,29 +617,29 @@ Auto. Qed. *) -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. @@ -655,25 +653,25 @@ Section misc. *** 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". (* UNEXPORTED End misc. diff --git a/matita/contribs/CoRN-Decl/algebra/COrdFields2.ma b/matita/contribs/CoRN-Decl/algebra/COrdFields2.ma index 35ccf3178..7d219b154 100644 --- a/matita/contribs/CoRN-Decl/algebra/COrdFields2.ma +++ b/matita/contribs/CoRN-Decl/algebra/COrdFields2.ma @@ -16,9 +16,9 @@ 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}}% *) @@ -38,7 +38,7 @@ Section Properties_of_leEq. %\end{convention}% *) -inline cic:/CoRN/algebra/COrdFields2/R.var. +inline "cic:/CoRN/algebra/COrdFields2/R.var". (* UNEXPORTED Section addition. @@ -48,61 +48,61 @@ Section addition. *** 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. *) -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 *) -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 *) -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. @@ -118,15 +118,15 @@ Section multiplication. 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. @@ -135,40 +135,40 @@ Hint Resolve recip_resp_leEq: algebra. (*#* Cancellation properties *) -inline cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con. +inline "cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con". (*#* 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. *) -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. @@ -182,59 +182,53 @@ Section misc. *** 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. *) -inline cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con. +inline "cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con". (* UNEXPORTED End Properties_of_leEq. @@ -254,37 +248,37 @@ Section PosP_properties. %\end{convention}% *) -inline cic:/CoRN/algebra/COrdFields2/R.var. +inline "cic:/CoRN/algebra/COrdFields2/R.var". (* 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. @@ -300,7 +294,7 @@ Hint Resolve mult_resp_nonneg. %\end{convention}% *) -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]. @@ -310,13 +304,13 @@ Implicit Arguments one_div_succ [R]. 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. @@ -326,7 +320,7 @@ End One_div_succ_properties. ** Properties of [Half] *) -inline cic:/CoRN/algebra/COrdFields2/Half.con. +inline "cic:/CoRN/algebra/COrdFields2/Half.con". (* UNEXPORTED Implicit Arguments Half [R]. @@ -342,23 +336,23 @@ Let [R] be an ordered field. %\end{convention}% *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma b/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma index d6839ae40..89dccc174 100644 --- a/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma +++ b/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma @@ -16,19 +16,17 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_ApZero". +include "CoRN.ma". + (* $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 *) -inline cic:/CoRN/algebra/CPoly_ApZero/distinct1.con. +inline "cic:/CoRN/algebra/CPoly_ApZero/distinct1.con". (* UNEXPORTED Implicit Arguments distinct1 [A]. @@ -47,87 +45,83 @@ has degree at most [n]. %\end{convention}% *) -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 *) -(* 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. *) -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. *) -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. *) -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. *) -inline cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con. +inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con". (* UNEXPORTED End Poly_Representation. @@ -142,11 +136,11 @@ If we are in a field of characteristic zero, the previous result can be strengthened. *) -inline cic:/CoRN/algebra/CPoly_ApZero/R.var. +inline "cic:/CoRN/algebra/CPoly_ApZero/R.var". (* begin show *) -inline cic:/CoRN/algebra/CPoly_ApZero/H.var. +inline "cic:/CoRN/algebra/CPoly_ApZero/H.var". (* end show *) @@ -154,13 +148,13 @@ inline cic:/CoRN/algebra/CPoly_ApZero/H.var. (* end hide *) -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. *) -inline cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con. +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con". (* UNEXPORTED End Characteristic_zero. @@ -174,13 +168,13 @@ End Characteristic_zero. Section Poly_ApZero_Interval. *) -inline cic:/CoRN/algebra/CPoly_ApZero/R.var. +inline "cic:/CoRN/algebra/CPoly_ApZero/R.var". (* 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. diff --git a/matita/contribs/CoRN-Decl/algebra/CPoly_Degree.ma b/matita/contribs/CoRN-Decl/algebra/CPoly_Degree.ma index a7551f2f7..35b49ac2c 100644 --- a/matita/contribs/CoRN-Decl/algebra/CPoly_Degree.ma +++ b/matita/contribs/CoRN-Decl/algebra/CPoly_Degree.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_Degree". +include "CoRN.ma". + (* $Id: CPoly_Degree.v,v 1.5 2004/04/23 10:00:53 lcf Exp $ *) -(* INCLUDE -CPoly_NthCoeff -*) +include "algebra/CPoly_NthCoeff.ma". -(* INCLUDE -CFields -*) +include "algebra/CFields.ma". (*#* *Degrees of Polynomials ** Degrees of polynomials over a ring @@ -38,7 +36,7 @@ over [R]. Section Degree_def. *) -inline cic:/CoRN/algebra/CPoly_Degree/R.var. +inline "cic:/CoRN/algebra/CPoly_Degree/R.var". (* begin hide *) @@ -53,7 +51,7 @@ is always [1] higher than the `degree' (assuming that the highest 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 @@ -70,17 +68,17 @@ X^(n-1)#, if $p_i \mathrel{\#}0$#pi apart from 0#, we can say that the 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. @@ -106,93 +104,93 @@ Implicit Arguments lth_of_poly [R]. Section Degree_props. *) -inline cic:/CoRN/algebra/CPoly_Degree/R.var. +inline "cic:/CoRN/algebra/CPoly_Degree/R.var". (* 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. *) -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. *) -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. @@ -216,19 +214,19 @@ polynomials over [F]. %\end{convention}% *) -inline cic:/CoRN/algebra/CPoly_Degree/F.var. +inline "cic:/CoRN/algebra/CPoly_Degree/F.var". (* 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. diff --git a/matita/contribs/CoRN-Decl/algebra/CPoly_NthCoeff.ma b/matita/contribs/CoRN-Decl/algebra/CPoly_NthCoeff.ma index 4d6d18498..d34fe2075 100644 --- a/matita/contribs/CoRN-Decl/algebra/CPoly_NthCoeff.ma +++ b/matita/contribs/CoRN-Decl/algebra/CPoly_NthCoeff.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_NthCoeff". +include "CoRN.ma". + (* $Id: CPoly_NthCoeff.v,v 1.6 2004/04/23 10:00:53 lcf Exp $ *) -(* INCLUDE -CPolynomials -*) +include "algebra/CPolynomials.ma". (*#* * Polynomials: Nth Coefficient @@ -35,7 +35,7 @@ polynomials over [R]. Section NthCoeff_def. *) -inline cic:/CoRN/algebra/CPoly_NthCoeff/R.var. +inline "cic:/CoRN/algebra/CPoly_NthCoeff/R.var". (* begin hide *) @@ -48,13 +48,13 @@ polynomial $a_0 +a_1 X +a_2 X^2 + \cdots + a_n X^n$ #a0 +a1 X +a2 X^2 + ... + 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}% @@ -70,24 +70,24 @@ to [((nth_coeff_fun n) p)]. %\end{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. *) -inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con. +inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con". (* 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. *) -inline cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con. +inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con". (* UNEXPORTED End NthCoeff_def. @@ -111,72 +111,72 @@ Section NthCoeff_props. (*#* ** Properties of [nth_coeff] *) -inline cic:/CoRN/algebra/CPoly_NthCoeff/R.var. +inline "cic:/CoRN/algebra/CPoly_NthCoeff/R.var". (* 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. *) -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. *) -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. *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/CPolynomials.ma b/matita/contribs/CoRN-Decl/algebra/CPolynomials.ma index 966c8113c..d34881497 100644 --- a/matita/contribs/CoRN-Decl/algebra/CPolynomials.ma +++ b/matita/contribs/CoRN-Decl/algebra/CPolynomials.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPolynomials". +include "CoRN.ma". + (* $Id: CPolynomials.v,v 1.9 2004/04/23 10:00:53 lcf Exp $ *) (*#* printing _X_ %\ensuremath{x}% *) @@ -28,9 +30,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPolynomials". (*#* 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 @@ -50,7 +50,7 @@ Section CPoly_CRing. %\end{convention}% *) -inline cic:/CoRN/algebra/CPolynomials/CR.var. +inline "cic:/CoRN/algebra/CPolynomials/CR.var". (*#* The intuition behind the type [cpoly] is the following @@ -60,54 +60,54 @@ 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. *) -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 *) -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 @@ -119,203 +119,203 @@ the most basic properties of equality and apartness 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 *) -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 *) -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 *) -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. @@ -329,7 +329,7 @@ Implicit Arguments _C_ [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]. @@ -350,69 +350,69 @@ elements of the ring. %\end{convention}% *) -inline cic:/CoRN/algebra/CPolynomials/CR.var. +inline "cic:/CoRN/algebra/CPolynomials/CR.var". (* 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. *) -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. @@ -426,13 +426,13 @@ Transparent cpoly_cgroup. 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. @@ -462,29 +462,29 @@ Let [R] be a ring and write [RX] for the ring of polynomials over [R]. Section Poly_properties. *) -inline cic:/CoRN/algebra/CPolynomials/R.var. +inline "cic:/CoRN/algebra/CPolynomials/R.var". (*#* *** 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. *) -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. @@ -492,19 +492,19 @@ Hint Resolve cpoly_lin: algebra. (* SUPERFLUOUS *) -inline cic:/CoRN/algebra/CPolynomials/poly_linear.con. +inline "cic:/CoRN/algebra/CPolynomials/poly_linear.con". (* 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". (* SUPERFLUOUS ? *) -inline cic:/CoRN/algebra/CPolynomials/lin_mult.con. +inline "cic:/CoRN/algebra/CPolynomials/lin_mult.con". (* UNEXPORTED Hint Resolve lin_mult: algebra. @@ -513,57 +513,57 @@ Hint Resolve lin_mult: algebra. (*#* *** 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. *) -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. *) -inline cic:/CoRN/algebra/CPolynomials/mult_apply.con. +inline "cic:/CoRN/algebra/CPolynomials/mult_apply.con". (* 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. *) -inline cic:/CoRN/algebra/CPolynomials/nexp_apply.con. +inline "cic:/CoRN/algebra/CPolynomials/nexp_apply.con". (* SUPERFLUOUS *) -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. @@ -576,9 +576,9 @@ End Poly_properties. 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. diff --git a/matita/contribs/CoRN-Decl/algebra/CRings.ma b/matita/contribs/CoRN-Decl/algebra/CRings.ma index 4d23037a5..b38bc3109 100644 --- a/matita/contribs/CoRN-Decl/algebra/CRings.ma +++ b/matita/contribs/CoRN-Decl/algebra/CRings.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CRings". +include "CoRN.ma". + (* $Id: CRings.v,v 1.8 2004/04/23 10:00:53 lcf Exp $ *) (*#* printing [*] %\ensuremath\times% #×# *) @@ -52,9 +54,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CRings". (*#* printing FortyEight %\ensuremath{\mathbf{48}}% #48# *) -(* INCLUDE -CSums -*) +include "algebra/CSums.ma". (* UNEXPORTED Transparent sym_eq. @@ -73,21 +73,23 @@ We actually define commutative rings with identity. ** 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]. *) -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". (* End_SpecReals *) @@ -114,27 +116,27 @@ Section CRing_axioms. %\end{convention}% *) -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". (* End_SpecReals *) -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". (* Begin_SpecReals *) @@ -153,13 +155,13 @@ Let [R] be a ring. %\end{convention}% *) -inline cic:/CoRN/algebra/CRings/R.var. +inline "cic:/CoRN/algebra/CRings/R.var". (*#* 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. @@ -177,33 +179,33 @@ Section Ring_unfolded. %\end{convention}% *) -inline cic:/CoRN/algebra/CRings/R.var. +inline "cic:/CoRN/algebra/CRings/R.var". (* begin hide *) -inline cic:/CoRN/algebra/CRings/mmR.con. +inline "cic:/CoRN/algebra/CRings/mmR.con". (* end hide *) -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. *) -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. *) -inline cic:/CoRN/algebra/CRings/ring_distl_unfolded.con. +inline "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con". (* UNEXPORTED End Ring_unfolded. @@ -231,13 +233,13 @@ Section Ring_basics. %\end{convention}% *) -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]. @@ -247,45 +249,45 @@ Implicit Arguments is_zero_rht [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. *) -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. *) -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. *) -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. *) -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. *) -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. @@ -334,17 +336,17 @@ Let [R] be a ring. %\end{convention}% *) -inline cic:/CoRN/algebra/CRings/R.var. +inline "cic:/CoRN/algebra/CRings/R.var". (* End_SpecReals *) -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". (* Begin_SpecReals *) @@ -370,7 +372,7 @@ Section nat_injection. %\end{convention}% *) -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]. @@ -378,15 +380,15 @@ Note that this need not really be an injection; when it is, the ring is said 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". (* End_SpecReals *) -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". (* Begin_SpecReals *) @@ -408,9 +410,9 @@ Implicit Arguments nring [R]. (* End_SpecReals *) -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. @@ -420,7 +422,7 @@ Hint Resolve one_plus_one x_plus_x: algebra. 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. @@ -433,7 +435,7 @@ Let [R] be a ring. %\end{convention}% *) -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, @@ -443,27 +445,27 @@ The first definition is now obsolete, having been replaced by a more efficient 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. *) -inline cic:/CoRN/algebra/CRings/zring_old_diff.con. +inline "cic:/CoRN/algebra/CRings/zring_old_diff.con". (* 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. *) -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. @@ -473,94 +475,94 @@ Hint Resolve zring_old_inv_nat: 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. *) -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. *) -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. *) -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. *) -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. *) -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. *) -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. *) -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. *) -inline cic:/CoRN/algebra/CRings/pring_convert.con. +inline "cic:/CoRN/algebra/CRings/pring_convert.con". (* 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. *) -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. @@ -586,7 +588,7 @@ Section Ring_sums. %\end{convention}% *) -inline cic:/CoRN/algebra/CRings/R.var. +inline "cic:/CoRN/algebra/CRings/R.var". (*#* *** Infinite Ring sums @@ -596,20 +598,20 @@ inline cic:/CoRN/algebra/CRings/R.var. 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. *) -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. @@ -622,13 +624,13 @@ Section 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. @@ -649,41 +651,41 @@ Let [R] be a ring. 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. *) -inline cic:/CoRN/algebra/CRings/dist_2a.con. +inline "cic:/CoRN/algebra/CRings/dist_2a.con". (* 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. *) -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. *) -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. *) -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. @@ -705,101 +707,101 @@ Let [R] be a ring. 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. *) -inline cic:/CoRN/algebra/CRings/nexp_plus.con. +inline "cic:/CoRN/algebra/CRings/nexp_plus.con". (* 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. *) -inline cic:/CoRN/algebra/CRings/mult_nexp.con. +inline "cic:/CoRN/algebra/CRings/mult_nexp.con". (* 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. *) -inline cic:/CoRN/algebra/CRings/zero_nexp.con. +inline "cic:/CoRN/algebra/CRings/zero_nexp.con". (* 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. *) -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. *) -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. *) -inline cic:/CoRN/algebra/CRings/nexp_one.con. +inline "cic:/CoRN/algebra/CRings/nexp_one.con". (* 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. *) -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. *) -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. *) -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. *) -inline cic:/CoRN/algebra/CRings/nexp_funny'.con. +inline "cic:/CoRN/algebra/CRings/nexp_funny'.con". (* UNEXPORTED Hint Resolve nexp_funny': algebra. @@ -831,17 +833,17 @@ respectively [P] and [Q]. %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) @@ -849,9 +851,9 @@ inline cic:/CoRN/algebra/CRings/Q.con. 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. @@ -861,11 +863,11 @@ End Part_Function_Mult. 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. @@ -876,25 +878,25 @@ End Part_Function_Nth_Power. %\end{convention}% *) -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. *) -inline cic:/CoRN/algebra/CRings/Fscalmult.con. +inline "cic:/CoRN/algebra/CRings/Fscalmult.con". (* UNEXPORTED Implicit Arguments Fmult [R]. @@ -912,21 +914,21 @@ Implicit Arguments Fnth [R]. 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". (* begin hide *) -inline cic:/CoRN/algebra/CRings/P.con. +inline "cic:/CoRN/algebra/CRings/P.con". (* end hide *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/CSemiGroups.ma b/matita/contribs/CoRN-Decl/algebra/CSemiGroups.ma index 1952e7ded..d7035869f 100644 --- a/matita/contribs/CoRN-Decl/algebra/CSemiGroups.ma +++ b/matita/contribs/CoRN-Decl/algebra/CSemiGroups.ma @@ -16,15 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSemiGroups". +include "CoRN.ma". + (* $Id: CSemiGroups.v,v 1.8 2004/04/22 14:49:43 lcf Exp $ *) (*#* printing [+] %\ensuremath+% #+# *) (*#* printing {+} %\ensuremath+% #+# *) -(* INCLUDE -CSetoidInc -*) +include "algebra/CSetoidInc.ma". (* Begin_SpecReals *) @@ -33,9 +33,11 @@ CSetoidInc **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}% @@ -60,11 +62,11 @@ The axiomatic properties of a semi group. 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. @@ -83,11 +85,11 @@ Let [G] be a semi-group. Section CSemiGroup_basics. *) -inline cic:/CoRN/algebra/CSemiGroups/G.var. +inline "cic:/CoRN/algebra/CSemiGroups/G.var". (* End_SpecReals *) -inline cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con. +inline "cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con". (* UNEXPORTED End CSemiGroup_basics. @@ -115,36 +117,36 @@ At this stage, we will always consider automorphisms; we %{\em %could%}% treat t 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". (* begin hide *) -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". (* end hide *) -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}% *) -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. @@ -173,15 +175,15 @@ predicate on the semi-group which is preserved by [[+]]. 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. diff --git a/matita/contribs/CoRN-Decl/algebra/CSetoidFun.ma b/matita/contribs/CoRN-Decl/algebra/CSetoidFun.ma index d183c70e8..eb912f902 100644 --- a/matita/contribs/CoRN-Decl/algebra/CSetoidFun.ma +++ b/matita/contribs/CoRN-Decl/algebra/CSetoidFun.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSetoidFun". +include "CoRN.ma". + (* $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. @@ -32,17 +32,17 @@ Let [S1], [S2] and [S3] be setoids, [f] a 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. @@ -52,11 +52,11 @@ End unary_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. @@ -69,9 +69,9 @@ End unary_and_binary_function_composition. 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. @@ -81,13 +81,13 @@ End function_projection. Section BinProj. *) -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. @@ -102,11 +102,11 @@ End BinProj. 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 @@ -118,11 +118,11 @@ Then [opOnFun] is the composition [op] after [f]. 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. @@ -173,23 +173,23 @@ welldefinedness. %\end{convention}% *) -inline cic:/CoRN/algebra/CSetoidFun/S.var. +inline "cic:/CoRN/algebra/CSetoidFun/S.var". (* 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. @@ -199,21 +199,21 @@ End Conjunction. Section Disjunction. *) -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). *) -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. @@ -227,19 +227,19 @@ Section 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. @@ -270,7 +270,9 @@ Implicit Arguments ext2 [S P R x]. 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]. @@ -280,11 +282,13 @@ Implicit Arguments bpfpfun [S1 S2]. 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. *) -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]. @@ -294,7 +298,7 @@ Implicit Arguments pfpfun [S]. 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: @@ -348,13 +352,13 @@ Hint Resolve CI: core. Section CSetoid_Ops. *) -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. *) -inline cic:/CoRN/algebra/CSetoidFun/total_eq_part.con. +inline "cic:/CoRN/algebra/CSetoidFun/total_eq_part.con". (* UNEXPORTED Section Part_Function_Const. @@ -367,9 +371,9 @@ In any setoid we can also define constant functions (one for each element of the %\end{convention}% *) -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. @@ -379,7 +383,7 @@ End Part_Function_Const. Section Part_Function_Id. *) -inline cic:/CoRN/algebra/CSetoidFun/Fid.con. +inline "cic:/CoRN/algebra/CSetoidFun/Fid.con". (* UNEXPORTED End Part_Function_Id. @@ -398,25 +402,25 @@ If we have two setoid functions [F] and [G] we can always compose them. The dom 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". (* begin hide *) -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". (* end hide *) -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. @@ -435,31 +439,31 @@ End CSetoid_Ops. 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". (* begin hide *) -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". (* end hide *) -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. @@ -485,11 +489,11 @@ Section bijections. (*#* **Bijections *) -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]. @@ -503,43 +507,43 @@ Implicit Arguments injective_weak [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]. *) -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]. *) -inline cic:/CoRN/algebra/CSetoidFun/invfun.con. +inline "cic:/CoRN/algebra/CSetoidFun/invfun.con". (* 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]. *) -inline cic:/CoRN/algebra/CSetoidFun/Inv_bij.con. +inline "cic:/CoRN/algebra/CSetoidFun/Inv_bij.con". (* UNEXPORTED End bijections. diff --git a/matita/contribs/CoRN-Decl/algebra/CSetoidInc.ma b/matita/contribs/CoRN-Decl/algebra/CSetoidInc.ma index 899a67f42..ad6490a75 100644 --- a/matita/contribs/CoRN-Decl/algebra/CSetoidInc.ma +++ b/matita/contribs/CoRN-Decl/algebra/CSetoidInc.ma @@ -16,13 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSetoidInc". +include "CoRN.ma". + (* $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. @@ -32,35 +32,35 @@ Section inclusion. 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. *) -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. @@ -72,23 +72,23 @@ by [P] and [Q], respectively, the domains of [F] and [G]. %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/CSetoids.ma b/matita/contribs/CoRN-Decl/algebra/CSetoids.ma index 8d33471fc..03bf94508 100644 --- a/matita/contribs/CoRN-Decl/algebra/CSetoids.ma +++ b/matita/contribs/CoRN-Decl/algebra/CSetoids.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSetoids". +include "CoRN.ma". + (* $Id.v,v 1.18 2002/11/25 14:43:42 lcf Exp $ *) (*#* printing [=] %\ensuremath{\equiv}% #≡# *) @@ -37,15 +39,11 @@ Definition of a constructive setoid with apartness, i.e.%\% a set with an equivalence relation and an apartness relation compatible with it. *) -(* INCLUDE -CLogic -*) +include "algebra/CLogic.ma". -(* INCLUDE -Step -*) +include "tactics/Step.ma". -inline cic:/CoRN/algebra/CSetoids/Relation.con. +inline "cic:/CoRN/algebra/CSetoids/Relation.con". (* End_SpecReals *) @@ -98,15 +96,15 @@ Notice that their type depends on the main logical connective. 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. @@ -129,9 +127,11 @@ Unset Implicit Arguments. 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]. @@ -143,7 +143,7 @@ Implicit Arguments cs_ap [c]. (* End_SpecReals *) -inline cic:/CoRN/algebra/CSetoids/cs_neq.con. +inline "cic:/CoRN/algebra/CSetoids/cs_neq.con". (* UNEXPORTED Implicit Arguments cs_neq [S]. @@ -168,17 +168,17 @@ Let [S] be a setoid. 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. @@ -197,7 +197,7 @@ End CSetoid_axioms. Section CSetoid_basics. *) -inline cic:/CoRN/algebra/CSetoids/S.var. +inline "cic:/CoRN/algebra/CSetoids/S.var". (* End_SpecReals *) @@ -205,13 +205,13 @@ 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. *) -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}% @@ -227,23 +227,23 @@ If lemma [a] is just an unfolding of lemma [b], the name of [a] is the name %\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". (* Begin_SpecReals *) -inline cic:/CoRN/algebra/CSetoids/ap_irreflexive_unfolded.con. +inline "cic:/CoRN/algebra/CSetoids/ap_irreflexive_unfolded.con". (* End_SpecReals *) -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}% @@ -256,19 +256,19 @@ Therefore we have to split the lemma into the following two lemmas [eq_imp_not_a %\end{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". (* Begin_SpecReals *) @@ -284,13 +284,13 @@ Section product_csetoid. (*#* **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. @@ -336,7 +336,7 @@ on predicates and relations. Section CSetoid_relations_and_predicates. *) -inline cic:/CoRN/algebra/CSetoids/S.var. +inline "cic:/CoRN/algebra/CSetoids/S.var". (* End_SpecReals *) @@ -352,19 +352,21 @@ At this stage, we consider [CProp]- and [Prop]-valued predicates on setoids. 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. *) -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]. *) @@ -372,11 +374,11 @@ inline cic:/CoRN/algebra/CSetoids/csp_wd.con. 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. @@ -384,9 +386,11 @@ End CSetoidPPredicates. (*#* ***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". (* Begin_SpecReals *) @@ -399,25 +403,25 @@ Let [R] be a relation on (the carrier of) [S]. 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". (* End_SpecReals *) -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". (* Begin_SpecReals *) @@ -428,7 +432,9 @@ End CsetoidRelations. (*#* ***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}% @@ -440,25 +446,25 @@ Let [R] be a relation on (the carrier of) [S]. 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". (* End_SpecReals *) -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". (* Begin_SpecReals *) @@ -470,25 +476,27 @@ End CCsetoidRelations. 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". (* End_SpecReals *) -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". (* Begin_SpecReals *) @@ -523,11 +531,11 @@ First we consider unary 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. @@ -538,15 +546,15 @@ In the following two definitions, [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". (* End_SpecReals *) -inline cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con. +inline "cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con". (* Begin_SpecReals *) @@ -554,13 +562,15 @@ inline cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con. End unary_functions. *) -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". (* End_SpecReals *) -inline cic:/CoRN/algebra/CSetoids/Const_CSetoid_fun.con. +inline "cic:/CoRN/algebra/CSetoids/Const_CSetoid_fun.con". (* Begin_SpecReals *) @@ -574,15 +584,15 @@ In the following two definitions, [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". (* End_SpecReals *) -inline cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con. +inline "cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con". (* Begin_SpecReals *) @@ -590,15 +600,17 @@ inline cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con. End binary_functions. *) -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. @@ -637,87 +649,91 @@ Let [S] be a setoid. Section csetoid_inner_ops. *) -inline cic:/CoRN/algebra/CSetoids/S.var. +inline "cic:/CoRN/algebra/CSetoids/S.var". (*#* 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. *) -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". (* End_SpecReals *) -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". (* begin hide *) +coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/un_op_fun.con" 0 (* compounds *). + (* end hide *) (* Begin_SpecReals *) -inline cic:/CoRN/algebra/CSetoids/cs_un_op_strext.con. +inline "cic:/CoRN/algebra/CSetoids/cs_un_op_strext.con". (* End_SpecReals *) -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. *) -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". (* Begin_SpecReals *) -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". (* End_SpecReals *) -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 *) +coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/bin_op_bin_fun.con" 0 (* compounds *). + (* 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". (* Begin_SpecReals *) @@ -753,31 +769,33 @@ Let [S1] and [S2] be setoids. 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. *) -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". (* begin hide *) +coercion "cic:/matita/CoRN-Decl/algebra/CSetoids/outer_op_bin_fun.con" 0 (* compounds *). + (* end hide *) -inline cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con. +inline "cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con". (* UNEXPORTED End csetoid_outer_ops. @@ -799,34 +817,36 @@ Let [S] be a setoid, and [P] a predicate on the carrier of [S]. Section SubCSetoids. *) -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. *) -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". (* End_SpecReals *) -inline cic:/CoRN/algebra/CSetoids/subcsetoid_equiv.con. +inline "cic:/CoRN/algebra/CSetoids/subcsetoid_equiv.con". (* Begin_SpecReals *) -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". (* End_SpecReals *) @@ -840,24 +860,24 @@ Let [f] be a unary setoid operation on [S]. 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}% *) -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. @@ -873,9 +893,9 @@ Let [f] be a binary setoid operation on [S]. 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}% @@ -883,17 +903,17 @@ Assume [bin_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_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. @@ -922,15 +942,15 @@ Tactic Notation "Step_final" constr(c) := Step_final c. (*#* **Miscellaneous *) -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. *) -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]. diff --git a/matita/contribs/CoRN-Decl/algebra/CSums.ma b/matita/contribs/CoRN-Decl/algebra/CSums.ma index 0177138c7..b0fc1c6a2 100644 --- a/matita/contribs/CoRN-Decl/algebra/CSums.ma +++ b/matita/contribs/CoRN-Decl/algebra/CSums.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSums". +include "CoRN.ma". + (* $Id: CSums.v,v 1.8 2004/04/23 10:00:54 lcf Exp $ *) (*#* printing Sum0 %\ensuremath{\sum_0}% #∑0# *) @@ -28,13 +30,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSums". (*#* printing Sumx %\ensuremath{\sum'}% #∑'&*) -(* INCLUDE -CAbGroups -*) - -(* INCLUDE -Peano_dec -*) +include "algebra/CAbGroups.ma". (*#* * Sums @@ -46,13 +42,13 @@ Peano_dec Section Sums. *) -inline cic:/CoRN/algebra/CSums/G.var. +inline "cic:/CoRN/algebra/CSums/G.var". (* 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 $\{0,\ldots,i-1\}$ @@ -60,137 +56,137 @@ 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]. *) -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)] *) -inline cic:/CoRN/algebra/CSums/Sum0.con. +inline "cic:/CoRN/algebra/CSums/Sum0.con". (*#* [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. *) -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. *) -inline cic:/CoRN/algebra/CSums/Sum_empty.con. +inline "cic:/CoRN/algebra/CSums/Sum_empty.con". (* 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. *) -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. *) -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. *) -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. *) -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. *) -inline cic:/CoRN/algebra/CSums/inv_Sum.con. +inline "cic:/CoRN/algebra/CSums/inv_Sum.con". (* 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. *) -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. *) -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". (* UNEXPORTED End Sums. @@ -223,15 +219,15 @@ often referred to as ``Mengolli Sums''. Section More_Sums. *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/CVectorSpace.ma b/matita/contribs/CoRN-Decl/algebra/CVectorSpace.ma index e10b4867a..afaa471d2 100644 --- a/matita/contribs/CoRN-Decl/algebra/CVectorSpace.ma +++ b/matita/contribs/CoRN-Decl/algebra/CVectorSpace.ma @@ -16,13 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/CVectorSpace". +include "CoRN.ma". + (* $Id: CVectorSpace.v,v 1.4 2004/04/23 10:00:54 lcf Exp $ *) (*#* printing ['] %{'}% #'# *) -(* INCLUDE -CFields -*) +include "algebra/CFields.ma". (*#* * Vector Spaces @@ -42,7 +42,9 @@ Unset Strict Implicit. (* end hide *) -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 *). (* begin hide *) @@ -74,43 +76,43 @@ Let [F] be a fiels and let [V] be a vector space over [F] Section VS_basics. *) -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. *) -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. *) -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. *) -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 *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/Cauchy_COF.ma b/matita/contribs/CoRN-Decl/algebra/Cauchy_COF.ma index f2ee13a49..7070c44d8 100644 --- a/matita/contribs/CoRN-Decl/algebra/Cauchy_COF.ma +++ b/matita/contribs/CoRN-Decl/algebra/Cauchy_COF.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/Cauchy_COF". +include "CoRN.ma". + (* $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 @@ -40,7 +38,7 @@ field [F], we can define a new ordered field of Cauchy sequences over [F]. Section Structure. *) -inline cic:/CoRN/algebra/Cauchy_COF/F.var. +inline "cic:/CoRN/algebra/Cauchy_COF/F.var". (*#* ** Setoid Structure @@ -52,31 +50,31 @@ onwards [(y n) [-] (x n)] is greater than some fixed, positive 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. *) -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. @@ -92,27 +90,27 @@ The group structure is just the expected one; the lemmas which 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. @@ -126,35 +124,35 @@ Section Ring_Structure. 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. @@ -170,17 +168,17 @@ that our ring is actually an integral domain. The rest then follows 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. @@ -195,19 +193,19 @@ Finally, we extend the field structure with the ordering we 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". (* UNEXPORTED End Order. @@ -222,19 +220,19 @@ Auxiliary characterizations of the main relations on [R_Set]. Section Auxiliary. *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/Expon.ma b/matita/contribs/CoRN-Decl/algebra/Expon.ma index 2b1085a7c..4a6ea69c3 100644 --- a/matita/contribs/CoRN-Decl/algebra/Expon.ma +++ b/matita/contribs/CoRN-Decl/algebra/Expon.ma @@ -16,21 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/Expon". +include "CoRN.ma". + (* $Id: Expon.v,v 1.5 2004/04/23 10:00:54 lcf Exp $ *) (*#* printing [^^] %\ensuremath{\hat{\ }}% #^# *) -(* INCLUDE -Arith -*) +include "algebra/COrdCauchy.ma". -(* INCLUDE -COrdCauchy -*) - -(* INCLUDE -Transparent_algebra -*) +include "tactics/Transparent_algebra.ma". (*#* *Exponentiation **More properties about [nexp] @@ -42,47 +36,47 @@ Transparent_algebra Section More_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. *) -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. *) -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. @@ -105,14 +99,14 @@ Implicit Arguments nexp_resp_ap_zero [R x]. Section Zexp_def. *) -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. *) -inline cic:/CoRN/algebra/Expon/zexp.con. +inline "cic:/CoRN/algebra/Expon/zexp.con". (* UNEXPORTED End Zexp_def. @@ -131,133 +125,133 @@ Implicit Arguments zexp [R]. 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. *) -inline cic:/CoRN/algebra/Expon/zexp_nexp.con. +inline "cic:/CoRN/algebra/Expon/zexp_nexp.con". (* 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. *) -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. *) -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. *) -inline cic:/CoRN/algebra/Expon/zexp_plus1.con. +inline "cic:/CoRN/algebra/Expon/zexp_plus1.con". (* 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. *) -inline cic:/CoRN/algebra/Expon/zexp_inv.con. +inline "cic:/CoRN/algebra/Expon/zexp_inv.con". (* 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. *) -inline cic:/CoRN/algebra/Expon/zexp_plus.con. +inline "cic:/CoRN/algebra/Expon/zexp_plus.con". (* 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. *) -inline cic:/CoRN/algebra/Expon/one_zexp.con. +inline "cic:/CoRN/algebra/Expon/one_zexp.con". (* 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. *) -inline cic:/CoRN/algebra/Expon/zexp_mult.con. +inline "cic:/CoRN/algebra/Expon/zexp_mult.con". (* 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. *) -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. *) -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. *) -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. *) -inline cic:/CoRN/algebra/Expon/zexp_funny.con. +inline "cic:/CoRN/algebra/Expon/zexp_funny.con". (* 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. *) -inline cic:/CoRN/algebra/Expon/zexp_pos.con. +inline "cic:/CoRN/algebra/Expon/zexp_pos.con". (* UNEXPORTED End Zexp_properties. @@ -278,11 +272,11 @@ Hint Resolve zexp_wd: algebra_c. Section Root_Unique. *) -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. diff --git a/matita/contribs/CoRN-Decl/algebra/ListType.ma b/matita/contribs/CoRN-Decl/algebra/ListType.ma index 004ba5565..1decb2491 100644 --- a/matita/contribs/CoRN-Decl/algebra/ListType.ma +++ b/matita/contribs/CoRN-Decl/algebra/ListType.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/algebra/ListType". +include "CoRN.ma". + (* begin hide *) (*#**********************************************************************) @@ -48,41 +50,37 @@ This file contains a variant of the development of lists in the standard library of Coq but moved to the Type level. *) -(* INCLUDE -Le -*) - (* 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. *) -inline cic:/CoRN/algebra/ListType/app_ass.con. +inline "cic:/CoRN/algebra/ListType/app_ass.con". (* 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. *) -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". (*#***************************************) @@ -90,7 +88,7 @@ inline cic:/CoRN/algebra/ListType/nil_cons.con. (*#***************************************) -inline cic:/CoRN/algebra/ListType/length.con. +inline "cic:/CoRN/algebra/ListType/length.con". (*#*****************************) @@ -102,33 +100,33 @@ inline cic:/CoRN/algebra/ListType/length.con. Section length_order. *) -inline cic:/CoRN/algebra/ListType/lel.con. +inline "cic:/CoRN/algebra/ListType/lel.con". (* 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. @@ -139,71 +137,71 @@ Hint Resolve lel_refl lel_cons_cons lel_cons lel_nil lel_nil nil_cons: list v62. *) -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. *) -inline cic:/CoRN/algebra/ListType/in_cons.con. +inline "cic:/CoRN/algebra/ListType/in_cons.con". (* 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. *) -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. *) -inline cic:/CoRN/algebra/ListType/incl.con. +inline "cic:/CoRN/algebra/ListType/incl.con". (* 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. *) -inline cic:/CoRN/algebra/ListType/incl_tl.con. +inline "cic:/CoRN/algebra/ListType/incl_tl.con". (* 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. *) -inline cic:/CoRN/algebra/ListType/incl_appr.con. +inline "cic:/CoRN/algebra/ListType/incl_appr.con". (* 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. *) -inline cic:/CoRN/algebra/ListType/incl_app.con. +inline "cic:/CoRN/algebra/ListType/incl_app.con". (* UNEXPORTED End List. @@ -225,13 +223,13 @@ Implicit Arguments cons [A]. Section Map. *) -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". (* UNEXPORTED End Map. diff --git a/matita/contribs/CoRN-Decl/complex/AbsCC.ma b/matita/contribs/CoRN-Decl/complex/AbsCC.ma index 8e4f5d578..e2d902b9b 100644 --- a/matita/contribs/CoRN-Decl/complex/AbsCC.ma +++ b/matita/contribs/CoRN-Decl/complex/AbsCC.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/complex/AbsCC". +include "CoRN.ma". + (* $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] *) @@ -29,61 +29,61 @@ CComplex 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. *) -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. *) -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. *) -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. *) -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. *) -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". (* begin hide *) -inline cic:/CoRN/complex/AbsCC/l_1_1_2.con. +inline "cic:/CoRN/complex/AbsCC/l_1_1_2.con". (* end hide *) @@ -91,7 +91,7 @@ inline cic:/CoRN/complex/AbsCC/l_1_1_2.con. 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. @@ -99,7 +99,7 @@ Hint Resolve AbsCC_square_Re_Im: algebra. (* begin hide *) -inline cic:/CoRN/complex/AbsCC/l_1_2_3_CC.con. +inline "cic:/CoRN/complex/AbsCC/l_1_2_3_CC.con". (* end hide *) @@ -107,7 +107,7 @@ inline cic:/CoRN/complex/AbsCC/l_1_2_3_CC.con. 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. @@ -115,7 +115,7 @@ Hint Resolve CC_conj_mult: algebra. (* begin hide *) -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. @@ -123,27 +123,27 @@ Hint Resolve l_2_1_2: algebra. (* end hide *) -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 *) -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". (* end hide *) @@ -163,7 +163,7 @@ Hint Resolve cc_inv_abs cc_mult_abs cc_div_abs cc_div_abs' cc_pow_abs (*#* ** 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". diff --git a/matita/contribs/CoRN-Decl/complex/CComplex.ma b/matita/contribs/CoRN-Decl/complex/CComplex.ma index 084598506..6cf6aa340 100644 --- a/matita/contribs/CoRN-Decl/complex/CComplex.ma +++ b/matita/contribs/CoRN-Decl/complex/CComplex.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/complex/CComplex". +include "CoRN.ma". + (* $Id: CComplex.v,v 1.8 2004/04/23 10:00:55 lcf Exp $ *) (*#* printing Re %\ensuremath{\Re}% #ℜ# *) @@ -32,9 +34,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/complex/CComplex". (*#* printing CCX %\ensuremath{\mathbb C[X]}% #C[X]# *) -(* INCLUDE -NRootIR -*) +include "reals/NRootIR.ma". (*#* * Complex Numbers ** Algebraic structure @@ -44,27 +44,27 @@ NRootIR 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). @@ -92,56 +92,56 @@ Split; Algebra. Qed. *) -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]. *) -inline cic:/CoRN/complex/CComplex/cc_inv_aid2.con. +inline "cic:/CoRN/complex/CComplex/cc_inv_aid2.con". (* REMARK KEPT FOR SENTIMENTAL REASONS... @@ -152,11 +152,11 @@ input (Re or Im) is NonZero (a Prop), we manage to construct the actual function. *) -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. @@ -166,27 +166,27 @@ Opaque cc_recip. Opaque cc_inv. *) -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] *) -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). *) -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. @@ -196,7 +196,7 @@ End Complex_Numbers. (* end hide *) -inline cic:/CoRN/complex/CComplex/II.con. +inline "cic:/CoRN/complex/CComplex/II.con". (*#* ** Properties of [II] *) @@ -204,43 +204,43 @@ inline cic:/CoRN/complex/CComplex/II.con. Section I_properties. *) -inline cic:/CoRN/complex/CComplex/I_square.con. +inline "cic:/CoRN/complex/CComplex/I_square.con". (* 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] *) -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. @@ -261,27 +261,27 @@ Hint Resolve I_wd Re_wd Im_wd: algebra_c. 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. *) -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. *) -inline cic:/CoRN/complex/CComplex/CC_conj_nexp.con. +inline "cic:/CoRN/complex/CComplex/CC_conj_nexp.con". (* UNEXPORTED End Conj_properties. @@ -298,51 +298,51 @@ Hint Resolve CC_conj_plus CC_conj_mult CC_conj_nexp CC_conj_conj 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. *) -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. *) -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. *) -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. *) -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. *) -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. @@ -367,17 +367,13 @@ Hint Resolve cc_IR_nring cc_IR_zero: algebra. (*#* ** [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". diff --git a/matita/contribs/CoRN-Decl/complex/Complex_Exponential.ma b/matita/contribs/CoRN-Decl/complex/Complex_Exponential.ma index 9bbab759a..228a19f5a 100644 --- a/matita/contribs/CoRN-Decl/complex/Complex_Exponential.ma +++ b/matita/contribs/CoRN-Decl/complex/Complex_Exponential.ma @@ -16,85 +16,81 @@ set "baseuri" "cic:/matita/CoRN-Decl/complex/Complex_Exponential". +include "CoRN.ma". + (* $Id: Complex_Exponential.v,v 1.4 2004/04/23 10:00:55 lcf Exp $ *) (*#* printing ExpCC %\ensuremath{\exp_{\mathbb C}}% *) -(* INCLUDE -AbsCC -*) +include "complex/AbsCC.ma". -(* INCLUDE -Exponential -*) +include "transc/Exponential.ma". -(* INCLUDE -Pi -*) +include "transc/Pi.ma". (*#* ** 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". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/complex/Complex_Exponential/ExpCC_plus.con. +inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_plus.con". (* 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. *) -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. *) -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. *) -inline cic:/CoRN/complex/Complex_Exponential/ExpCC_pow.con. +inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_pow.con". (* 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. *) -inline cic:/CoRN/complex/Complex_Exponential/ExpCC_Periodic.con. +inline "cic:/CoRN/complex/Complex_Exponential/ExpCC_Periodic.con". (* 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. @@ -104,5 +100,5 @@ Hint Resolve ExpCC_Exp: algebra. Opaque Sin Cos Exp. *) -inline cic:/CoRN/complex/Complex_Exponential/Euler.con. +inline "cic:/CoRN/complex/Complex_Exponential/Euler.con". diff --git a/matita/contribs/CoRN-Decl/complex/NRootCC.ma b/matita/contribs/CoRN-Decl/complex/NRootCC.ma index 48688c5ee..b8fe0878b 100644 --- a/matita/contribs/CoRN-Decl/complex/NRootCC.ma +++ b/matita/contribs/CoRN-Decl/complex/NRootCC.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/complex/NRootCC". +include "CoRN.ma". + (* $Id: NRootCC.v,v 1.9 2004/04/23 10:00:55 lcf Exp $ *) (*#* printing sqrt_Half %\ensuremath{\sqrt{\frac12}}% *) @@ -26,17 +28,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/complex/NRootCC". (*#* printing nroot_minus_I %\ensuremath{\sqrt[n]{-\imath}}% *) -(* INCLUDE -CComplex -*) - -(* INCLUDE -Wf_nat -*) - -(* INCLUDE -ArithRing -*) +include "complex/CComplex.ma". (*#* * Roots of Complex Numbers @@ -47,9 +39,9 @@ Properties of non-zero complex numbers Section CC_ap_zero. *) -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. @@ -61,7 +53,7 @@ End CC_ap_zero. Section Imag_to_Real. *) -inline cic:/CoRN/complex/NRootCC/imag_to_real.con. +inline "cic:/CoRN/complex/NRootCC/imag_to_real.con". (* UNEXPORTED End Imag_to_Real. @@ -73,25 +65,25 @@ End Imag_to_Real. Section NRootI. *) -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. *) -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. @@ -117,77 +109,77 @@ Define [c2 := a[^]2[+]b[^]2], [c := sqrt c2], [a'2 := (c[+]a) [*]Half], %\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". (* begin hide *) -inline cic:/CoRN/complex/NRootCC/c2.con. +inline "cic:/CoRN/complex/NRootCC/c2.con". (* end hide *) -inline cic:/CoRN/complex/NRootCC/nrCC1_c2pos.con. +inline "cic:/CoRN/complex/NRootCC/nrCC1_c2pos.con". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/complex/NRootCC/nrCC1_a'2pos.con. +inline "cic:/CoRN/complex/NRootCC/nrCC1_a'2pos.con". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/complex/NRootCC/nrCC1_b'2pos.con. +inline "cic:/CoRN/complex/NRootCC/nrCC1_b'2pos.con". (* begin hide *) -inline cic:/CoRN/complex/NRootCC/b'.con. +inline "cic:/CoRN/complex/NRootCC/b'.con". (* end hide *) -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. *) -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. *) -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. *) -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. @@ -206,19 +198,19 @@ Section NRootCC_1_ap_imag. %\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/a_.var. +inline "cic:/CoRN/complex/NRootCC/a_.var". (* begin hide *) -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". (* end hide *) @@ -226,7 +218,7 @@ inline cic:/CoRN/complex/NRootCC/b'.con. 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. @@ -234,7 +226,7 @@ End NRootCC_1_ap_imag. (*#* 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. @@ -249,17 +241,17 @@ Section NRootCC_2. %\end{convention}% *) -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. @@ -269,44 +261,44 @@ End NRootCC_2. Section NRootCC_3. *) -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}% *) -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. *) -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. @@ -316,15 +308,15 @@ Hint Resolve nth_coeff_p_mult_c_: 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. *) -inline cic:/CoRN/complex/NRootCC/nrootCC_3_.con. +inline "cic:/CoRN/complex/NRootCC/nrootCC_3_.con". (* UNEXPORTED Hint Resolve nrootCC_3_: algebra. @@ -334,7 +326,7 @@ Hint Resolve nrootCC_3_: 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. @@ -344,7 +336,7 @@ Hint Resolve nrCC3_a2: 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. @@ -359,17 +351,17 @@ Section NRootCC_3'. %\end{convention}% *) -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'. @@ -389,19 +381,19 @@ Section NRootCC_4_ap_real. %\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/n_.var. +inline "cic:/CoRN/complex/NRootCC/n_.var". (* begin hide *) -inline cic:/CoRN/complex/NRootCC/c.con. +inline "cic:/CoRN/complex/NRootCC/c.con". (* end hide *) @@ -413,24 +405,24 @@ Section NRootCC_4_solutions. 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}% *) -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. *) -inline cic:/CoRN/complex/NRootCC/nrCC4_a1'.con. +inline "cic:/CoRN/complex/NRootCC/nrCC4_a1'.con". (* UNEXPORTED End NRootCC_4_solutions. @@ -447,53 +439,53 @@ and [(y2[*] (r[^] (2) [+]One)) [^]n [=] a[^] (2) [+]b[^] (2)]. %\end{convention}% *) -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. *) -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. *) -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. @@ -509,39 +501,39 @@ and [(odd n)]; define [c' := (a[+I*]b) [*]II := a'[+I*]b']. %\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/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". (* begin hide *) -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". (* end hide *) -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. *) -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. *) -inline cic:/CoRN/complex/NRootCC/nrootCC_4.con. +inline "cic:/CoRN/complex/NRootCC/nrootCC_4.con". (* UNEXPORTED End NRootCC_4. @@ -553,9 +545,9 @@ End NRootCC_4. Section NRootCC_5. *) -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. @@ -566,13 +558,13 @@ Hint Resolve nrCC_5a3: algebra. %\end{convention}% *) -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. @@ -580,5 +572,5 @@ End NRootCC_5. (*#* Final definition *) -inline cic:/CoRN/complex/NRootCC/CnrootCC.con. +inline "cic:/CoRN/complex/NRootCC/CnrootCC.con". diff --git a/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma b/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma index c1295ea7d..f99d50781 100644 --- a/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma +++ b/matita/contribs/CoRN-Decl/devel/loeb/IDA/Ch6.ma @@ -16,45 +16,39 @@ set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/IDA/Ch6". -(* INCLUDE -CSemiGroups -*) +include "CoRN.ma". + +include "algebra/CSemiGroups.ma". (* Remark blz 65 1 *) -inline cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation.con. +inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation.con". -(* INCLUDE -Zsetoid -*) +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". (* Remark blz 65 2 *) -(* INCLUDE -csetfun -*) +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 -Nsetoid -*) +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". (* blz 65 Example 1 *) @@ -77,9 +71,7 @@ Geen goed voorbeeld: monoids komen hier al in voor en het is een heel onoverzich (* Print Zmult_is_assoc.*) -(* INCLUDE -Qsetoid -*) +include "model/setoids/Qsetoid.ma". (* Print Qplus_is_assoc.*) @@ -91,13 +83,13 @@ Qsetoid Section p66E2. *) -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.*) @@ -109,17 +101,15 @@ End p66E2. (* 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". (* blz 66 Example % 3 *) -inline cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con. +inline "cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con". (* blz 66 Example % 4 *) @@ -127,43 +117,41 @@ inline cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con. Section p66E2b4. *) -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. @@ -171,15 +159,13 @@ End p66E2b4. (* Definition 5 *) -inline cic:/CoRN/devel/loeb/IDA/Ch6/is_unit.con. +inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit.con". (* blz 67 Remark 1 *) -(* INCLUDE -Zmonoid -*) +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". (* blz 67 Remark 2 *) @@ -187,9 +173,9 @@ inline cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con. Section p67R2. *) -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". (* UNEXPORTED End p67R2. @@ -197,23 +183,19 @@ End p67R2. (* blz 67 Remark 3 *) -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". (* Lemma 6 *) -inline cic:/CoRN/devel/loeb/IDA/Ch6/unique_unit.con. +inline "cic:/CoRN/devel/loeb/IDA/Ch6/unique_unit.con". (* blz 67 Example 1 *) -(* INCLUDE -Nmonoid -*) +include "model/monoids/Nmonoid.ma". (* Print nat_is_CMonoid.*) -(* INCLUDE -Zmonoid -*) +include "model/monoids/Zmonoid.ma". (* Print Z_is_CMonoid.*) @@ -229,75 +211,73 @@ Zmonoid Section p68E1b1. *) -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. @@ -315,27 +295,25 @@ End p68E1b1. (* Definition 9 *) -(* INCLUDE -CMonoids -*) +include "algebra/CMonoids.ma". (* 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". (* UNEXPORTED End D9S. @@ -345,17 +323,17 @@ End D9S. Section D9M. *) -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". (* UNEXPORTED End D9M. @@ -367,13 +345,13 @@ End D9M. Section p69E1. *) -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". (* UNEXPORTED End p69E1. @@ -385,21 +363,21 @@ End p69E1. Section Th11. *) -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". (* UNEXPORTED End Th11. @@ -411,15 +389,15 @@ End Th11. Section Th12. *) -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". (* UNEXPORTED End Th12. @@ -431,25 +409,23 @@ End Th12. Section p70text. *) -(* INCLUDE -lst2fun -*) +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. @@ -461,13 +437,13 @@ End p70text. Section Th13. *) -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". (* UNEXPORTED End Th13. @@ -479,23 +455,23 @@ End Th13. Section p71E1. *) -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". (* UNEXPORTED End p71E1. @@ -505,9 +481,9 @@ End p71E1. Section p71E1'. *) -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'. @@ -519,15 +495,15 @@ End p71E1'. Section p71E2. *) -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". (* UNEXPORTED End p71E2. @@ -539,11 +515,11 @@ End p71E2. Section p71R1. *) -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". (* UNEXPORTED End p71R1. @@ -553,9 +529,9 @@ End p71R1. Section p71R2. *) -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". (* UNEXPORTED End p71R2. @@ -567,17 +543,17 @@ End p71R2. Section Th14. *) -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". (* UNEXPORTED End Th14. @@ -589,9 +565,9 @@ End Th14. Section p71E2b1. *) -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. @@ -601,17 +577,17 @@ End p71E2b1. Section p71E2b2. *) -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. @@ -621,29 +597,29 @@ End p71E2b2. Section Th15. *) -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]. *) -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". (* UNEXPORTED End Th15. diff --git a/matita/contribs/CoRN-Decl/devel/loeb/per/csetfun.ma b/matita/contribs/CoRN-Decl/devel/loeb/per/csetfun.ma index 895e95c48..88fcfbeb9 100644 --- a/matita/contribs/CoRN-Decl/devel/loeb/per/csetfun.ma +++ b/matita/contribs/CoRN-Decl/devel/loeb/per/csetfun.ma @@ -16,67 +16,59 @@ set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/per/csetfun". -(* INCLUDE -CSetoids -*) +include "CoRN.ma". -(* 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. *) -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 -CGroups -*) +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), @@ -130,13 +122,13 @@ set (H6 := ap_imp_neq B (f0 x) (f0 b) H4) in *. intuition. Qed.*) -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! *) diff --git a/matita/contribs/CoRN-Decl/devel/loeb/per/lst2fun.ma b/matita/contribs/CoRN-Decl/devel/loeb/per/lst2fun.ma index d58280c01..07af75c50 100644 --- a/matita/contribs/CoRN-Decl/devel/loeb/per/lst2fun.ma +++ b/matita/contribs/CoRN-Decl/devel/loeb/per/lst2fun.ma @@ -16,33 +16,37 @@ set "baseuri" "cic:/matita/CoRN-Decl/devel/loeb/per/lst2fun". -inline cic:/CoRN/devel/loeb/per/lst2fun/F'.con. +include "CoRN.ma". -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]. *) -(* 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". diff --git a/matita/contribs/CoRN-Decl/fta/CC_Props.ma b/matita/contribs/CoRN-Decl/fta/CC_Props.ma index 5adea747f..01b3ef4bc 100644 --- a/matita/contribs/CoRN-Decl/fta/CC_Props.ma +++ b/matita/contribs/CoRN-Decl/fta/CC_Props.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/CC_Props". +include "CoRN.ma". + (* $Id: CC_Props.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *) -(* INCLUDE -AbsCC -*) +include "complex/AbsCC.ma". (*#* * More properties of complex numbers ** Sequences and limits *) @@ -29,39 +29,41 @@ AbsCC 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] *) @@ -75,25 +77,25 @@ Section Continuity_for_CC. %\end{convention}% *) -inline cic:/CoRN/fta/CC_Props/f.var. +inline "cic:/CoRN/fta/CC_Props/f.var". (* (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. *) -inline cic:/CoRN/fta/CC_Props/seq_yields_zero.con. +inline "cic:/CoRN/fta/CC_Props/seq_yields_zero.con". diff --git a/matita/contribs/CoRN-Decl/fta/CPoly_Contin1.ma b/matita/contribs/CoRN-Decl/fta/CPoly_Contin1.ma index cee3b569c..c331e5e37 100644 --- a/matita/contribs/CoRN-Decl/fta/CPoly_Contin1.ma +++ b/matita/contribs/CoRN-Decl/fta/CPoly_Contin1.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/CPoly_Contin1". +include "CoRN.ma". + (* $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 *) @@ -29,11 +29,11 @@ CC_Props 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. @@ -48,11 +48,11 @@ Section CPoly_CC_Continuous. %\end{convention}% *) -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. diff --git a/matita/contribs/CoRN-Decl/fta/CPoly_Rev.ma b/matita/contribs/CoRN-Decl/fta/CPoly_Rev.ma index e4e160d11..32961ffe2 100644 --- a/matita/contribs/CoRN-Decl/fta/CPoly_Rev.ma +++ b/matita/contribs/CoRN-Decl/fta/CPoly_Rev.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/CPoly_Rev". +include "CoRN.ma". + (* $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 *) @@ -35,47 +35,47 @@ polynomials over this ring. %\end{convention}% *) -inline cic:/CoRN/fta/CPoly_Rev/R.var. +inline "cic:/CoRN/fta/CPoly_Rev/R.var". (* begin hide *) -inline cic:/CoRN/fta/CPoly_Rev/RX.con. +inline "cic:/CoRN/fta/CPoly_Rev/RX.con". (* end hide *) -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. *) -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. *) -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. *) -inline cic:/CoRN/fta/CPoly_Rev/monom_mult'.con. +inline "cic:/CoRN/fta/CPoly_Rev/monom_mult'.con". (* 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. @@ -93,73 +93,73 @@ Implicit Arguments monom [R]. Section Poly_Reverse. *) -inline cic:/CoRN/fta/CPoly_Rev/R.var. +inline "cic:/CoRN/fta/CPoly_Rev/R.var". (* begin hide *) -inline cic:/CoRN/fta/CPoly_Rev/RX.con. +inline "cic:/CoRN/fta/CPoly_Rev/RX.con". (* end hide *) -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. *) -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. *) -inline cic:/CoRN/fta/CPoly_Rev/Rev_rev.con. +inline "cic:/CoRN/fta/CPoly_Rev/Rev_rev.con". (* 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. *) -inline cic:/CoRN/fta/CPoly_Rev/Rev_zero.con. +inline "cic:/CoRN/fta/CPoly_Rev/Rev_zero.con". (* 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. *) -inline cic:/CoRN/fta/CPoly_Rev/Rev_minus.con. +inline "cic:/CoRN/fta/CPoly_Rev/Rev_minus.con". (* 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. *) -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. diff --git a/matita/contribs/CoRN-Decl/fta/CPoly_Shift.ma b/matita/contribs/CoRN-Decl/fta/CPoly_Shift.ma index ba74e35fe..e0875e59f 100644 --- a/matita/contribs/CoRN-Decl/fta/CPoly_Shift.ma +++ b/matita/contribs/CoRN-Decl/fta/CPoly_Shift.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/CPoly_Shift". +include "CoRN.ma". + (* $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 @@ -32,23 +32,23 @@ and we only need it for [CC]. Section Poly_Shifted. *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/fta/FTA.ma b/matita/contribs/CoRN-Decl/fta/FTA.ma index 3060032a7..ba69c7ec6 100644 --- a/matita/contribs/CoRN-Decl/fta/FTA.ma +++ b/matita/contribs/CoRN-Decl/fta/FTA.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/FTA". +include "CoRN.ma". + (* $Id: FTA.v,v 1.6 2004/04/23 10:00:57 lcf Exp $ *) -(* INCLUDE -CPoly_Rev -*) +include "fta/CPoly_Rev.ma". -(* INCLUDE -FTAreg -*) +include "fta/FTAreg.ma". (*#* * Fundamental Theorem of Algebra %\begin{convention}% Let [n:nat] and [f] be a complex polynomial of @@ -36,13 +34,13 @@ degree [(S n)]. Section 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/FTA_reg'.con. +inline "cic:/CoRN/fta/FTA/FTA_reg'.con". (* UNEXPORTED End FTA_reg'. @@ -59,25 +57,25 @@ less than or equal to [(S n)] and [c] be a complex number such that Section FTA_1. *) -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". (* UNEXPORTED End FTA_1. @@ -87,11 +85,11 @@ End FTA_1. Section Fund_Thm_Alg. *) -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. diff --git a/matita/contribs/CoRN-Decl/fta/FTAreg.ma b/matita/contribs/CoRN-Decl/fta/FTAreg.ma index fed20062f..f0f50b0d8 100644 --- a/matita/contribs/CoRN-Decl/fta/FTAreg.ma +++ b/matita/contribs/CoRN-Decl/fta/FTAreg.ma @@ -16,19 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/FTAreg". +include "CoRN.ma". + (* $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 @@ -40,9 +36,9 @@ CPoly_Contin1 Section Seq_Exists. *) -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 @@ -59,41 +55,45 @@ Let [p] be a monic polynomial over the complex numbers with degree 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. @@ -106,7 +106,7 @@ Section Seq_Exists_Main. (*#* **Main results *) -inline cic:/CoRN/fta/FTAreg/seq_exists.con. +inline "cic:/CoRN/fta/FTAreg/seq_exists.con". (* UNEXPORTED End Seq_Exists_Main. @@ -120,31 +120,31 @@ End Seq_Exists. Section N_Exists. *) -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 hide *) -inline cic:/CoRN/fta/FTAreg/q_.con. +inline "cic:/CoRN/fta/FTAreg/q_.con". (* end hide *) -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. @@ -156,19 +156,19 @@ Section Seq_is_CC_CAuchy. (*#* ** 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] @@ -181,39 +181,39 @@ inline cic:/CoRN/fta/FTAreg/zltc.var. (* begin hide *) -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". (* end hide *) -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. *) -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". diff --git a/matita/contribs/CoRN-Decl/fta/KeyLemma.ma b/matita/contribs/CoRN-Decl/fta/KeyLemma.ma index 00a0b30c4..caf87bea1 100644 --- a/matita/contribs/CoRN-Decl/fta/KeyLemma.ma +++ b/matita/contribs/CoRN-Decl/fta/KeyLemma.ma @@ -16,19 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/KeyLemma". -(* $Id: KeyLemma.v,v 1.5 2004/04/23 10:00:57 lcf Exp $ *) - -(* INCLUDE -ZArith -*) +include "CoRN.ma". -(* INCLUDE -Compare -*) +(* $Id: KeyLemma.v,v 1.5 2004/04/23 10:00:57 lcf Exp $ *) -(* INCLUDE -NRootIR -*) +include "reals/NRootIR.ma". (*#* printing p3m %\ensuremath{\frac13\hat{\ }}% *) @@ -49,119 +41,119 @@ and [eps : IR] such that [(Zero [<] eps)] and [(eps [<=] a_0)]. %\end{convention}% *) -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. *) -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. *) -inline cic:/CoRN/fta/KeyLemma/p3m_0.con. +inline "cic:/CoRN/fta/KeyLemma/p3m_0.con". (* 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. *) -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. *) -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. *) -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. *) -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". (* end hide *) diff --git a/matita/contribs/CoRN-Decl/fta/KneserLemma.ma b/matita/contribs/CoRN-Decl/fta/KneserLemma.ma index 84cd55eb6..fbbeb1c49 100644 --- a/matita/contribs/CoRN-Decl/fta/KneserLemma.ma +++ b/matita/contribs/CoRN-Decl/fta/KneserLemma.ma @@ -16,23 +16,19 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/KneserLemma". +include "CoRN.ma". + (* $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}% #η0# *) -(* INCLUDE -NRootCC -*) +include "complex/NRootCC.ma". -(* INCLUDE -AbsCC -*) +include "complex/AbsCC.ma". -(* INCLUDE -MainLemma -*) +include "fta/MainLemma.ma". (*#* ** Kneser Lemma *) @@ -47,25 +43,25 @@ such that [0 < n], [b_0 := b 0], [b_n := (b n) [=] One] and %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) -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: @@ -81,69 +77,69 @@ inline cic:/CoRN/fta/KneserLemma/b_0_lt_c.var. (* begin hide *) -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". (* end hide *) -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}. *) -inline cic:/CoRN/fta/KneserLemma/eps_exists.con. +inline "cic:/CoRN/fta/KneserLemma/eps_exists.con". (* begin hide *) -inline cic:/CoRN/fta/KneserLemma/a.con. +inline "cic:/CoRN/fta/KneserLemma/a.con". (* end hide *) -inline cic:/CoRN/fta/KneserLemma/z_exists.con. +inline "cic:/CoRN/fta/KneserLemma/z_exists.con". (* end hide *) -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". (* end hide *) -inline cic:/CoRN/fta/KneserLemma/Kneser_2c.con. +inline "cic:/CoRN/fta/KneserLemma/Kneser_2c.con". (* end hide *) -inline cic:/CoRN/fta/KneserLemma/Kneser_2.con. +inline "cic:/CoRN/fta/KneserLemma/Kneser_2.con". (* end hide *) -inline cic:/CoRN/fta/KneserLemma/Kneser_3.con. +inline "cic:/CoRN/fta/KneserLemma/Kneser_3.con". (* UNEXPORTED End Kneser_Lemma. *) -inline cic:/CoRN/fta/KneserLemma/Kneser.con. +inline "cic:/CoRN/fta/KneserLemma/Kneser.con". diff --git a/matita/contribs/CoRN-Decl/fta/MainLemma.ma b/matita/contribs/CoRN-Decl/fta/MainLemma.ma index b180a093f..350e62138 100644 --- a/matita/contribs/CoRN-Decl/fta/MainLemma.ma +++ b/matita/contribs/CoRN-Decl/fta/MainLemma.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/MainLemma". +include "CoRN.ma". + (* $Id: MainLemma.v,v 1.3 2004/04/23 10:00:57 lcf Exp $ *) (*#* printing two_n %\ensuremath{2n}% #2n# *) @@ -24,13 +26,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/fta/MainLemma". (*#* printing Smaller %\ensuremath{\frac13^{2n^2}}% *) -(* INCLUDE -CSumsReals -*) +include "reals/CSumsReals.ma". -(* INCLUDE -KeyLemma -*) +include "fta/KeyLemma.ma". (*#* ** Main Lemma *) @@ -47,25 +45,25 @@ Let [a : nat->IR], [n : nat], [a_0 : IR] and [eps : IR] such that [0 < n], %\end{convention}% *) -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: @@ -78,49 +76,49 @@ inline cic:/CoRN/fta/MainLemma/a_0_pos.con. (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/fta/MainLemma/Main_1a'.con. +inline "cic:/CoRN/fta/MainLemma/Main_1a'.con". (* end hide *) -inline cic:/CoRN/fta/MainLemma/Main_1b'.con. +inline "cic:/CoRN/fta/MainLemma/Main_1b'.con". (* end hide *) -inline cic:/CoRN/fta/MainLemma/Main_1a.con. +inline "cic:/CoRN/fta/MainLemma/Main_1a.con". (* end hide *) -inline cic:/CoRN/fta/MainLemma/Main_1b.con. +inline "cic:/CoRN/fta/MainLemma/Main_1b.con". (* end hide *) -inline cic:/CoRN/fta/MainLemma/Main_1.con. +inline "cic:/CoRN/fta/MainLemma/Main_1.con". (* end hide *) -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". (* end hide *) -inline cic:/CoRN/fta/MainLemma/Main_3a.con. +inline "cic:/CoRN/fta/MainLemma/Main_3a.con". (* end hide *) -inline cic:/CoRN/fta/MainLemma/Main_3.con. +inline "cic:/CoRN/fta/MainLemma/Main_3.con". (* end hide *) -inline cic:/CoRN/fta/MainLemma/Main.con. +inline "cic:/CoRN/fta/MainLemma/Main.con". (* end hide *) diff --git a/matita/contribs/CoRN-Decl/ftc/COrdLemmas.ma b/matita/contribs/CoRN-Decl/ftc/COrdLemmas.ma index fc8a38805..bf7461582 100644 --- a/matita/contribs/CoRN-Decl/ftc/COrdLemmas.ma +++ b/matita/contribs/CoRN-Decl/ftc/COrdLemmas.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/COrdLemmas". +include "CoRN.ma". + (* $Id: COrdLemmas.v,v 1.2 2004/04/23 10:00:57 lcf Exp $ *) -(* INCLUDE -COrdCauchy -*) +include "algebra/COrdCauchy.ma". (* UNEXPORTED Section Lemmas. @@ -39,39 +39,39 @@ the proof that any two partitions with no common point have a common refinement). *) -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". (* begin hide *) -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". (* end hide *) @@ -83,17 +83,17 @@ structure of the arguments is analyzed in more detail. (* begin show *) -inline cic:/CoRN/ftc/COrdLemmas/Sumx_Sum_Sum +inline "cic:/CoRN/ftc/COrdLemmas/Sumx_Sum_Sum (* end show *) - (* begin hide *).con. + (* begin hide *).con". (* end hide *) (* begin show *) -inline cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum +inline "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum (* end show *) - (* begin hide *).con. + (* begin hide *).con". (* UNEXPORTED End Lemmas. @@ -103,17 +103,17 @@ End Lemmas. Section More_Lemmas. *) -inline cic:/CoRN/ftc/COrdLemmas/f'.con. +inline "cic:/CoRN/ftc/COrdLemmas/f'.con". (* end hide *) -inline cic:/CoRN/ftc/COrdLemmas/F.var. +inline "cic:/CoRN/ftc/COrdLemmas/F.var". (* begin show *) -inline cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum' +inline "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum' (* end show *) - (* begin hide *).con. + (* begin hide *).con". (* end hide *) diff --git a/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma b/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma index 57fcf425c..6e43129c3 100644 --- a/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma +++ b/matita/contribs/CoRN-Decl/ftc/CalculusTheorems.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/CalculusTheorems". +include "CoRN.ma". + (* $Id: CalculusTheorems.v,v 1.6 2004/04/23 10:00:57 lcf Exp $ *) -(* INCLUDE -Rolle -*) +include "ftc/Rolle.ma". -(* INCLUDE -DiffTactics3 -*) +include "tactics/DiffTactics3.ma". (* UNEXPORTED Opaque Min Max. @@ -45,52 +43,52 @@ continuous function commutes with the limit of a numerical sequence (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]]. *) -inline cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con. +inline "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con". (*#* 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. *) -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. *) -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. *) -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. *) -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 @@ -99,11 +97,11 @@ quite similar the proofs are completely different, both from the 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! @@ -117,7 +115,7 @@ Opaque nring. Transparent nring. *) -inline cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con. +inline "cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con". (* UNEXPORTED End Various_Theorems. diff --git a/matita/contribs/CoRN-Decl/ftc/Composition.ma b/matita/contribs/CoRN-Decl/ftc/Composition.ma index 81debe755..124656d5b 100644 --- a/matita/contribs/CoRN-Decl/ftc/Composition.ma +++ b/matita/contribs/CoRN-Decl/ftc/Composition.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/Composition". +include "CoRN.ma". + (* $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. @@ -53,49 +53,49 @@ mapped into another compact interval. We define this concept for 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". (* begin hide *) -inline cic:/CoRN/ftc/Composition/I.con. +inline "cic:/CoRN/ftc/Composition/I.con". (* end hide *) (* begin show *) -inline cic:/CoRN/ftc/Composition/Hf.var. +inline "cic:/CoRN/ftc/Composition/Hf.var". (* end show *) -inline cic:/CoRN/ftc/Composition/maps_into_compacts.con. +inline "cic:/CoRN/ftc/Composition/maps_into_compacts.con". (* begin show *) -inline cic:/CoRN/ftc/Composition/maps.var. +inline "cic:/CoRN/ftc/Composition/maps.var". (* end show *) -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. @@ -114,33 +114,33 @@ As was the case for division of partial functions, this condition 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". (* begin show *) -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". (* end show *) -inline cic:/CoRN/ftc/Composition/included_comp.con. +inline "cic:/CoRN/ftc/Composition/included_comp.con". (* UNEXPORTED End Mapping. @@ -155,39 +155,39 @@ Section Interval_Continuity. 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". (* begin hide *) -inline cic:/CoRN/ftc/Composition/I.con. +inline "cic:/CoRN/ftc/Composition/I.con". (* end hide *) -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". (* begin show *) -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". (* end show *) -inline cic:/CoRN/ftc/Composition/Continuous_I_comp.con. +inline "cic:/CoRN/ftc/Composition/Continuous_I_comp.con". (* UNEXPORTED End Interval_Continuity. @@ -202,57 +202,57 @@ Section Derivative. 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". (* begin hide *) -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 *) -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". (* end show *) -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. *) -inline cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con. +inline "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con". (* UNEXPORTED End Derivative. @@ -267,43 +267,43 @@ Section 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". (* begin hide *) -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 *) -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". (* end show *) -inline cic:/CoRN/ftc/Composition/Diffble_I_comp.con. +inline "cic:/CoRN/ftc/Composition/Diffble_I_comp.con". (* UNEXPORTED End Differentiability. @@ -321,45 +321,45 @@ We now generalize this results to arbitrary intervals. We begin by generalizing %\end{convention}% *) -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: *) -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". (* begin show *) -inline cic:/CoRN/ftc/Composition/Hmap.var. +inline "cic:/CoRN/ftc/Composition/Hmap.var". (* end show *) -inline cic:/CoRN/ftc/Composition/Continuous_comp.con. +inline "cic:/CoRN/ftc/Composition/Continuous_comp.con". (* begin show *) -inline cic:/CoRN/ftc/Composition/Hmap'.var. +inline "cic:/CoRN/ftc/Composition/Hmap'.var". (* end show *) -inline cic:/CoRN/ftc/Composition/Derivative_comp.con. +inline "cic:/CoRN/ftc/Composition/Derivative_comp.con". (* UNEXPORTED End Generalized_Intervals. @@ -373,21 +373,21 @@ Section Corollaries. 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. *) -inline cic:/CoRN/ftc/Composition/Diffble_comp.con. +inline "cic:/CoRN/ftc/Composition/Diffble_comp.con". (* UNEXPORTED End Corollaries. diff --git a/matita/contribs/CoRN-Decl/ftc/Continuity.ma b/matita/contribs/CoRN-Decl/ftc/Continuity.ma index 2ea7152a0..113b47653 100644 --- a/matita/contribs/CoRN-Decl/ftc/Continuity.ma +++ b/matita/contribs/CoRN-Decl/ftc/Continuity.ma @@ -16,17 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/Continuity". +include "CoRN.ma". + (* $Id: Continuity.v,v 1.6 2004/04/23 10:00:58 lcf Exp $ *) (*#* printing Norm_Funct %\ensuremath{\|\cdot\|}% *) -(* INCLUDE -NRootIR -*) +include "reals/NRootIR.ma". -(* INCLUDE -FunctSums -*) +include "ftc/FunctSums.ma". (* UNEXPORTED Section Definitions_and_Basic_Results. @@ -56,103 +54,103 @@ respectively [P, Q] and [R]. 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". (* begin hide *) -inline cic:/CoRN/ftc/Continuity/I.con. +inline "cic:/CoRN/ftc/Continuity/I.con". (* end hide *) -inline cic:/CoRN/ftc/Continuity/F.var. +inline "cic:/CoRN/ftc/Continuity/F.var". (* begin hide *) -inline cic:/CoRN/ftc/Continuity/P.con. +inline "cic:/CoRN/ftc/Continuity/P.con". (* end hide *) -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. *) -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]. *) -inline cic:/CoRN/ftc/Continuity/contF.var. +inline "cic:/CoRN/ftc/Continuity/contF.var". (* begin hide *) -inline cic:/CoRN/ftc/Continuity/Hinc'.con. +inline "cic:/CoRN/ftc/Continuity/Hinc'.con". (* end hide *) -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. *) -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. *) -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). *) -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. *) -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: *) -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. *) -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. @@ -175,77 +173,77 @@ Section Local_Results. 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". (* begin hide *) -inline cic:/CoRN/ftc/Continuity/I.con. +inline "cic:/CoRN/ftc/Continuity/I.con". (* end hide *) -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". (* begin hide *) -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". (* end hide *) -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. *) -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. *) -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. *) -inline cic:/CoRN/ftc/Continuity/included_imp_contin.con. +inline "cic:/CoRN/ftc/Continuity/included_imp_contin.con". (*#* 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. *) -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. @@ -255,17 +253,17 @@ Opaque AbsIR Max. Transparent AbsIR Max. *) -inline cic:/CoRN/ftc/Continuity/Continuous_I_max.con. +inline "cic:/CoRN/ftc/Continuity/Continuous_I_max.con". (* begin show *) -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". (* end show *) -inline cic:/CoRN/ftc/Continuity/Continuous_I_recip.con. +inline "cic:/CoRN/ftc/Continuity/Continuous_I_recip.con". (* UNEXPORTED End Local_Results. @@ -279,33 +277,33 @@ Hint Resolve contin_imp_inc: included. Section Corolaries. *) -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". (* begin hide *) -inline cic:/CoRN/ftc/Continuity/I.con. +inline "cic:/CoRN/ftc/Continuity/I.con". (* end hide *) -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". (* begin hide *) -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". (* end hide *) -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 @@ -314,21 +312,21 @@ exponentiation is proved by induction, appealing to the results on 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. @@ -346,25 +344,25 @@ Section Sums. 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". (* begin hide *) -inline cic:/CoRN/ftc/Continuity/I.con. +inline "cic:/CoRN/ftc/Continuity/I.con". (* end hide *) -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". (* UNEXPORTED End Sums. @@ -374,27 +372,27 @@ End Sums. 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. *) -inline cic:/CoRN/ftc/Continuity/leEq_glb.con. +inline "cic:/CoRN/ftc/Continuity/leEq_glb.con". (*#* 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. *) -inline cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con. +inline "cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con". (* UNEXPORTED End Other. diff --git a/matita/contribs/CoRN-Decl/ftc/Derivative.ma b/matita/contribs/CoRN-Decl/ftc/Derivative.ma index 37588736a..4551cb741 100644 --- a/matita/contribs/CoRN-Decl/ftc/Derivative.ma +++ b/matita/contribs/CoRN-Decl/ftc/Derivative.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/Derivative". +include "CoRN.ma". + (* $Id: Derivative.v,v 1.7 2004/04/23 10:00:58 lcf Exp $ *) -(* INCLUDE -Continuity -*) +include "ftc/Continuity.ma". (* UNEXPORTED Section Definitions. @@ -53,29 +53,29 @@ will be partial functions with domains respectively [P, P', Q, Q'] and %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/ftc/Derivative/F.var. +inline "cic:/CoRN/ftc/Derivative/F.var". (* begin hide *) -inline cic:/CoRN/ftc/Derivative/P.con. +inline "cic:/CoRN/ftc/Derivative/P.con". (* end hide *) -inline cic:/CoRN/ftc/Derivative/Derivative_I.con. +inline "cic:/CoRN/ftc/Derivative/Derivative_I.con". (* UNEXPORTED End Definitions. @@ -92,17 +92,17 @@ Section 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". (* begin hide *) -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". (* end hide *) @@ -110,7 +110,7 @@ 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. *) -inline cic:/CoRN/ftc/Derivative/Derivative_I_char.con. +inline "cic:/CoRN/ftc/Derivative/Derivative_I_char.con". (* end hide *) @@ -118,29 +118,29 @@ inline cic:/CoRN/ftc/Derivative/Derivative_I_char.con. 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". (* begin hide *) -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". (* end hide *) -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". (* begin hide *) -inline cic:/CoRN/ftc/Derivative/Derivative_I_unique_lemma.con. +inline "cic:/CoRN/ftc/Derivative/Derivative_I_unique_lemma.con". (* end hide *) @@ -148,25 +148,25 @@ inline cic:/CoRN/ftc/Derivative/Derivative_I_unique_lemma.con. Derivative is unique. *) -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. *) -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. *) -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. @@ -176,5 +176,5 @@ 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. *) -inline cic:/CoRN/ftc/Derivative/included_imp_deriv.con. +inline "cic:/CoRN/ftc/Derivative/included_imp_deriv.con". diff --git a/matita/contribs/CoRN-Decl/ftc/DerivativeOps.ma b/matita/contribs/CoRN-Decl/ftc/DerivativeOps.ma index 18b016072..25a674c26 100644 --- a/matita/contribs/CoRN-Decl/ftc/DerivativeOps.ma +++ b/matita/contribs/CoRN-Decl/ftc/DerivativeOps.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/DerivativeOps". +include "CoRN.ma". + (* $Id: DerivativeOps.v,v 1.3 2004/04/23 10:00:58 lcf Exp $ *) -(* INCLUDE -Derivative -*) +include "ftc/Derivative.ma". (* UNEXPORTED Section Lemmas. @@ -38,33 +38,33 @@ context.%}.% 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". (* begin hide *) -inline cic:/CoRN/ftc/DerivativeOps/I.con. +inline "cic:/CoRN/ftc/DerivativeOps/I.con". (* end hide *) -inline cic:/CoRN/ftc/DerivativeOps/F.var. +inline "cic:/CoRN/ftc/DerivativeOps/F.var". (* begin hide *) -inline cic:/CoRN/ftc/DerivativeOps/P.con. +inline "cic:/CoRN/ftc/DerivativeOps/P.con". (* end hide *) (* begin show *) -inline cic:/CoRN/ftc/DerivativeOps/Fbnd.var. +inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var". (* end show *) -inline cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con. +inline "cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con". (* UNEXPORTED End Lemmas. @@ -83,41 +83,41 @@ Section Local_Results. 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". (* begin hide *) -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". (* end hide *) -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. @@ -125,11 +125,11 @@ As was the case for continuity, the rule for the reciprocal function has a side (* begin show *) -inline cic:/CoRN/ftc/DerivativeOps/Fbnd.var. +inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var". (* end show *) -inline cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con. +inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con". (* UNEXPORTED End Local_Results. @@ -148,45 +148,45 @@ Hint Resolve Derivative_I_const Derivative_I_id Derivative_I_plus Section Corolaries. *) -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". (* begin hide *) -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". (* end hide *) -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. *) -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. @@ -205,25 +205,25 @@ Section Derivative_Sums. 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". (* begin hide *) -inline cic:/CoRN/ftc/DerivativeOps/I.con. +inline "cic:/CoRN/ftc/DerivativeOps/I.con". (* end hide *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/Differentiability.ma b/matita/contribs/CoRN-Decl/ftc/Differentiability.ma index 898232c0e..ded63db55 100644 --- a/matita/contribs/CoRN-Decl/ftc/Differentiability.ma +++ b/matita/contribs/CoRN-Decl/ftc/Differentiability.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/Differentiability". +include "CoRN.ma". + (* $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. @@ -60,7 +58,7 @@ interval and eliminate the existencial quantifier without any problems. *) -inline cic:/CoRN/ftc/Differentiability/Diffble_I.con. +inline "cic:/CoRN/ftc/Differentiability/Diffble_I.con". (* UNEXPORTED End Definitions. @@ -80,33 +78,33 @@ From this point on, we just prove results analogous to the ones for derivability 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. *) -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". (* begin hide *) -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". (* end hide *) -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. *) -inline cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con. +inline "cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con". (* UNEXPORTED End Local_Properties. @@ -124,17 +122,17 @@ Section Operations. 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". (* begin hide *) -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". (* end hide *) @@ -142,9 +140,9 @@ inline cic:/CoRN/ftc/Differentiability/I.con. Section Constants. *) -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. @@ -154,39 +152,39 @@ End Constants. 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. *) -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". (* begin show *) -inline cic:/CoRN/ftc/Differentiability/Gbnd.var. +inline "cic:/CoRN/ftc/Differentiability/Gbnd.var". (* end show *) -inline cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con. +inline "cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con". (* UNEXPORTED End Operations. @@ -196,37 +194,37 @@ End Operations. Section Corollaries. *) -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". (* begin hide *) -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". (* end hide *) -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. @@ -241,17 +239,17 @@ Differentiability of families of functions is proved by 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. @@ -264,7 +262,7 @@ Finally, a differentiable function is continuous. %\end{convention}% *) -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 diff --git a/matita/contribs/CoRN-Decl/ftc/FTC.ma b/matita/contribs/CoRN-Decl/ftc/FTC.ma index 6042eee7a..75d572a5c 100644 --- a/matita/contribs/CoRN-Decl/ftc/FTC.ma +++ b/matita/contribs/CoRN-Decl/ftc/FTC.ma @@ -16,17 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/FTC". +include "CoRN.ma". + (* $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. @@ -53,21 +51,21 @@ and [a] be a point in [I]. %\end{convention}% *) -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. @@ -92,41 +90,41 @@ indefinite integral of [F] from [x0]. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/FTC/G.con. +inline "cic:/CoRN/ftc/FTC/G.con". (* end hide *) -inline cic:/CoRN/ftc/FTC/Continuous_prim.con. +inline "cic:/CoRN/ftc/FTC/Continuous_prim.con". (*#* 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. *) -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. @@ -134,7 +132,7 @@ The following is another statement of the Fundamental Theorem of Calculus, also (* begin hide *) -inline cic:/CoRN/ftc/FTC/G0_inc.con. +inline "cic:/CoRN/ftc/FTC/G0_inc.con". (* end hide *) @@ -142,7 +140,7 @@ inline cic:/CoRN/ftc/FTC/G0_inc.con. Opaque G. *) -inline cic:/CoRN/ftc/FTC/Barrow.con. +inline "cic:/CoRN/ftc/FTC/Barrow.con". (* end hide *) @@ -178,15 +176,15 @@ then the sequence of their primitives also converges, and the limit 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. @@ -202,45 +200,45 @@ continuous in [[a,b]], $x0\in[a,b]$#x0∈[a,b]#; denote by %\end{convention}% *) -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". (* begin show *) -inline cic:/CoRN/ftc/FTC/convF.var. +inline "cic:/CoRN/ftc/FTC/convF.var". (* end show *) -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". (* begin hide *) -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 *) -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". (* end show *) -inline cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con. +inline "cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con". (* UNEXPORTED End Compact. @@ -250,9 +248,9 @@ End Compact. 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. @@ -264,27 +262,27 @@ Finally, with [x0, g, G] as before, (* begin show *) -inline cic:/CoRN/ftc/FTC/convF.var. +inline "cic:/CoRN/ftc/FTC/convF.var". (* end show *) -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". (* begin hide *) -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 *) -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. @@ -305,33 +303,33 @@ Similar results hold for the sequence of derivatives of a converging sequence; t %\end{convention}% *) -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. @@ -345,25 +343,25 @@ Section Derivative_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". (* begin show *) -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". (* end show *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/FunctSequence.ma b/matita/contribs/CoRN-Decl/ftc/FunctSequence.ma index c5c588036..768b71285 100644 --- a/matita/contribs/CoRN-Decl/ftc/FunctSequence.ma +++ b/matita/contribs/CoRN-Decl/ftc/FunctSequence.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSequence". +include "CoRN.ma". + (* $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. @@ -54,77 +52,77 @@ be defined. For a discussion on the different notions of convergent see Bishop 1967. *) -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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSequence/I.con. +inline "cic:/CoRN/ftc/FunctSequence/I.con". (* end hide *) -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". (* begin hide *) -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". (* end hide *) -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. *) -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. *) -inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con. +inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con". (* UNEXPORTED End Definitions. @@ -134,21 +132,21 @@ End 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSequence/I.con. +inline "cic:/CoRN/ftc/FunctSequence/I.con". (* end hide *) -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 @@ -156,7 +154,7 @@ continuous function. Notice that we do not quantify directly over 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: @@ -164,11 +162,11 @@ It is useful to extract the limit as a partial function: (* begin show *) -inline cic:/CoRN/ftc/FunctSequence/H.var. +inline "cic:/CoRN/ftc/FunctSequence/H.var". (* end show *) -inline cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con. +inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con". (* UNEXPORTED End More_Definitions. @@ -183,47 +181,47 @@ Section Irrelevance_of_Proofs. 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSequence/I.con. +inline "cic:/CoRN/ftc/FunctSequence/I.con". (* end hide *) -inline cic:/CoRN/ftc/FunctSequence/f.var. +inline "cic:/CoRN/ftc/FunctSequence/f.var". (* begin show *) -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". (* end show *) -inline cic:/CoRN/ftc/FunctSequence/F.var. +inline "cic:/CoRN/ftc/FunctSequence/F.var". (* begin show *) -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". (* end show *) -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. @@ -233,7 +231,7 @@ End Irrelevance_of_Proofs. 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. @@ -250,79 +248,79 @@ limit; the limit is a continuous function; and convergence is well 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSequence/I.con. +inline "cic:/CoRN/ftc/FunctSequence/I.con". (* end hide *) -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". (* begin show *) -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". (* end show *) -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". (* begin show *) -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". (* end show *) -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. *) -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. *) -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. @@ -341,76 +339,76 @@ Section Algebraic_Properties. 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSequence/I.con. +inline "cic:/CoRN/ftc/FunctSequence/I.con". (* end hide *) -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. *) -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. *) -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. *) -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". (* begin show *) -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 *) -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". (* end hide *) -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. @@ -420,25 +418,25 @@ End 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSequence/I.con. +inline "cic:/CoRN/ftc/FunctSequence/I.con". (* end hide *) -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. @@ -446,23 +444,23 @@ The same is true if we don't make the limits explicit. (* begin hide *) -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". (* end hide *) -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. @@ -472,31 +470,31 @@ End 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSequence/I.con. +inline "cic:/CoRN/ftc/FunctSequence/I.con". (* end hide *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma b/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma index 70dddf1d4..869a6a3f9 100644 --- a/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma +++ b/matita/contribs/CoRN-Decl/ftc/FunctSeries.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSeries". +include "CoRN.ma". + (* $Id: FunctSeries.v,v 1.6 2004/04/23 10:00:58 lcf Exp $ *) -(* INCLUDE -FunctSequence -*) +include "ftc/FunctSequence.ma". -(* INCLUDE -Series -*) +include "reals/Series.ma". (*#* printing fun_seq_part_sum %\ensuremath{\sum^n}% #∑n# *) @@ -55,25 +53,25 @@ defined in a compact interval. For this, partial sums are defined and 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSeries/I.con. +inline "cic:/CoRN/ftc/FunctSeries/I.con". (* end hide *) -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 @@ -81,7 +79,7 @@ series of functions implies pointwise convergence of the corresponding real number series. *) -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. @@ -89,21 +87,21 @@ the corresponding series. (* begin show *) -inline cic:/CoRN/ftc/FunctSeries/H.var. +inline "cic:/CoRN/ftc/FunctSeries/H.var". (* 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". (* end hide *) -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. @@ -121,17 +119,17 @@ Hint Resolve fun_seq_part_sum_cont: continuous. 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. *) -inline cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con". (* UNEXPORTED End More_Definitions. @@ -146,70 +144,70 @@ Section Operations. 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSeries/I.con. +inline "cic:/CoRN/ftc/FunctSeries/I.con". (* end hide *) -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". (* begin show *) -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". (* end show *) -inline cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con". (* begin show *) -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". (* end show *) -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}% *) -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. @@ -219,25 +217,25 @@ End 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSeries/I.con. +inline "cic:/CoRN/ftc/FunctSeries/I.con". (* end hide *) -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. @@ -247,15 +245,15 @@ End More_Operations. 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 @@ -263,15 +261,15 @@ partial sums; as a corollary we get the continuity of the sum of the series. *) -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. @@ -290,21 +288,21 @@ Section Convergence_Criteria. 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". (* begin hide *) -inline cic:/CoRN/ftc/FunctSeries/I.con. +inline "cic:/CoRN/ftc/FunctSeries/I.con". (* end hide *) -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. @@ -346,21 +344,21 @@ Transparent 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. *) -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. *) -inline cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con. +inline "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con". (* UNEXPORTED End Convergence_Criteria. diff --git a/matita/contribs/CoRN-Decl/ftc/FunctSums.ma b/matita/contribs/CoRN-Decl/ftc/FunctSums.ma index 5006a55f9..aeed9200c 100644 --- a/matita/contribs/CoRN-Decl/ftc/FunctSums.ma +++ b/matita/contribs/CoRN-Decl/ftc/FunctSums.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSums". +include "CoRN.ma". + (* $Id: FunctSums.v,v 1.5 2004/04/23 10:00:59 lcf Exp $ *) (*#* printing FSum0 %\ensuremath{\sum_0}% #∑0# *) @@ -24,13 +26,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/FunctSums". (*#* printing FSumx %\ensuremath{\sum'}% #∑'&*) -(* INCLUDE -CSumsReals -*) +include "reals/CSumsReals.ma". -(* INCLUDE -PartFunEquality -*) +include "ftc/PartFunEquality.ma". (*#* *Sums of Functions @@ -48,9 +46,9 @@ $\sum_{i=m}^nf_i$#the sum of fm through fn# ( [FSum]). *) -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 @@ -62,37 +60,37 @@ mentioned, their forming too big a type makes it impossible to use those results. *) -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 @@ -100,15 +98,15 @@ $\{f_i\}_{i=0}^{n-1}$ of #exactly n# functions; in this case we need 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. *) -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 @@ -117,9 +115,9 @@ explicitly assume that $f_i$#f1# is independent of the proof that function $f_i$#fi#. *) -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]. @@ -133,35 +131,35 @@ 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: *) -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. *) -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. *) -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". diff --git a/matita/contribs/CoRN-Decl/ftc/Integral.ma b/matita/contribs/CoRN-Decl/ftc/Integral.ma index 9241494f9..8ed0891f7 100644 --- a/matita/contribs/CoRN-Decl/ftc/Integral.ma +++ b/matita/contribs/CoRN-Decl/ftc/Integral.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/Integral". +include "CoRN.ma". + (* $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}% #∫I# *) @@ -32,9 +32,9 @@ RefLemma Section Lemmas. *) -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. @@ -59,21 +59,21 @@ continuous functions in [I]. %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) @@ -81,11 +81,11 @@ inline cic:/CoRN/ftc/Integral/contF'.con. Section Darboux_Sum. *) -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. @@ -106,31 +106,31 @@ respecting [P]. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/Integral/d.con. +inline "cic:/CoRN/ftc/Integral/d.con". (* end hide *) -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. @@ -148,15 +148,15 @@ Section Basic_Properties. 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". (* begin hide *) -inline cic:/CoRN/ftc/Integral/I.con. +inline "cic:/CoRN/ftc/Integral/I.con". (* end hide *) @@ -164,21 +164,21 @@ inline cic:/CoRN/ftc/Integral/I.con. 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. @@ -196,25 +196,25 @@ Opaque Even_Partition. The integral is a linear and monotonous function; in order to prove these facts we also need the important equalities $\int_a^bdx=b-a$#∫abdx=b-a# and $\int_a^af(x)dx=0$#∫aa=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. *) -inline cic:/CoRN/ftc/Integral/integral_empty.con. +inline "cic:/CoRN/ftc/Integral/integral_empty.con". (* UNEXPORTED End Linearity_and_Monotonicity. @@ -224,13 +224,13 @@ End 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 @@ -238,25 +238,25 @@ inline cic:/CoRN/ftc/Integral/contG.var. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/Integral/h.con. +inline "cic:/CoRN/ftc/Integral/h.con". (* end hide *) -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. *) -inline cic:/CoRN/ftc/Integral/monotonous_integral.con. +inline "cic:/CoRN/ftc/Integral/monotonous_integral.con". (* UNEXPORTED Transparent nring. @@ -270,33 +270,33 @@ End Linearity_and_Monotonicity'. Section Corollaries. *) -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. *) -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. *) -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. @@ -315,19 +315,19 @@ $c\in[a,b]$#c∈[a,b]#. %\end{convention}% *) -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. @@ -345,41 +345,41 @@ inequality). %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/Integral/partition_join_aux.con. +inline "cic:/CoRN/ftc/Integral/partition_join_aux.con". (* end hide *) -inline cic:/CoRN/ftc/Integral/partition_join_fun.con. +inline "cic:/CoRN/ftc/Integral/partition_join_fun.con". (* begin hide *) -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". (* end hide *) @@ -388,39 +388,39 @@ inline cic:/CoRN/ftc/Integral/partition_join.con. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/Integral/partition_join_aux'.con. +inline "cic:/CoRN/ftc/Integral/partition_join_aux'.con". (* end hide *) -inline cic:/CoRN/ftc/Integral/partition_join_pts.con. +inline "cic:/CoRN/ftc/Integral/partition_join_pts.con". (* begin hide *) -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". (* end hide *) -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. @@ -446,9 +446,9 @@ Opaque minus. Transparent minus. *) -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. @@ -462,7 +462,7 @@ With these results in mind, the following is a trivial consequence: 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. @@ -480,11 +480,11 @@ End Basic_Properties. 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". (* end hide *) -inline cic:/CoRN/ftc/Integral/integral_gt_zero.con. +inline "cic:/CoRN/ftc/Integral/integral_gt_zero.con". (* end hide *) diff --git a/matita/contribs/CoRN-Decl/ftc/IntervalFunct.ma b/matita/contribs/CoRN-Decl/ftc/IntervalFunct.ma index 9001c6b48..bf128f9a0 100644 --- a/matita/contribs/CoRN-Decl/ftc/IntervalFunct.ma +++ b/matita/contribs/CoRN-Decl/ftc/IntervalFunct.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/IntervalFunct". +include "CoRN.ma". + (* $Id: IntervalFunct.v,v 1.5 2004/04/08 15:28:06 lcf Exp $ *) -(* INCLUDE -PartFunEquality -*) +include "ftc/PartFunEquality.ma". (* UNEXPORTED Section Operations. @@ -47,21 +47,21 @@ type [I -> IR]. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/IntervalFunct/I.con. +inline "cic:/CoRN/ftc/IntervalFunct/I.con". (* end hide *) -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. @@ -74,39 +74,39 @@ Constant and identity functions are defined. %\end{convention}% *) -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. *) -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. *) -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. @@ -116,11 +116,11 @@ Section Nth_Power. 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. @@ -136,17 +136,17 @@ Section Recip_Div. (* begin show *) -inline cic:/CoRN/ftc/IntervalFunct/Hg.var. +inline "cic:/CoRN/ftc/IntervalFunct/Hg.var". (* end show *) -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. @@ -156,9 +156,9 @@ End Recip_Div. 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. @@ -186,39 +186,39 @@ compact interval [[a',b']], and let [g] be a setoid function of type Section Composition. *) -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". (* begin hide *) -inline cic:/CoRN/ftc/IntervalFunct/I.con. +inline "cic:/CoRN/ftc/IntervalFunct/I.con". (* end hide *) -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". (* begin hide *) -inline cic:/CoRN/ftc/IntervalFunct/I'.con. +inline "cic:/CoRN/ftc/IntervalFunct/I'.con". (* end hide *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma b/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma index 0aae72baa..20eaa0dcd 100644 --- a/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma +++ b/matita/contribs/CoRN-Decl/ftc/MoreFunSeries.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreFunSeries". +include "CoRN.ma". + (* $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}}% #∑'∞# *) @@ -54,35 +52,35 @@ Some of the definitions do not make sense in this more general setting 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. *) -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. @@ -96,21 +94,21 @@ Section More_Definitions. 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". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/conv.var. +inline "cic:/CoRN/ftc/MoreFunSeries/conv.var". (* end show *) -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. @@ -125,33 +123,33 @@ Section Irrelevance_of_Proofs. 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". (* begin show *) -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". (* end show *) -inline cic:/CoRN/ftc/MoreFunSeries/F.var. +inline "cic:/CoRN/ftc/MoreFunSeries/F.var". (* begin show *) -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". (* end show *) -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. @@ -165,55 +163,55 @@ Opaque Cauchy_fun_seq_Lim_IR. 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". (* begin show *) -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". (* end show *) -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". (* begin show *) -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". (* end show *) -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. @@ -232,45 +230,45 @@ Section Algebraic_Properties. 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". (* begin show *) -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". (* end show *) -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. @@ -284,39 +282,39 @@ Section More_Algebraic_Properties. 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". (* begin show *) -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". (* end show *) -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. @@ -331,15 +329,15 @@ Section Other. 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. *) -inline cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con. +inline "cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con". (* UNEXPORTED End Other. @@ -356,35 +354,35 @@ We now consider series of functions defined in arbitrary intervals. 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". (* begin show *) -inline cic:/CoRN/ftc/MoreFunSeries/H.var. +inline "cic:/CoRN/ftc/MoreFunSeries/H.var". (* end show *) -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 *) -inline cic:/CoRN/ftc/MoreFunSeries/h.con. +inline "cic:/CoRN/ftc/MoreFunSeries/h.con". (* end hide *) -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. @@ -398,15 +396,15 @@ Implicit Arguments FSeries_Sum [J f]. 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. *) -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. @@ -420,17 +418,17 @@ Section Convergence_Results. 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. @@ -453,58 +451,58 @@ Section 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". (* begin show *) -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". (* end show *) -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}% *) -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. @@ -520,19 +518,19 @@ The most important tests for convergence of series still apply: the 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. @@ -551,21 +549,21 @@ $f_i$#fi# and inserting the null function in the first 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. diff --git a/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma b/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma index 8f0aeeda6..71333c0bd 100644 --- a/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma +++ b/matita/contribs/CoRN-Decl/ftc/MoreFunctions.ma @@ -16,13 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreFunctions". +include "CoRN.ma". + (* $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. @@ -44,38 +44,38 @@ arbitrary intervals. **Continuity *) -inline cic:/CoRN/ftc/MoreFunctions/I.var. +inline "cic:/CoRN/ftc/MoreFunctions/I.var". (*#* Trivial stuff. *) -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}% *) -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". (* begin show *) -inline cic:/CoRN/ftc/MoreFunctions/Hinc.var. +inline "cic:/CoRN/ftc/MoreFunctions/Hinc.var". (* end show *) -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. @@ -93,45 +93,45 @@ Section Other_Results. The usual stuff. *) -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". (* begin show *) -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". (* end show *) -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. @@ -151,21 +151,21 @@ Hint Immediate included_imp_Continuous Included_imp_Continuous: continuous. Section Corollaries. *) -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. @@ -179,22 +179,22 @@ Hint Resolve Continuous_div: continuous. Section Sums. *) -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}% *) -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". (* UNEXPORTED End Sums. @@ -216,29 +216,29 @@ Derivative is not that much different. %\end{convention}% *) -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. @@ -257,48 +257,48 @@ Hint Immediate Derivative_imp_Continuous Derivative_imp_Continuous': Section More_Results. *) -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}% *) -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. @@ -308,29 +308,29 @@ End More_Results. 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". (* begin show *) -inline cic:/CoRN/ftc/MoreFunctions/Gbnd.var. +inline "cic:/CoRN/ftc/MoreFunctions/Gbnd.var". (* end show *) -inline cic:/CoRN/ftc/MoreFunctions/Derivative_div.con. +inline "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con". (* UNEXPORTED End More_Corollaries. @@ -340,25 +340,25 @@ End More_Corollaries. Section More_Sums. *) -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". (* begin show *) -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". (* end show *) -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. @@ -373,50 +373,50 @@ Section Diffble_Basic_Properties. 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}% *) -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. @@ -430,25 +430,25 @@ Hint Immediate Diffble_imp_inc: included. 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. @@ -463,9 +463,9 @@ Section Nth_Derivative. 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. @@ -476,24 +476,24 @@ Section Definitions. %\end{convention}% *) -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". (* end hide *) -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. @@ -507,39 +507,39 @@ Section Basic_Results. 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. @@ -553,21 +553,21 @@ Section More_Results. 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. *) -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. @@ -581,17 +581,17 @@ Section Derivating_Diffble. As a special case we get a differentiation operator%\ldots%#...# *) -inline cic:/CoRN/ftc/MoreFunctions/F.var. +inline "cic:/CoRN/ftc/MoreFunctions/F.var". (* begin show *) -inline cic:/CoRN/ftc/MoreFunctions/diffF.var. +inline "cic:/CoRN/ftc/MoreFunctions/diffF.var". (* end show *) -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. @@ -605,19 +605,19 @@ Section Corollaries. %\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. *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/MoreIntegrals.ma b/matita/contribs/CoRN-Decl/ftc/MoreIntegrals.ma index 062018bf9..50a087bf7 100644 --- a/matita/contribs/CoRN-Decl/ftc/MoreIntegrals.ma +++ b/matita/contribs/CoRN-Decl/ftc/MoreIntegrals.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreIntegrals". +include "CoRN.ma". + (* $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. @@ -50,15 +48,15 @@ partial functions continuous in [[Min(a,b),Max(a,b)]]. 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. @@ -76,23 +74,23 @@ classical definition, and it collapses to the old one in the case [a [<=] b]. *) -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. @@ -112,55 +110,55 @@ All our old properties carry over to this new definition---and some 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. *) -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. *) -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. *) -inline cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con. +inline "cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con". (* UNEXPORTED End Properties_of_Integral. @@ -174,9 +172,9 @@ Section More_Properties. 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. @@ -185,81 +183,81 @@ And now we can prove the addition law for domains with our general operator. %\end{convention}% *) -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". (* begin show *) -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 *) -inline cic:/CoRN/ftc/MoreIntegrals/F.var. +inline "cic:/CoRN/ftc/MoreIntegrals/F.var". (* begin show *) -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 *) -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". (* end hide *) -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 @@ -274,31 +272,31 @@ End More_Properties. Section Corollaries. *) -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: *) -inline cic:/CoRN/ftc/MoreIntegrals/Integral_op.con. +inline "cic:/CoRN/ftc/MoreIntegrals/Integral_op.con". (*#* 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. *) -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". diff --git a/matita/contribs/CoRN-Decl/ftc/MoreIntervals.ma b/matita/contribs/CoRN-Decl/ftc/MoreIntervals.ma index 9f87239b1..b428e2ee5 100644 --- a/matita/contribs/CoRN-Decl/ftc/MoreIntervals.ma +++ b/matita/contribs/CoRN-Decl/ftc/MoreIntervals.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/MoreIntervals". +include "CoRN.ma". + (* $Id: MoreIntervals.v,v 1.6 2004/04/23 10:00:59 lcf Exp $ *) -(* INCLUDE -NthDerivative -*) +include "ftc/NthDerivative.ma". (* UNEXPORTED Opaque Min Max. @@ -101,16 +101,18 @@ from this point on we can work with any kind of intervals in exactly the same way. *) -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: *) -inline cic:/CoRN/ftc/MoreIntervals/iprop.con. +inline "cic:/CoRN/ftc/MoreIntervals/iprop.con". (* begin hide *) +coercion "cic:/matita/CoRN-Decl/ftc/MoreIntervals/iprop.con" 0 (* compounds *). + (* end hide *) (*#* @@ -121,67 +123,67 @@ We now define what it means for an interval to be nonvoid, proper, 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. *) -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. *) -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. *) -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. *) -inline cic:/CoRN/ftc/MoreIntervals/Lend_leEq_Rend.con. +inline "cic:/CoRN/ftc/MoreIntervals/Lend_leEq_Rend.con". (*#* 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. *) -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. *) -inline cic:/CoRN/ftc/MoreIntervals/iprop_wd.con. +inline "cic:/CoRN/ftc/MoreIntervals/iprop_wd.con". (* UNEXPORTED End Intervals. @@ -214,25 +216,25 @@ such that [P(x)] holds. %\end{convention}% *) -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#. *) -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. @@ -242,7 +244,7 @@ End Single_Compact_Interval. 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. @@ -258,49 +260,49 @@ Section Proper_Compact_with_One_or_Two_Points. (* begin hide *) -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". (* end hide *) -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 @@ -309,43 +311,43 @@ stage, which is why we formalized this result as a functional 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. *) -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. @@ -355,9 +357,9 @@ End Proper_Compact_with_One_or_Two_Points. 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# @@ -365,7 +367,7 @@ and [J] is proper, then we can find a proper interval [[a',b']] such that $[a,b]\subseteq[a',b']\subseteq J$#[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. @@ -387,19 +389,19 @@ previously defined concepts. %\end{convention}% *) -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. @@ -413,17 +415,17 @@ Section Reflexivity_Properties. 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. @@ -437,11 +439,11 @@ Section Lemmas. 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. diff --git a/matita/contribs/CoRN-Decl/ftc/NthDerivative.ma b/matita/contribs/CoRN-Decl/ftc/NthDerivative.ma index 7f918465b..0900e8703 100644 --- a/matita/contribs/CoRN-Decl/ftc/NthDerivative.ma +++ b/matita/contribs/CoRN-Decl/ftc/NthDerivative.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/NthDerivative". +include "CoRN.ma". + (* $Id: NthDerivative.v,v 1.5 2004/04/20 22:38:50 hinderer Exp $ *) -(* INCLUDE -Differentiability -*) +include "ftc/Differentiability.ma". (* UNEXPORTED Section Nth_Derivative. @@ -42,21 +42,21 @@ We now study higher order differentiability. 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". (* begin hide *) -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". (* end hide *) -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 @@ -65,7 +65,7 @@ to be [n] times differentiable instead of quantifying over the [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. @@ -88,27 +88,27 @@ Section Trivia. 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". (* begin hide *) -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". (* end hide *) -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. @@ -126,17 +126,17 @@ the relation of [n] times derivative, but focus rather on the 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". (* begin hide *) -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". (* end hide *) @@ -144,15 +144,15 @@ inline cic:/CoRN/ftc/NthDerivative/I.con. 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]. *) -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] @@ -160,31 +160,31 @@ times differentiable if we can build from it a chain of [n] derivatives. *) -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. *) -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. *) -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. *) -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. @@ -196,17 +196,17 @@ First order differentiability is just a special case. (* begin show *) -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". (* end show *) -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". (* UNEXPORTED End aux. @@ -216,15 +216,15 @@ End aux. 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. *) -inline cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con. +inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con". (* UNEXPORTED End Basic_Results. @@ -234,17 +234,17 @@ End Basic_Results. Section More_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". (* begin hide *) -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". (* end hide *) @@ -256,27 +256,27 @@ elimination which we would get if we had defined nth differentiability 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. *) -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. *) -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. @@ -290,11 +290,11 @@ Section More_on_n_deriv. 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. diff --git a/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma b/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma index 0ca5ba98a..c3b8f1c56 100644 --- a/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma +++ b/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma @@ -16,17 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/PartFunEquality". +include "CoRN.ma". + (* $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. @@ -42,7 +40,7 @@ given predicate rather than to the predicate itself. The following 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 @@ -54,7 +52,7 @@ it is easier to consider a generic case%.}%. This file is concerned 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, @@ -89,32 +87,32 @@ by [P] and [Q], respectively, the domains of [F] and [G]. %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) -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: *) -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. @@ -132,7 +130,7 @@ Section Some_More. 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. @@ -158,17 +156,17 @@ the domain of [F]. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/PartFunEquality/P.con. +inline "cic:/CoRN/ftc/PartFunEquality/P.con". (* end hide *) -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]. @@ -176,15 +174,15 @@ If [F] is bounded away from zero in [I] then [F] is necessarily apart from zero (* begin show *) -inline cic:/CoRN/ftc/PartFunEquality/Hf.var. +inline "cic:/CoRN/ftc/PartFunEquality/Hf.var". (* end show *) -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. @@ -197,31 +195,31 @@ Boundedness away from zero is preserved through restriction of the set. %\end{convention}% *) -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. *) -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: *) -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. @@ -263,23 +261,23 @@ partial functions. %\end{convention}% *) -inline cic:/CoRN/ftc/PartFunEquality/I.var. +inline "cic:/CoRN/ftc/PartFunEquality/I.var". (* 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. @@ -293,31 +291,31 @@ Section Operations. 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. @@ -325,13 +323,13 @@ Notice that in the case of division we only need to require boundedness away fro 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. *) -inline cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con. +inline "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con". (* UNEXPORTED End Operations. @@ -357,27 +355,27 @@ equality relation. %\end{convention}% *) -inline cic:/CoRN/ftc/PartFunEquality/F.var. +inline "cic:/CoRN/ftc/PartFunEquality/F.var". (* begin hide *) -inline cic:/CoRN/ftc/PartFunEquality/P.con. +inline "cic:/CoRN/ftc/PartFunEquality/P.con". (* end hide *) -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. @@ -393,25 +391,25 @@ is included in the domain of [F]. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/PartFunEquality/I.con. +inline "cic:/CoRN/ftc/PartFunEquality/I.con". (* end hide *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/PartInterval.ma b/matita/contribs/CoRN-Decl/ftc/PartInterval.ma index b4f8515cf..47e164663 100644 --- a/matita/contribs/CoRN-Decl/ftc/PartInterval.ma +++ b/matita/contribs/CoRN-Decl/ftc/PartInterval.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/PartInterval". +include "CoRN.ma". + (* $Id: PartInterval.v,v 1.6 2004/04/23 10:01:00 lcf Exp $ *) -(* INCLUDE -IntervalFunct -*) +include "ftc/IntervalFunct.ma". (* UNEXPORTED Section Conversion. @@ -45,25 +45,25 @@ that [I [=] [a,b]] is included in the domain of [F]. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/PartInterval/I.con. +inline "cic:/CoRN/ftc/PartInterval/I.con". (* end hide *) -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. @@ -82,23 +82,23 @@ To go the other way around, we simply take a setoid function [f] with 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". (* begin hide *) -inline cic:/CoRN/ftc/PartInterval/I.con. +inline "cic:/CoRN/ftc/PartInterval/I.con". (* end hide *) -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. @@ -116,7 +116,7 @@ Section 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. @@ -137,57 +137,57 @@ type [I->IR] equal respectively to [F] and [G] in [I]. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/PartInterval/I.con. +inline "cic:/CoRN/ftc/PartInterval/I.con". (* end hide *) -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". (* begin show *) -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". (* end show *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/Partitions.ma b/matita/contribs/CoRN-Decl/ftc/Partitions.ma index 6c29c9ece..e6a6dabb6 100644 --- a/matita/contribs/CoRN-Decl/ftc/Partitions.ma +++ b/matita/contribs/CoRN-Decl/ftc/Partitions.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/Partitions". +include "CoRN.ma". + (* $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}% #∑P# *) @@ -50,15 +50,17 @@ coercion); *) -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]. *) -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 @@ -67,9 +69,9 @@ important role in much of our future work, so we take some care to define it. *) -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 @@ -83,11 +85,11 @@ of defining the minimum and maximum of the empty list to be [0] actually 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) @@ -95,38 +97,38 @@ will also play a central role in our work; the first two lemmas are 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. *) -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. *) -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 @@ -137,11 +139,11 @@ For this, we again need a choice function [x] which has to satisfy 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. @@ -163,15 +165,15 @@ We now formalize some trivial and helpful constructions. %\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/Hab.var. +inline "cic:/CoRN/ftc/Partitions/Hab.var". (* begin hide *) -inline cic:/CoRN/ftc/Partitions/I.con. +inline "cic:/CoRN/ftc/Partitions/I.con". (* end hide *) @@ -188,15 +190,15 @@ partition. %\end{convention}% *) -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. @@ -206,11 +208,11 @@ 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]]. *) -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. @@ -273,21 +275,21 @@ Section Lemmas. 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. *) -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. *) -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 @@ -298,27 +300,27 @@ with [n] points. %\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". (* begin hide *) -inline cic:/CoRN/ftc/Partitions/I.con. +inline "cic:/CoRN/ftc/Partitions/I.con". (* end hide *) -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. @@ -331,40 +333,40 @@ Section Even_Partitions. (*#* 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. *) -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}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/Partitions/I.con. +inline "cic:/CoRN/ftc/Partitions/I.con". (* end hide *) -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]. *) -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 @@ -375,23 +377,23 @@ denote by [P] and [Q] the even partitions with, respectively, [m] and 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". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/ftc/Partitions/even_partition_refinement.con. +inline "cic:/CoRN/ftc/Partitions/even_partition_refinement.con". (* UNEXPORTED End Even_Partitions. @@ -406,13 +408,13 @@ Section More_Definitions. 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 @@ -424,15 +426,15 @@ respectively, [n] and [m] points. %\end{convention}% *) -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. @@ -450,23 +452,23 @@ Implicit Arguments Separated [a b Hab n m]. 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". (* begin hide *) -inline cic:/CoRN/ftc/Partitions/I.con. +inline "cic:/CoRN/ftc/Partitions/I.con". (* end hide *) -inline cic:/CoRN/ftc/Partitions/Hab.var. +inline "cic:/CoRN/ftc/Partitions/Hab.var". (*#* 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 @@ -474,11 +476,11 @@ are the same; moreover, if the partition is separated and the 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. diff --git a/matita/contribs/CoRN-Decl/ftc/RefLemma.ma b/matita/contribs/CoRN-Decl/ftc/RefLemma.ma index 485ca2433..e0bfd909a 100644 --- a/matita/contribs/CoRN-Decl/ftc/RefLemma.ma +++ b/matita/contribs/CoRN-Decl/ftc/RefLemma.ma @@ -16,19 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefLemma". +include "CoRN.ma". + (* $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. @@ -85,27 +81,27 @@ Using the results from these files, we prove our main lemma in several steps %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/RefLemma/I.con. +inline "cic:/CoRN/ftc/RefLemma/I.con". (* end hide *) -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". (* begin hide *) -inline cic:/CoRN/ftc/RefLemma/contF'.con. +inline "cic:/CoRN/ftc/RefLemma/contF'.con". (* end hide *) @@ -128,87 +124,87 @@ respectively. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/RefLemma/d.con. +inline "cic:/CoRN/ftc/RefLemma/d.con". (* end hide *) -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". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con. +inline "cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con". (* UNEXPORTED End First_Refinement_Lemma. @@ -234,55 +230,55 @@ and [R], respectively. %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) -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. @@ -308,117 +304,117 @@ respectively; %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) -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". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con. +inline "cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con". (* UNEXPORTED End Third_Refinement_Lemma. @@ -430,9 +426,9 @@ Section Fourth_Refinement_Lemma. (* begin hide *) -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". (* end hide *) @@ -441,53 +437,53 @@ Finally, this is inequality (2.6.7) exactly as stated (same conventions as above) *) -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". (* begin hide *) -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". (* end hide *) -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". (* begin show *) -inline cic:/CoRN/ftc/RefLemma/Hab'.var. +inline "cic:/CoRN/ftc/RefLemma/Hab'.var". (* end show *) -inline cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con. +inline "cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con". (* UNEXPORTED End Fourth_Refinement_Lemma. @@ -499,47 +495,47 @@ Section Main_Refinement_Lemma. (*#* 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". (* begin hide *) -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". (* end hide *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/RefSepRef.ma b/matita/contribs/CoRN-Decl/ftc/RefSepRef.ma index 99a1c3183..ab403b372 100644 --- a/matita/contribs/CoRN-Decl/ftc/RefSepRef.ma +++ b/matita/contribs/CoRN-Decl/ftc/RefSepRef.ma @@ -16,131 +16,129 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefSepRef". +include "CoRN.ma". + (* $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. *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/RefSeparated.ma b/matita/contribs/CoRN-Decl/ftc/RefSeparated.ma index a65a4ecda..186466579 100644 --- a/matita/contribs/CoRN-Decl/ftc/RefSeparated.ma +++ b/matita/contribs/CoRN-Decl/ftc/RefSeparated.ma @@ -16,155 +16,153 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefSeparated". +include "CoRN.ma". + (* $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. *) -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'. *) -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'. *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/RefSeparating.ma b/matita/contribs/CoRN-Decl/ftc/RefSeparating.ma index 1710d161c..7ad89a0f2 100644 --- a/matita/contribs/CoRN-Decl/ftc/RefSeparating.ma +++ b/matita/contribs/CoRN-Decl/ftc/RefSeparating.ma @@ -16,151 +16,149 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/RefSeparating". +include "CoRN.ma". + (* $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. *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/Rolle.ma b/matita/contribs/CoRN-Decl/ftc/Rolle.ma index c8e8cdc4f..21e3b8c34 100644 --- a/matita/contribs/CoRN-Decl/ftc/Rolle.ma +++ b/matita/contribs/CoRN-Decl/ftc/Rolle.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/Rolle". +include "CoRN.ma". + (* $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. @@ -44,113 +42,113 @@ We now begin to work with partial functions. We begin by stating and proving Ro (* begin hide *) -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 *) -inline cic:/CoRN/ftc/Rolle/Fab.var. +inline "cic:/CoRN/ftc/Rolle/Fab.var". (* 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". (* end hide *) -inline cic:/CoRN/ftc/Rolle/Rolle.con. +inline "cic:/CoRN/ftc/Rolle/Rolle.con". (* UNEXPORTED End Rolle. @@ -164,35 +162,35 @@ Section Law_of_the_Mean. 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". (* begin hide *) -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". (* end hide *) -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". (* begin show *) -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 show *) -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. @@ -206,29 +204,29 @@ Section Corollaries. 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". (* begin hide *) -inline cic:/CoRN/ftc/Rolle/Hab.con. +inline "cic:/CoRN/ftc/Rolle/Hab.con". (* end hide *) -inline cic:/CoRN/ftc/Rolle/F.var. +inline "cic:/CoRN/ftc/Rolle/F.var". (* begin show *) -inline cic:/CoRN/ftc/Rolle/HF.var. +inline "cic:/CoRN/ftc/Rolle/HF.var". (* end show *) -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. @@ -248,35 +246,35 @@ state it also in this form. %\end{convention}% *) -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". (* begin show *) -inline cic:/CoRN/ftc/Rolle/derF.var. +inline "cic:/CoRN/ftc/Rolle/derF.var". (* 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". (* end hide *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/ftc/StrongIVT.ma b/matita/contribs/CoRN-Decl/ftc/StrongIVT.ma index b27af136a..fe8820e0a 100644 --- a/matita/contribs/CoRN-Decl/ftc/StrongIVT.ma +++ b/matita/contribs/CoRN-Decl/ftc/StrongIVT.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/StrongIVT". +include "CoRN.ma". + (* $Id: StrongIVT.v,v 1.5 2004/04/23 10:01:01 lcf Exp $ *) -(* INCLUDE -WeakIVT -*) +include "ftc/WeakIVT.ma". -(* INCLUDE -CalculusTheorems -*) +include "ftc/CalculusTheorems.ma". (* UNEXPORTED Section IVT'. @@ -38,103 +36,103 @@ part, we will simply do that, repeating the previous construction. 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". (* begin hide *) -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". (* end hide *) -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". (* begin hide *) -inline cic:/CoRN/ftc/StrongIVT/incF.con. +inline "cic:/CoRN/ftc/StrongIVT/incF.con". (* end hide *) (* begin show *) -inline cic:/CoRN/ftc/StrongIVT/incrF.var. +inline "cic:/CoRN/ftc/StrongIVT/incrF.var". (* 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 *) -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". (* end show *) -inline cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con. +inline "cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con". (* end hide *) -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". (* UNEXPORTED End IVT'. @@ -146,21 +144,21 @@ We now generalize the various statements of the intermediate value 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. *) -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. *) -inline cic:/CoRN/ftc/StrongIVT/IVT'_dec.con. +inline "cic:/CoRN/ftc/StrongIVT/IVT'_dec.con". diff --git a/matita/contribs/CoRN-Decl/ftc/Taylor.ma b/matita/contribs/CoRN-Decl/ftc/Taylor.ma index e636e5518..9a9437ade 100644 --- a/matita/contribs/CoRN-Decl/ftc/Taylor.ma +++ b/matita/contribs/CoRN-Decl/ftc/Taylor.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/Taylor". +include "CoRN.ma". + (* $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. @@ -39,53 +39,53 @@ The generalization to arbitrary intervals just needs a few more definitions. %\end{convention}% *) -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". (* begin show *) -inline cic:/CoRN/ftc/Taylor/deriv_Sn.con. +inline "cic:/CoRN/ftc/Taylor/deriv_Sn.con". (* end show *) -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". (* begin show *) -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". (* end show *) -inline cic:/CoRN/ftc/Taylor/Taylor_Seq'.con. +inline "cic:/CoRN/ftc/Taylor/Taylor_Seq'.con". (* begin hide *) -inline cic:/CoRN/ftc/Taylor/TaylorB.con. +inline "cic:/CoRN/ftc/Taylor/TaylorB.con". (* end hide *) -inline cic:/CoRN/ftc/Taylor/Taylor_Rem.con. +inline "cic:/CoRN/ftc/Taylor/Taylor_Rem.con". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/ftc/Taylor/Taylor'.con. +inline "cic:/CoRN/ftc/Taylor/Taylor'.con". (* UNEXPORTED End More_Taylor_Defs. @@ -104,51 +104,51 @@ order up to [n] and [F'] be the nth-derivative of [F]. %\end{convention}% *) -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". (* begin show *) -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". (* end show *) -inline cic:/CoRN/ftc/Taylor/Taylor_aux.con. +inline "cic:/CoRN/ftc/Taylor/Taylor_aux.con". (* UNEXPORTED Transparent N_Deriv. *) -inline cic:/CoRN/ftc/Taylor/Taylor.con. +inline "cic:/CoRN/ftc/Taylor/Taylor.con". (* UNEXPORTED End Taylor_Theorem. diff --git a/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma b/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma index 0fc554356..7e6851627 100644 --- a/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma +++ b/matita/contribs/CoRN-Decl/ftc/TaylorLemma.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/TaylorLemma". +include "CoRN.ma". + (* $Id: TaylorLemma.v,v 1.8 2004/04/23 10:01:01 lcf Exp $ *) -(* INCLUDE -Rolle -*) +include "ftc/Rolle.ma". (* UNEXPORTED Opaque Min. @@ -44,31 +44,31 @@ define the nth order derivative of [F] in the interval [[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". (* begin hide *) -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". (* end hide *) -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". (* begin show *) -inline cic:/CoRN/ftc/TaylorLemma/fi.con. +inline "cic:/CoRN/ftc/TaylorLemma/fi.con". (* end show *) @@ -79,7 +79,7 @@ $f_i=f^{(i)}$#fi=f(i)#. (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con". (* end hide *) @@ -94,41 +94,41 @@ corresponding to [a] and [b]. (* begin hide *) -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 *) -inline cic:/CoRN/ftc/TaylorLemma/funct_i.con. +inline "cic:/CoRN/ftc/TaylorLemma/funct_i.con". (* 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". (* end hide *) @@ -137,13 +137,13 @@ Adding the previous expressions up to a given bound [n] gives us the Taylor sum of order [n]. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con". (* begin hide *) -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". (* end hide *) @@ -151,21 +151,21 @@ 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]. *) -inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con. +inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con". (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/g.con. +inline "cic:/CoRN/ftc/TaylorLemma/g.con". (* UNEXPORTED Opaque Taylor_seq'_aux Taylor_rem. @@ -191,7 +191,7 @@ Opaque funct_i'. Opaque funct_i. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con". (* UNEXPORTED Transparent funct_i funct_i'. @@ -213,15 +213,15 @@ Opaque FSumx. Opaque funct_i'. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con". (* 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 := @@ -245,9 +245,9 @@ Ltac Lazy_Eq := | 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. @@ -257,15 +257,15 @@ Opaque 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. *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con". (* UNEXPORTED Transparent Taylor_rem funct_aux. @@ -280,25 +280,25 @@ Now Taylor's theorem. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con. +inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con". (* end hide *) (* begin show *) -inline cic:/CoRN/ftc/TaylorLemma/deriv_Sn'.con. +inline "cic:/CoRN/ftc/TaylorLemma/deriv_Sn'.con". (* end show *) (* begin hide *) -inline cic:/CoRN/ftc/TaylorLemma/TLH.con. +inline "cic:/CoRN/ftc/TaylorLemma/TLH.con". (* end hide *) @@ -314,7 +314,7 @@ Opaque Taylor_rem. 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. diff --git a/matita/contribs/CoRN-Decl/ftc/WeakIVT.ma b/matita/contribs/CoRN-Decl/ftc/WeakIVT.ma index a66df65e1..640b150a6 100644 --- a/matita/contribs/CoRN-Decl/ftc/WeakIVT.ma +++ b/matita/contribs/CoRN-Decl/ftc/WeakIVT.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/WeakIVT". +include "CoRN.ma". + (* $Id: WeakIVT.v,v 1.9 2004/04/23 10:01:01 lcf Exp $ *) (*#* printing ** %\ensuremath\times% #×# *) @@ -24,9 +26,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/ftc/WeakIVT". (* end hide *) -(* INCLUDE -Continuity -*) +include "ftc/Continuity.ma". (*#* *IVT for Partial Functions @@ -43,21 +43,21 @@ will prove them here. Section 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". (* begin hide *) -inline cic:/CoRN/ftc/WeakIVT/I.con. +inline "cic:/CoRN/ftc/WeakIVT/I.con". (* end hide *) -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". (*#* **First Lemmas @@ -70,7 +70,7 @@ We begin by proving that, if [f(a) [<] f(b)], then for every [y] in enough to [z]. *) -inline cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con. +inline "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con". (* UNEXPORTED End Lemma1. @@ -80,27 +80,27 @@ End Lemma1. Section Lemma2. *) -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". (* begin hide *) -inline cic:/CoRN/ftc/WeakIVT/I.con. +inline "cic:/CoRN/ftc/WeakIVT/I.con". (* end hide *) -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: *) -inline cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con. +inline "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con". (* UNEXPORTED End Lemma2. @@ -118,53 +118,53 @@ these assumptions, we can build two sequences of values which 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". (* begin hide *) -inline cic:/CoRN/ftc/WeakIVT/I.con. +inline "cic:/CoRN/ftc/WeakIVT/I.con". (* end hide *) -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". (* begin hide *) -inline cic:/CoRN/ftc/WeakIVT/incF.con. +inline "cic:/CoRN/ftc/WeakIVT/incF.con". (* end hide *) (* begin show *) -inline cic:/CoRN/ftc/WeakIVT/incrF.var. +inline "cic:/CoRN/ftc/WeakIVT/incrF.var". (* 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 *) -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". (* end show *) @@ -173,7 +173,7 @@ we can find [x' [<] y'] such that $|x'-y'|=\frac23|x-y|$#|x'-y'|=2/3|x-y|# and [x' [<=] z [<=] y']. *) -inline cic:/CoRN/ftc/WeakIVT/IVT_seq_lemma.con. +inline "cic:/CoRN/ftc/WeakIVT/IVT_seq_lemma.con". (* end hide *) @@ -181,51 +181,51 @@ inline cic:/CoRN/ftc/WeakIVT/IVT_seq_lemma.con. 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]. *) -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". (* UNEXPORTED End IVT. diff --git a/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma b/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma index 7996af496..3b0591a80 100644 --- a/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma +++ b/matita/contribs/CoRN-Decl/metrics/CMetricSpaces.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/metrics/CMetricSpaces". +include "CoRN.ma". + (* $Id: CMetricSpaces.v,v 1.4 2004/04/23 10:01:01 lcf Exp $ *) -(* INCLUDE -Prod_Sub -*) +include "metrics/Prod_Sub.ma". -(* INCLUDE -Equiv -*) +include "metrics/Equiv.ma". (* UNEXPORTED Section Definition_MS. @@ -33,7 +31,9 @@ Section Definition_MS. (*#* **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. @@ -46,11 +46,11 @@ Section MS_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. @@ -67,9 +67,9 @@ Section prodandsub. 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. @@ -79,9 +79,9 @@ A subspace of a metric space is again a metric space. 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]. @@ -102,69 +102,69 @@ Section Zeroff. 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: *) -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: *) -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: *) -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. @@ -187,17 +187,17 @@ Implicit Arguments MSseqLimit [X]. (* begin hide *) -inline cic:/CoRN/metrics/CMetricSpaces/nz.con. +inline "cic:/CoRN/metrics/CMetricSpaces/nz.con". (* end hide *) (* begin hide *) -inline cic:/CoRN/metrics/CMetricSpaces/d_wd.con. +inline "cic:/CoRN/metrics/CMetricSpaces/d_wd.con". (* end hide *) -inline cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con. +inline "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con". (* UNEXPORTED End Limitt. diff --git a/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma b/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma index fe04f4fb1..aef56d5a9 100644 --- a/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma +++ b/matita/contribs/CoRN-Decl/metrics/CPMSTheory.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/metrics/CPMSTheory". +include "CoRN.ma". + (* $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. @@ -37,19 +37,19 @@ finite sets of representants, instead of finite subsetoids. This seems to make the proofs a bit easier. *) -inline cic:/CoRN/metrics/CPMSTheory/MSmember.con. +inline "cic:/CoRN/metrics/CPMSTheory/MSmember.con". (* 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, @@ -57,14 +57,14 @@ it is an element of the list in the sense of [member], 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 $l$ #l# is member of the list of images of elements of $l$ #l#. *) -inline cic:/CoRN/metrics/CPMSTheory/map_member.con. +inline "cic:/CoRN/metrics/CPMSTheory/map_member.con". (* UNEXPORTED End lists. @@ -77,13 +77,13 @@ Section loc_and_bound. (*#* **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]. @@ -94,11 +94,11 @@ Again we see that the image under a certain mapping of an element of a list $l$ #l# is member of the list of images of elements of $l$ #l#. *) -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. @@ -108,18 +108,18 @@ Total boundedness is preserved under uniformly continuous mappings. 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. *) -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 $P$#P# of a pseudo metric space $X$#X# is said to be located if for all @@ -131,25 +131,25 @@ between $x$#x# and the elements of $P$#P#. 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]. *) -inline cic:/CoRN/metrics/CPMSTheory/located'.con. +inline "cic:/CoRN/metrics/CPMSTheory/located'.con". (* 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. *) -inline cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con. +inline "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con". (*#* For all $x$#x# in a pseudo metric space $X$#X#, for all located subspaces $P$#P# of $X$#X#, @@ -160,9 +160,9 @@ $d(x,y)\leq \mbox{inf}\{d(x,p)|p \in P\}+(n+1)^{-1}$ 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 $P$#P# of a totally bounded pseudo metric space $X$ @@ -170,33 +170,33 @@ A located subset $P$#P# of a totally bounded pseudo metric space $X$ bounded. *) -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: *) -inline cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con. +inline "cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con". (* 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. *) -inline cic:/CoRN/metrics/CPMSTheory/MSCompact.con. +inline "cic:/CoRN/metrics/CPMSTheory/MSCompact.con". (*#* A subset $P$#P# is %\emph{open}%#open# if for all $x$#x# in $P$#P# there exists an open sphere with centre $x$#x# that is contained in $P$#P#. *) -inline cic:/CoRN/metrics/CPMSTheory/open.con. +inline "cic:/CoRN/metrics/CPMSTheory/open.con". (* UNEXPORTED Implicit Arguments open [X]. @@ -208,7 +208,7 @@ element $x$#x# of a located pseudo metric space $X$#X# and the ele subspace $P$#P# of $X$#X#. *) -inline cic:/CoRN/metrics/CPMSTheory/infima.con. +inline "cic:/CoRN/metrics/CPMSTheory/infima.con". (* UNEXPORTED Implicit Arguments infima [X]. @@ -220,7 +220,7 @@ A non-empty totally bounded sub-pseudo-metric-space $P$#P# is said to be all points that are in some sense close to $P$#P#. *) -inline cic:/CoRN/metrics/CPMSTheory/well_contained.con. +inline "cic:/CoRN/metrics/CPMSTheory/well_contained.con". (* UNEXPORTED End loc_and_bound. diff --git a/matita/contribs/CoRN-Decl/metrics/CPseudoMSpaces.ma b/matita/contribs/CoRN-Decl/metrics/CPseudoMSpaces.ma index aacad5411..da7593236 100644 --- a/matita/contribs/CoRN-Decl/metrics/CPseudoMSpaces.ma +++ b/matita/contribs/CoRN-Decl/metrics/CPseudoMSpaces.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/metrics/CPseudoMSpaces". +include "CoRN.ma". + (* $Id: CPseudoMSpaces.v,v 1.3 2004/04/23 10:01:02 lcf Exp $ *) -(* INCLUDE -Intervals -*) +include "reals/Intervals.ma". (*#* *Metric Spaces *) @@ -35,9 +35,9 @@ Let [A : CSetoid], [d : (CSetoid_bin_fun A A IR)]. %\end{convention}% *) -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. @@ -47,13 +47,13 @@ Set Implicit Arguments. 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. @@ -63,9 +63,9 @@ Set Strict Implicit. 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. @@ -83,9 +83,11 @@ A pseudo metric space consists of a setoid and a %''pseudo metric''% #"pseudo me %''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. @@ -105,17 +107,17 @@ Let [A] be a pseudo metric space. %\end{convention}% *) -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. @@ -131,20 +133,20 @@ Let [Y] be a pseudo metric space. %\end{convention}% *) -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]. *) -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. @@ -162,23 +164,23 @@ Every setoid forms with the binary function that always returns zero, 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". (* UNEXPORTED End Zerof. diff --git a/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma b/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma index b4fa70689..0f93560af 100644 --- a/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma +++ b/matita/contribs/CoRN-Decl/metrics/ContFunctions.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/metrics/ContFunctions". +include "CoRN.ma". + (* $Id: ContFunctions.v,v 1.3 2004/04/23 10:01:02 lcf Exp $ *) -(* INCLUDE -CPseudoMSpaces -*) +include "metrics/CPseudoMSpaces.ma". (* UNEXPORTED Section Continuous_functions. @@ -32,27 +32,27 @@ Let [A] and [B] be pseudo metric spaces. %\end{convention}% *) -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. *) -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. @@ -92,32 +92,32 @@ Section Lemmas. (* begin hide *) -inline cic:/CoRN/metrics/ContFunctions/nexp_power.con. +inline "cic:/CoRN/metrics/ContFunctions/nexp_power.con". (* end hide *) -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. *) -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. @@ -135,11 +135,11 @@ The identity function is Lipschitz. 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. @@ -160,15 +160,15 @@ Any constant function is Lipschitz. 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. @@ -191,21 +191,21 @@ The composition of two Lipschitz/uniformly continous/continuous functions is 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. @@ -218,29 +218,29 @@ Section Limit. (*#* **Limit *) -inline cic:/CoRN/metrics/ContFunctions/MSseqLimit.con. +inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit.con". (* UNEXPORTED Implicit Arguments MSseqLimit [X]. *) -inline cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con. +inline "cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con". (* 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]. *) -inline cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con. +inline "cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con". (* UNEXPORTED End Limit. diff --git a/matita/contribs/CoRN-Decl/metrics/Equiv.ma b/matita/contribs/CoRN-Decl/metrics/Equiv.ma index 7001e836c..037029733 100644 --- a/matita/contribs/CoRN-Decl/metrics/Equiv.ma +++ b/matita/contribs/CoRN-Decl/metrics/Equiv.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/metrics/Equiv". +include "CoRN.ma". + (* $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. @@ -34,31 +34,31 @@ We say that two pseudo metric spaces are equivalent, when there exists a 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]. *) -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: *) -inline cic:/CoRN/metrics/Equiv/MSequivalent_discr.con. +inline "cic:/CoRN/metrics/Equiv/MSequivalent_discr.con". (* UNEXPORTED End equivalent. diff --git a/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma b/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma index 1df53a8ea..1bd2da730 100644 --- a/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma +++ b/matita/contribs/CoRN-Decl/metrics/IR_CPMSpace.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/metrics/IR_CPMSpace". +include "CoRN.ma". + (* $Id: IR_CPMSpace.v,v 1.4 2004/04/23 10:01:02 lcf Exp $ *) -(* INCLUDE -ContFunctions -*) +include "metrics/ContFunctions.ma". (* UNEXPORTED Section Reals. @@ -39,43 +39,43 @@ Let [X] be 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". (* begin hide *) -inline cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con. +inline "cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con". (* end hide *) -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. *) -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". (* UNEXPORTED End Reals. @@ -93,11 +93,11 @@ The sum of two Lipschitz/uniformly continous/continuous functions is again 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. diff --git a/matita/contribs/CoRN-Decl/metrics/Prod_Sub.ma b/matita/contribs/CoRN-Decl/metrics/Prod_Sub.ma index c1a6e78ed..f30b3c65d 100644 --- a/matita/contribs/CoRN-Decl/metrics/Prod_Sub.ma +++ b/matita/contribs/CoRN-Decl/metrics/Prod_Sub.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/metrics/Prod_Sub". +include "CoRN.ma". + (* $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. @@ -37,15 +37,15 @@ This is %\emph{not}% #not# the one used to make the metric of $\RR^{2}$ #IR2# 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. @@ -63,45 +63,45 @@ The pseudo metric on a subspace $Y$ #Y# of a pseudo metric space $X$ #X# is 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]. *) -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]. *) -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]. *) -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]. *) -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"#. @@ -109,21 +109,21 @@ It enables one to speak about a distance between an element of a 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]. *) -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]. *) -inline cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con. +inline "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con". (* UNEXPORTED End subpsmetrics. diff --git a/matita/contribs/CoRN-Decl/model/abgroups/QSposabgroup.ma b/matita/contribs/CoRN-Decl/model/abgroups/QSposabgroup.ma index 7c06302c1..4e6f57e8c 100644 --- a/matita/contribs/CoRN-Decl/model/abgroups/QSposabgroup.ma +++ b/matita/contribs/CoRN-Decl/model/abgroups/QSposabgroup.ma @@ -16,21 +16,19 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/QSposabgroup". +include "CoRN.ma". + (* $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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/abgroups/Qabgroup.ma b/matita/contribs/CoRN-Decl/model/abgroups/Qabgroup.ma index 1998b5209..57c6da7d6 100644 --- a/matita/contribs/CoRN-Decl/model/abgroups/Qabgroup.ma +++ b/matita/contribs/CoRN-Decl/model/abgroups/Qabgroup.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/Qabgroup". +include "CoRN.ma". + (* $Id: Qabgroup.v,v 1.5 2004/04/08 08:20:31 lcf Exp $ *) -(* INCLUDE -Qgroup -*) +include "model/groups/Qgroup.ma". -(* INCLUDE -CAbGroups -*) +include "algebra/CAbGroups.ma". (*#* **Example of an abelian group: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩# *) @@ -33,7 +31,7 @@ CAbGroups CAbGroup. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/abgroups/Qposabgroup.ma b/matita/contribs/CoRN-Decl/model/abgroups/Qposabgroup.ma index 49d70cf79..4c5f2b2d9 100644 --- a/matita/contribs/CoRN-Decl/model/abgroups/Qposabgroup.ma +++ b/matita/contribs/CoRN-Decl/model/abgroups/Qposabgroup.ma @@ -16,21 +16,19 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/Qposabgroup". +include "CoRN.ma". + (* $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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/abgroups/Zabgroup.ma b/matita/contribs/CoRN-Decl/model/abgroups/Zabgroup.ma index 42e2f9ca8..0cfc20cca 100644 --- a/matita/contribs/CoRN-Decl/model/abgroups/Zabgroup.ma +++ b/matita/contribs/CoRN-Decl/model/abgroups/Zabgroup.ma @@ -16,22 +16,20 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/abgroups/Zabgroup". +include "CoRN.ma". + (* $Id: Zabgroup.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *) -(* INCLUDE -Zgroup -*) +include "model/groups/Zgroup.ma". -(* INCLUDE -CAbGroups -*) +include "algebra/CAbGroups.ma". (*#* **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. *) diff --git a/matita/contribs/CoRN-Decl/model/fields/Qfield.ma b/matita/contribs/CoRN-Decl/model/fields/Qfield.ma index fd1dc5896..8024b79f3 100644 --- a/matita/contribs/CoRN-Decl/model/fields/Qfield.ma +++ b/matita/contribs/CoRN-Decl/model/fields/Qfield.ma @@ -16,22 +16,20 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/fields/Qfield". +include "CoRN.ma". + (* $Id: Qfield.v,v 1.8 2004/04/08 08:20:32 lcf Exp $ *) -(* INCLUDE -Qring -*) +include "model/rings/Qring.ma". -(* INCLUDE -CFields -*) +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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/groups/QSposgroup.ma b/matita/contribs/CoRN-Decl/model/groups/QSposgroup.ma index ef659adb0..99993bd80 100644 --- a/matita/contribs/CoRN-Decl/model/groups/QSposgroup.ma +++ b/matita/contribs/CoRN-Decl/model/groups/QSposgroup.ma @@ -16,22 +16,20 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/groups/QSposgroup". +include "CoRN.ma". + (* $Id: QSposgroup.v,v 1.6 2004/04/08 08:20:32 lcf Exp $ *) -(* INCLUDE -QSposmonoid -*) +include "model/monoids/QSposmonoid.ma". -(* INCLUDE -CGroups -*) +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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/groups/Qgroup.ma b/matita/contribs/CoRN-Decl/model/groups/Qgroup.ma index 36c474ba8..e508583d6 100644 --- a/matita/contribs/CoRN-Decl/model/groups/Qgroup.ma +++ b/matita/contribs/CoRN-Decl/model/groups/Qgroup.ma @@ -16,21 +16,19 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/groups/Qgroup". +include "CoRN.ma". + (* $Id: Qgroup.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *) -(* INCLUDE -Qmonoid -*) +include "model/monoids/Qmonoid.ma". -(* INCLUDE -CGroups -*) +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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/groups/Qposgroup.ma b/matita/contribs/CoRN-Decl/model/groups/Qposgroup.ma index e798d7067..02e0b6c33 100644 --- a/matita/contribs/CoRN-Decl/model/groups/Qposgroup.ma +++ b/matita/contribs/CoRN-Decl/model/groups/Qposgroup.ma @@ -16,21 +16,19 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/groups/Qposgroup". +include "CoRN.ma". + (* $Id: Qposgroup.v,v 1.6 2004/04/08 08:20:32 lcf Exp $ *) -(* INCLUDE -Qposmonoid -*) +include "model/monoids/Qposmonoid.ma". -(* INCLUDE -CGroups -*) +include "algebra/CGroups.ma". (*#* **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". diff --git a/matita/contribs/CoRN-Decl/model/groups/Zgroup.ma b/matita/contribs/CoRN-Decl/model/groups/Zgroup.ma index dcde2c59f..3f5430193 100644 --- a/matita/contribs/CoRN-Decl/model/groups/Zgroup.ma +++ b/matita/contribs/CoRN-Decl/model/groups/Zgroup.ma @@ -16,22 +16,20 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/groups/Zgroup". +include "CoRN.ma". + (* $Id: Zgroup.v,v 1.5 2004/04/08 08:20:32 lcf Exp $ *) -(* INCLUDE -Zmonoid -*) +include "model/monoids/Zmonoid.ma". -(* INCLUDE -CGroups -*) +include "algebra/CGroups.ma". (*#* **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. *) diff --git a/matita/contribs/CoRN-Decl/model/monoids/Nmonoid.ma b/matita/contribs/CoRN-Decl/model/monoids/Nmonoid.ma index 80ea8fdc0..4eac5c0c6 100644 --- a/matita/contribs/CoRN-Decl/model/monoids/Nmonoid.ma +++ b/matita/contribs/CoRN-Decl/model/monoids/Nmonoid.ma @@ -16,29 +16,27 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Nmonoid". +include "CoRN.ma". + (* $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. *) -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 ##%\emph{%the monoid of natural numbers%}%##: *) -inline cic:/CoRN/model/monoids/Nmonoid/nat_as_CMonoid.con. +inline "cic:/CoRN/model/monoids/Nmonoid/nat_as_CMonoid.con". diff --git a/matita/contribs/CoRN-Decl/model/monoids/Nposmonoid.ma b/matita/contribs/CoRN-Decl/model/monoids/Nposmonoid.ma index ab289b85b..1d23f7d4a 100644 --- a/matita/contribs/CoRN-Decl/model/monoids/Nposmonoid.ma +++ b/matita/contribs/CoRN-Decl/model/monoids/Nposmonoid.ma @@ -16,29 +16,27 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Nposmonoid". +include "CoRN.ma". + (* $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. *) -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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/monoids/QSposmonoid.ma b/matita/contribs/CoRN-Decl/model/monoids/QSposmonoid.ma index 53c3e0472..0ec63cd7b 100644 --- a/matita/contribs/CoRN-Decl/model/monoids/QSposmonoid.ma +++ b/matita/contribs/CoRN-Decl/model/monoids/QSposmonoid.ma @@ -16,26 +16,24 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/QSposmonoid". +include "CoRN.ma". + (* $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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/monoids/Qmonoid.ma b/matita/contribs/CoRN-Decl/model/monoids/Qmonoid.ma index ce930fdff..e19460778 100644 --- a/matita/contribs/CoRN-Decl/model/monoids/Qmonoid.ma +++ b/matita/contribs/CoRN-Decl/model/monoids/Qmonoid.ma @@ -16,38 +16,36 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Qmonoid". +include "CoRN.ma". + (* $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. *) -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]. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/monoids/Qposmonoid.ma b/matita/contribs/CoRN-Decl/model/monoids/Qposmonoid.ma index 30150d664..e8f9f96ee 100644 --- a/matita/contribs/CoRN-Decl/model/monoids/Qposmonoid.ma +++ b/matita/contribs/CoRN-Decl/model/monoids/Qposmonoid.ma @@ -16,25 +16,23 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Qposmonoid". +include "CoRN.ma". + (* $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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/monoids/Zmonoid.ma b/matita/contribs/CoRN-Decl/model/monoids/Zmonoid.ma index f0b1558e1..d6b0ddea4 100644 --- a/matita/contribs/CoRN-Decl/model/monoids/Zmonoid.ma +++ b/matita/contribs/CoRN-Decl/model/monoids/Zmonoid.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/monoids/Zmonoid". +include "CoRN.ma". + (* $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],[[+]]$\rangle$#⟩# @@ -32,13 +30,13 @@ We use the addition [ZERO] (defined in the standard library) as the unit of monoid: *) -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. @@ -47,13 +45,13 @@ As the multiplicative unit we should use [`1`], which is [(POS xH)] in 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]. *) diff --git a/matita/contribs/CoRN-Decl/model/non_examples/N_no_group.ma b/matita/contribs/CoRN-Decl/model/non_examples/N_no_group.ma index 7e36247dc..260cc8d68 100644 --- a/matita/contribs/CoRN-Decl/model/non_examples/N_no_group.ma +++ b/matita/contribs/CoRN-Decl/model/non_examples/N_no_group.ma @@ -16,24 +16,22 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/non_examples/N_no_group". +include "CoRN.ma". + (* $Id: N_no_group.v,v 1.5 2004/04/08 08:20:33 lcf Exp $ *) -(* INCLUDE -Nmonoid -*) +include "model/monoids/Nmonoid.ma". -(* INCLUDE -CGroups -*) +include "algebra/CGroups.ma". (*#* **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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/non_examples/Npos_no_group.ma b/matita/contribs/CoRN-Decl/model/non_examples/Npos_no_group.ma index adb7edac1..7f86667be 100644 --- a/matita/contribs/CoRN-Decl/model/non_examples/Npos_no_group.ma +++ b/matita/contribs/CoRN-Decl/model/non_examples/Npos_no_group.ma @@ -16,24 +16,22 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/non_examples/Npos_no_group". +include "CoRN.ma". + (* $Id: Npos_no_group.v,v 1.6 2004/04/08 08:20:33 lcf Exp $ *) -(* INCLUDE -CGroups -*) +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. *) -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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/non_examples/Npos_no_monoid.ma b/matita/contribs/CoRN-Decl/model/non_examples/Npos_no_monoid.ma index a17dec061..7dbff7050 100644 --- a/matita/contribs/CoRN-Decl/model/non_examples/Npos_no_monoid.ma +++ b/matita/contribs/CoRN-Decl/model/non_examples/Npos_no_monoid.ma @@ -16,25 +16,23 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/non_examples/Npos_no_monoid". +include "CoRN.ma". + (* $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. *) -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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/ordfields/Qordfield.ma b/matita/contribs/CoRN-Decl/model/ordfields/Qordfield.ma index 415153a2f..0729946f3 100644 --- a/matita/contribs/CoRN-Decl/model/ordfields/Qordfield.ma +++ b/matita/contribs/CoRN-Decl/model/ordfields/Qordfield.ma @@ -16,25 +16,23 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/ordfields/Qordfield". +include "CoRN.ma". + (* $Id: Qordfield.v,v 1.9 2004/04/23 10:01:03 lcf Exp $ *) -(* INCLUDE -Qfield -*) +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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/reals/Cauchy_IR.ma b/matita/contribs/CoRN-Decl/model/reals/Cauchy_IR.ma index 0fcc213db..a355fe3ed 100644 --- a/matita/contribs/CoRN-Decl/model/reals/Cauchy_IR.ma +++ b/matita/contribs/CoRN-Decl/model/reals/Cauchy_IR.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/reals/Cauchy_IR". +include "CoRN.ma". + (* $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 @@ -32,7 +30,7 @@ arbitrary archimedian ordered field. Plugging in [Q] we get the model 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]. *) diff --git a/matita/contribs/CoRN-Decl/model/rings/Qring.ma b/matita/contribs/CoRN-Decl/model/rings/Qring.ma index aaac446c5..5a1723d1c 100644 --- a/matita/contribs/CoRN-Decl/model/rings/Qring.ma +++ b/matita/contribs/CoRN-Decl/model/rings/Qring.ma @@ -16,41 +16,33 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/rings/Qring". +include "CoRN.ma". + (* $Id: Qring.v,v 1.8 2004/04/23 10:01:03 lcf Exp $ *) -(* INCLUDE -Qabgroup -*) +include "model/abgroups/Qabgroup.ma". -(* INCLUDE -CRings -*) +include "algebra/CRings.ma". -(* INCLUDE -Zring -*) +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. *) -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. *) -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". -(* INCLUDE -ZArith -*) +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". diff --git a/matita/contribs/CoRN-Decl/model/rings/Zring.ma b/matita/contribs/CoRN-Decl/model/rings/Zring.ma index 87005b766..3927f4332 100644 --- a/matita/contribs/CoRN-Decl/model/rings/Zring.ma +++ b/matita/contribs/CoRN-Decl/model/rings/Zring.ma @@ -16,26 +16,24 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/rings/Zring". +include "CoRN.ma". + (* $Id: Zring.v,v 1.6 2004/04/08 08:20:34 lcf Exp $ *) -(* INCLUDE -Zabgroup -*) +include "model/abgroups/Zabgroup.ma". -(* INCLUDE -CRings -*) +include "algebra/CRings.ma". (*#* **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. *) diff --git a/matita/contribs/CoRN-Decl/model/semigroups/Npossemigroup.ma b/matita/contribs/CoRN-Decl/model/semigroups/Npossemigroup.ma index c68610e53..466677d04 100644 --- a/matita/contribs/CoRN-Decl/model/semigroups/Npossemigroup.ma +++ b/matita/contribs/CoRN-Decl/model/semigroups/Npossemigroup.ma @@ -16,19 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Npossemigroup". +include "CoRN.ma". + (* $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],[[+]]$\rangle$#⟩# @@ -36,13 +32,13 @@ The positive natural numbers form together with addition a subsemigroup 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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/semigroups/Nsemigroup.ma b/matita/contribs/CoRN-Decl/model/semigroups/Nsemigroup.ma index 676845781..393e00359 100644 --- a/matita/contribs/CoRN-Decl/model/semigroups/Nsemigroup.ma +++ b/matita/contribs/CoRN-Decl/model/semigroups/Nsemigroup.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Nsemigroup". +include "CoRN.ma". + (* $Id: Nsemigroup.v,v 1.6 2004/04/08 08:20:34 lcf Exp $ *) -(* INCLUDE -Nsetoid -*) +include "model/setoids/Nsetoid.ma". -(* INCLUDE -CSemiGroups -*) +include "algebra/CSemiGroups.ma". (*#* **Example of a semi-group: $\langle$#⟨#[nat],[[+]]$\rangle$#⟩# *) @@ -32,5 +30,5 @@ CSemiGroups (*#* 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". diff --git a/matita/contribs/CoRN-Decl/model/semigroups/QSpossemigroup.ma b/matita/contribs/CoRN-Decl/model/semigroups/QSpossemigroup.ma index a101b2388..54eb20c11 100644 --- a/matita/contribs/CoRN-Decl/model/semigroups/QSpossemigroup.ma +++ b/matita/contribs/CoRN-Decl/model/semigroups/QSpossemigroup.ma @@ -16,20 +16,18 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/QSpossemigroup". +include "CoRN.ma". + (* $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. *) -inline cic:/CoRN/model/semigroups/QSpossemigroup/Qpos_multdiv2_as_CSemiGroup.con. +inline "cic:/CoRN/model/semigroups/QSpossemigroup/Qpos_multdiv2_as_CSemiGroup.con". diff --git a/matita/contribs/CoRN-Decl/model/semigroups/Qpossemigroup.ma b/matita/contribs/CoRN-Decl/model/semigroups/Qpossemigroup.ma index 42e9e6aa3..f4336222a 100644 --- a/matita/contribs/CoRN-Decl/model/semigroups/Qpossemigroup.ma +++ b/matita/contribs/CoRN-Decl/model/semigroups/Qpossemigroup.ma @@ -16,19 +16,17 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Qpossemigroup". +include "CoRN.ma". + (* $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. *) -inline cic:/CoRN/model/semigroups/Qpossemigroup/Qpos_mult_as_CSemiGroup.con. +inline "cic:/CoRN/model/semigroups/Qpossemigroup/Qpos_mult_as_CSemiGroup.con". diff --git a/matita/contribs/CoRN-Decl/model/semigroups/Qsemigroup.ma b/matita/contribs/CoRN-Decl/model/semigroups/Qsemigroup.ma index 4437e0240..09fbc4aca 100644 --- a/matita/contribs/CoRN-Decl/model/semigroups/Qsemigroup.ma +++ b/matita/contribs/CoRN-Decl/model/semigroups/Qsemigroup.ma @@ -16,24 +16,22 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Qsemigroup". +include "CoRN.ma". + (* $Id: Qsemigroup.v,v 1.6 2004/04/08 08:20:35 lcf Exp $ *) -(* INCLUDE -Qsetoid -*) +include "model/setoids/Qsetoid.ma". -(* INCLUDE -CSemiGroups -*) +include "algebra/CSemiGroups.ma". (*#* **Examples of semi-groups: $\langle$#⟨#[Q],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Q],[[*]]$\rangle$#⟩# ***$\langle$#⟨#[Q],[[+]]$\rangle$#⟩# *) -inline cic:/CoRN/model/semigroups/Qsemigroup/Q_as_CSemiGroup.con. +inline "cic:/CoRN/model/semigroups/Qsemigroup/Q_as_CSemiGroup.con". (*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩# *) -inline cic:/CoRN/model/semigroups/Qsemigroup/Q_mul_as_CSemiGroup.con. +inline "cic:/CoRN/model/semigroups/Qsemigroup/Q_mul_as_CSemiGroup.con". diff --git a/matita/contribs/CoRN-Decl/model/semigroups/Zsemigroup.ma b/matita/contribs/CoRN-Decl/model/semigroups/Zsemigroup.ma index 70bead366..4ec6a0ac6 100644 --- a/matita/contribs/CoRN-Decl/model/semigroups/Zsemigroup.ma +++ b/matita/contribs/CoRN-Decl/model/semigroups/Zsemigroup.ma @@ -16,26 +16,24 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/semigroups/Zsemigroup". +include "CoRN.ma". + (* $Id: Zsemigroup.v,v 1.6 2004/04/08 08:20:35 lcf Exp $ *) -(* INCLUDE -Zsetoid -*) +include "model/setoids/Zsetoid.ma". -(* INCLUDE -CSemiGroups -*) +include "algebra/CSemiGroups.ma". (*#* **Examples of semi-groups: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩# and $\langle$#⟨#[Z],[[*]]$\rangle$#⟩# ***$\langle$#⟨#[Z],[[+]]$\rangle$#⟩# *) -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],[[*]]$\rangle$#⟩# *) -inline cic:/CoRN/model/semigroups/Zsemigroup/Z_mul_as_CSemiGroup.con. +inline "cic:/CoRN/model/semigroups/Zsemigroup/Z_mul_as_CSemiGroup.con". diff --git a/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma b/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma index 0d883959c..23363a170 100644 --- a/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma +++ b/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma @@ -16,19 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Npossetoid". +include "CoRN.ma". + (* $Id: Npossetoid.v,v 1.3 2004/04/06 15:46:04 lcf Exp $ *) -(* INCLUDE -Nsetoid -*) +include "model/setoids/Nsetoid.ma". -(* INCLUDE -Npossec -*) +include "model/structures/Npossec.ma". -(* INCLUDE -CSetoidFun -*) +include "algebra/CSetoidFun.ma". (*#* **Example of a setoid: [Npos] @@ -37,38 +33,38 @@ The positive natural numbers [Npos] will be defined as a subsetoid of the natural numbers. *) -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. *) -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. *) -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. *) -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. *) -inline cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con. +inline "cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con". diff --git a/matita/contribs/CoRN-Decl/model/setoids/Nsetoid.ma b/matita/contribs/CoRN-Decl/model/setoids/Nsetoid.ma index b7045b8e2..b3bf1fc3d 100644 --- a/matita/contribs/CoRN-Decl/model/setoids/Nsetoid.ma +++ b/matita/contribs/CoRN-Decl/model/setoids/Nsetoid.ma @@ -16,53 +16,51 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Nsetoid". +include "CoRN.ma". + (* $Id: Nsetoid.v,v 1.4 2004/04/06 15:46:04 lcf Exp $ *) -(* INCLUDE -Nsec -*) +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. *) -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". (*#* ***Addition *) -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. *) -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 *) -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". diff --git a/matita/contribs/CoRN-Decl/model/setoids/Qpossetoid.ma b/matita/contribs/CoRN-Decl/model/setoids/Qpossetoid.ma index 3dc6087f4..9557dc175 100644 --- a/matita/contribs/CoRN-Decl/model/setoids/Qpossetoid.ma +++ b/matita/contribs/CoRN-Decl/model/setoids/Qpossetoid.ma @@ -16,19 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Qpossetoid". +include "CoRN.ma". + (* $Id: Qpossetoid.v,v 1.4 2004/04/06 15:46:05 lcf Exp $ *) -(* INCLUDE -Qsetoid -*) +include "model/setoids/Qsetoid.ma". -(* INCLUDE -CSetoidFun -*) +include "algebra/CSetoidFun.ma". -(* INCLUDE -Qpossec -*) +include "model/structures/Qpossec.ma". (*#* **Example of a setoid: [Qpos] ***Setoid @@ -36,18 +32,18 @@ We will examine the subsetoid of positive rationals of the setoid of rational numbers. *) -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. *) -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 @@ -55,49 +51,49 @@ As we have seen, multiplication preserves positivity, so we can restrict it nice properties. *) -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. *) -inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con. +inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con". (*#* 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. *) -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. *) -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#. *) -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#. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/setoids/Qsetoid.ma b/matita/contribs/CoRN-Decl/model/setoids/Qsetoid.ma index 8938e482f..71cdafa4a 100644 --- a/matita/contribs/CoRN-Decl/model/setoids/Qsetoid.ma +++ b/matita/contribs/CoRN-Decl/model/setoids/Qsetoid.ma @@ -16,77 +16,75 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Qsetoid". +include "CoRN.ma". + (* $Id: Qsetoid.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *) -(* INCLUDE -Qsec -*) +include "model/structures/Qsec.ma". -(* INCLUDE -CSetoidFun -*) +include "algebra/CSetoidFun.ma". (*#* **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". (*#* ***Addition *) -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. *) -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". (*#* ***Opposite *) -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 *) -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. *) -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". (*#* ***Less-than *) -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". diff --git a/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma b/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma index 36b8ce6c9..84541c4db 100644 --- a/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma +++ b/matita/contribs/CoRN-Decl/model/setoids/Zsetoid.ma @@ -16,71 +16,69 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Zsetoid". +include "CoRN.ma". + (* $Id: Zsetoid.v,v 1.5 2004/04/07 15:08:08 lcf Exp $ *) -(* INCLUDE -Zsec -*) +include "model/structures/Zsec.ma". -(* INCLUDE -CSetoidFun -*) +include "algebra/CSetoidFun.ma". (*#* **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. *) -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. *) -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. *) -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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/structures/Npossec.ma b/matita/contribs/CoRN-Decl/model/structures/Npossec.ma index 3f36a84bb..7a47323f6 100644 --- a/matita/contribs/CoRN-Decl/model/structures/Npossec.ma +++ b/matita/contribs/CoRN-Decl/model/structures/Npossec.ma @@ -16,26 +16,22 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Npossec". +include "CoRN.ma". + (* $Id: Npossec.v,v 1.3 2004/04/06 15:46:05 lcf Exp $ *) (*#* printing Npos $\mathbb{N}^{+}$ #N+# *) -(* 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. *) -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". diff --git a/matita/contribs/CoRN-Decl/model/structures/Nsec.ma b/matita/contribs/CoRN-Decl/model/structures/Nsec.ma index 00d090efa..82d341b27 100644 --- a/matita/contribs/CoRN-Decl/model/structures/Nsec.ma +++ b/matita/contribs/CoRN-Decl/model/structures/Nsec.ma @@ -16,21 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Nsec". +include "CoRN.ma". + (* $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] @@ -40,33 +32,33 @@ We prove some basic lemmas of the natural numbers. 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". (*#* ***Apartness *) -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". (*#* ***Addition *) -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 *) -inline cic:/CoRN/model/structures/Nsec/no_inverse0.con. +inline "cic:/CoRN/model/structures/Nsec/no_inverse0.con". (*#* ***Multiplication *) -inline cic:/CoRN/model/structures/Nsec/mult_strext0.con. +inline "cic:/CoRN/model/structures/Nsec/mult_strext0.con". diff --git a/matita/contribs/CoRN-Decl/model/structures/Qpossec.ma b/matita/contribs/CoRN-Decl/model/structures/Qpossec.ma index 5ea8081aa..38f43ac38 100644 --- a/matita/contribs/CoRN-Decl/model/structures/Qpossec.ma +++ b/matita/contribs/CoRN-Decl/model/structures/Qpossec.ma @@ -16,17 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Qpossec". +include "CoRN.ma". + (* $Id: Qpossec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *) (*#* printing Qpos $\mathbb{Q}^{+}$ #Q+# *) -(* INCLUDE -Qsec -*) +include "model/structures/Qsec.ma". -(* INCLUDE -CLogic -*) +include "algebra/CLogic.ma". (*#* **About [Qpos] We will prove some lemmas concerning rationals bigger than 0. @@ -35,28 +33,28 @@ We will prove some lemmas concerning rationals bigger than 0. 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. *) -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. *) -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. *) -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) @@ -64,9 +62,9 @@ Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y) \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". diff --git a/matita/contribs/CoRN-Decl/model/structures/Qsec.ma b/matita/contribs/CoRN-Decl/model/structures/Qsec.ma index 7692c62e5..9a8cb4f64 100644 --- a/matita/contribs/CoRN-Decl/model/structures/Qsec.ma +++ b/matita/contribs/CoRN-Decl/model/structures/Qsec.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Qsec". +include "CoRN.ma". + (* $Id: Qsec.v,v 1.7 2004/04/08 08:20:35 lcf Exp $ *) (*#* printing Q %\ensuremath{\mathbb{Q}}% *) @@ -28,21 +30,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Qsec". (*#* printing QFOUR %\ensuremath{4_\mathbb{Q}}% #4Q# *) -(* INCLUDE -CLogic -*) - -(* INCLUDE -Arith -*) - -(* INCLUDE -Peano_dec -*) +include "algebra/CLogic.ma". -(* INCLUDE -Zsec -*) +include "model/structures/Zsec.ma". (*#* *[Q] **About [Q] @@ -60,25 +50,25 @@ inverse an de constants 0 and 1. *) Section Q. *) -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". (* UNEXPORTED End Q. @@ -87,164 +77,166 @@ End Q. (*#* ***Constants *) -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 ##%\emph{%not equal%}%## 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: *) -inline cic:/CoRN/model/structures/Qsec/dec_Qeq.con. +inline "cic:/CoRN/model/structures/Qsec/dec_Qeq.con". (*#* ***Apartness *) -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". (*#* ***Addition *) -inline cic:/CoRN/model/structures/Qsec/Qplus_simpl.con. +inline "cic:/CoRN/model/structures/Qsec/Qplus_simpl.con". (*#* 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: *) -inline cic:/CoRN/model/structures/Qsec/QZERO_right.con. +inline "cic:/CoRN/model/structures/Qsec/QZERO_right.con". (*#* 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: *) -inline cic:/CoRN/model/structures/Qsec/Qopp_simpl.con. +inline "cic:/CoRN/model/structures/Qsec/Qopp_simpl.con". (*#* 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 *) -inline cic:/CoRN/model/structures/Qsec/Qmult_simpl.con. +inline "cic:/CoRN/model/structures/Qsec/Qmult_simpl.con". (*#* 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: *) -inline cic:/CoRN/model/structures/Qsec/Qmult_n_1.con. +inline "cic:/CoRN/model/structures/Qsec/Qmult_n_1.con". (*#* 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]: *) -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". (*#* ***Inverse *) -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". (*#* ***Less-than *) -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. *) -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. *) -inline cic:/CoRN/model/structures/Qsec/Q_is_archemaedian0.con. +inline "cic:/CoRN/model/structures/Qsec/Q_is_archemaedian0.con". diff --git a/matita/contribs/CoRN-Decl/model/structures/Zsec.ma b/matita/contribs/CoRN-Decl/model/structures/Zsec.ma index 26164cfeb..ce9fb1518 100644 --- a/matita/contribs/CoRN-Decl/model/structures/Zsec.ma +++ b/matita/contribs/CoRN-Decl/model/structures/Zsec.ma @@ -16,17 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Zsec". +include "CoRN.ma". + (* $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". (*#* *[Z] ** About [Z] @@ -37,62 +33,64 @@ datatype [Z] as defined in [ZArith], in the standard library). 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: *) -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. *) -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: *) -inline cic:/CoRN/model/structures/Zsec/Zmult_strext0.con. +inline "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con". (*#* ***Miscellaneous *) -inline cic:/CoRN/model/structures/Zsec/Zpos.con. +inline "cic:/CoRN/model/structures/Zsec/Zpos.con". (* begin hide *) +coercion "cic:/matita/CoRN-Decl/model/structures/Zsec/Zpos.con" 0 (* compounds *). + (* end hide *) -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". diff --git a/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma b/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma index 1ec3771ae..6222ed54c 100644 --- a/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma +++ b/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB". +include "CoRN.ma". + (* begin hide *) (* file : least_upper_bound_principle.v *) @@ -32,19 +34,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB". (* description : proof of the Bridges' least upper bound principle *) -(* INCLUDE -iso_CReals -*) +include "reals/iso_CReals.ma". -(* INCLUDE -Expon -*) +include "algebra/Expon.ma". (* UNEXPORTED Section LUBP. *) -inline cic:/CoRN/reals/Bridges_LUB/R1.var. +inline "cic:/CoRN/reals/Bridges_LUB/R1.var". (* SUBSECTION ON GENRAL DEFINITIONS *) @@ -52,33 +50,33 @@ inline cic:/CoRN/reals/Bridges_LUB/R1.var. 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 *) -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. @@ -90,121 +88,121 @@ End lub_definitions. 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 *) -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 *) -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 *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/Bridges_iso.ma b/matita/contribs/CoRN-Decl/reals/Bridges_iso.ma index 9603f1af7..e2a8ca76c 100644 --- a/matita/contribs/CoRN-Decl/reals/Bridges_iso.ma +++ b/matita/contribs/CoRN-Decl/reals/Bridges_iso.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_iso". +include "CoRN.ma". + (* begin hide *) (* file : bridges_gives_our.v *) @@ -32,89 +34,87 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_iso". (* 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 *) -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. *) -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. *) -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. *) -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) @@ -185,13 +185,13 @@ Proof. Qed. *) -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. @@ -209,97 +209,97 @@ End supremum. 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! *) -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. *) -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! *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/CMetricFields.ma b/matita/contribs/CoRN-Decl/reals/CMetricFields.ma index 755ac27b2..24c9b7593 100644 --- a/matita/contribs/CoRN-Decl/reals/CMetricFields.ma +++ b/matita/contribs/CoRN-Decl/reals/CMetricFields.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/CMetricFields". +include "CoRN.ma". + (* $Id: CMetricFields.v,v 1.6 2004/04/23 10:01:03 lcf Exp $ *) -(* INCLUDE -CReals1 -*) +include "reals/CReals1.ma". (* UNEXPORTED Section CMetric_Fields. @@ -28,9 +28,11 @@ Section CMetric_Fields. (*#* *Metric 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. @@ -40,11 +42,11 @@ End CMetric_Fields. Section basics. *) -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". (* end hide *) @@ -56,20 +58,22 @@ End basics. 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}% *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/CPoly_Contin.ma b/matita/contribs/CoRN-Decl/reals/CPoly_Contin.ma index f087eb2e4..0c8b3653a 100644 --- a/matita/contribs/CoRN-Decl/reals/CPoly_Contin.ma +++ b/matita/contribs/CoRN-Decl/reals/CPoly_Contin.ma @@ -16,19 +16,19 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/CPoly_Contin". +include "CoRN.ma". + (* $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". diff --git a/matita/contribs/CoRN-Decl/reals/CReals.ma b/matita/contribs/CoRN-Decl/reals/CReals.ma index 9be4d7416..9e22fbae5 100644 --- a/matita/contribs/CoRN-Decl/reals/CReals.ma +++ b/matita/contribs/CoRN-Decl/reals/CReals.ma @@ -16,13 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/CReals". +include "CoRN.ma". + (* $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 @@ -35,13 +35,15 @@ proof that this number is the limit. (* Begin_SpecReals *) -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 *). (* End_SpecReals *) -inline cic:/CoRN/reals/CReals/Lim.con. +inline "cic:/CoRN/reals/CReals/Lim.con". (* UNEXPORTED Implicit Arguments Lim [IR]. diff --git a/matita/contribs/CoRN-Decl/reals/CReals1.ma b/matita/contribs/CoRN-Decl/reals/CReals1.ma index c87c3e978..21dc9e6e4 100644 --- a/matita/contribs/CoRN-Decl/reals/CReals1.ma +++ b/matita/contribs/CoRN-Decl/reals/CReals1.ma @@ -16,19 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/CReals1". +include "CoRN.ma". + (* $Id: CReals1.v,v 1.4 2004/04/23 10:01:04 lcf Exp $ *) -(* INCLUDE -Max_AbsIR -*) +include "reals/Max_AbsIR.ma". -(* INCLUDE -Expon -*) +include "algebra/Expon.ma". -(* INCLUDE -CPoly_ApZero -*) +include "algebra/CPoly_ApZero.ma". (* UNEXPORTED Section More_Cauchy_Props. @@ -42,20 +38,20 @@ more useful properties about them. 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. *) -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. @@ -81,35 +77,35 @@ Finally, for some of our results it is important to assume that [seq2] is monotonous. *) -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". (* begin hide *) -inline cic:/CoRN/reals/CReals1/mon_F'.con. +inline "cic:/CoRN/reals/CReals1/mon_F'.con". (* end hide *) -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. @@ -119,23 +115,23 @@ End 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. @@ -150,13 +146,13 @@ Section Properties_of_Exponentiation. 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. @@ -164,9 +160,9 @@ End Properties_of_Exponentiation. (*#* *** [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". diff --git a/matita/contribs/CoRN-Decl/reals/CSumsReals.ma b/matita/contribs/CoRN-Decl/reals/CSumsReals.ma index 2a9a0760a..5799a997a 100644 --- a/matita/contribs/CoRN-Decl/reals/CSumsReals.ma +++ b/matita/contribs/CoRN-Decl/reals/CSumsReals.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/CSumsReals". +include "CoRN.ma". + (* $Id: CSumsReals.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *) -(* INCLUDE -CReals1 -*) +include "reals/CReals1.ma". (*#* * Sums over Reals @@ -36,15 +36,15 @@ $\Sigma_{m\leq i \leq n}~c^k = \frac{c^{n+1}-c^m}{c-1}.$ 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. *) -inline cic:/CoRN/reals/CSumsReals/Sum_c_exp.con. +inline "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con". (* UNEXPORTED Hint Resolve Sum_c_exp. @@ -52,7 +52,7 @@ Hint Resolve Sum_c_exp. (*#* 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'. @@ -66,29 +66,29 @@ End Sums_over_Reals. 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. *) -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". diff --git a/matita/contribs/CoRN-Decl/reals/CauchySeq.ma b/matita/contribs/CoRN-Decl/reals/CauchySeq.ma index 56b09f62f..e019be073 100644 --- a/matita/contribs/CoRN-Decl/reals/CauchySeq.ma +++ b/matita/contribs/CoRN-Decl/reals/CauchySeq.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/CauchySeq". +include "CoRN.ma". + (* $Id: CauchySeq.v,v 1.8 2004/04/23 10:01:04 lcf Exp $ *) (*#* printing IR %\ensuremath{\mathbb R}% *) @@ -28,9 +30,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/CauchySeq". (*#* printing AbsIR %\ensuremath{|\cdot|_{\mathbb R}}% *) -(* INCLUDE -CReals -*) +include "reals/CReals.ma". (*#* *Real Number Structures %\begin{convention}% Let [IR] be a structure for real numbers. @@ -43,11 +43,9 @@ Definition IR : CReals := Concrete_R. Opaque IR. *) -inline cic:/CoRN/reals/CauchySeq/IR.var. +inline "cic:/CoRN/reals/CauchySeq/IR.var". -(* INCLUDE -Transparent_algebra -*) +include "tactics/Transparent_algebra.ma". (* begin hide *) @@ -59,21 +57,21 @@ Section 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. *) -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. *) -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. @@ -136,19 +134,19 @@ and [[<=]] being a negative statement, this makes proofs 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. @@ -162,39 +160,39 @@ Section Inequalities. 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]. *) -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. @@ -206,47 +204,47 @@ Section Equiv_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. *) -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. @@ -263,33 +261,33 @@ Some of these lemmas are now obsolete, because they were reproved for arbitrary 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. diff --git a/matita/contribs/CoRN-Decl/reals/Cauchy_CReals.ma b/matita/contribs/CoRN-Decl/reals/Cauchy_CReals.ma index a1511bbf0..259de7122 100644 --- a/matita/contribs/CoRN-Decl/reals/Cauchy_CReals.ma +++ b/matita/contribs/CoRN-Decl/reals/Cauchy_CReals.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Cauchy_CReals". +include "CoRN.ma". + (* $Id: Cauchy_CReals.v,v 1.5 2004/04/23 10:01:04 lcf Exp $ *) -(* INCLUDE -Cauchy_COF -*) +include "algebra/Cauchy_COF.ma". -(* INCLUDE -CReals -*) +include "reals/CReals.ma". (* UNEXPORTED Section R_CReals. @@ -42,91 +40,91 @@ We start by showing how to inject the rational numbers in the field of Cauchy se %\end{convention}% *) -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. *) -inline cic:/CoRN/reals/Cauchy_CReals/ing_div_three.con. +inline "cic:/CoRN/reals/Cauchy_CReals/ing_div_three.con". (* 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. *) -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". (* begin hide *) -inline cic:/CoRN/reals/Cauchy_CReals/PT.con. +inline "cic:/CoRN/reals/Cauchy_CReals/PT.con". (* end hide *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/IVT.ma b/matita/contribs/CoRN-Decl/reals/IVT.ma index 3bdb45a7c..7da887f6a 100644 --- a/matita/contribs/CoRN-Decl/reals/IVT.ma +++ b/matita/contribs/CoRN-Decl/reals/IVT.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/IVT". +include "CoRN.ma". + (* $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. @@ -39,53 +39,53 @@ Section Nested_Intervals. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/reals/IVT/a'.con. +inline "cic:/CoRN/reals/IVT/a'.con". (* end hide *) -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}% *) -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)]. *) -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. @@ -97,19 +97,19 @@ Section Bisection. (*#* ** Bissections *) -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]. @@ -118,29 +118,29 @@ inline cic:/CoRN/reals/IVT/f_b.var. (* begin hide *) -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". (* end hide *) -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. *) -inline cic:/CoRN/reals/IVT/Cbisect'.con. +inline "cic:/CoRN/reals/IVT/Cbisect'.con". (* UNEXPORTED End Bisection. @@ -150,23 +150,23 @@ End Bisection. 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". (* begin hide *) -inline cic:/CoRN/reals/IVT/Small.con. +inline "cic:/CoRN/reals/IVT/Small.con". (* end hide *) -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. @@ -180,43 +180,43 @@ Section IVT_Op. 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". (* begin hide *) -inline cic:/CoRN/reals/IVT/Small.con. +inline "cic:/CoRN/reals/IVT/Small.con". (* end hide *) -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. @@ -228,7 +228,7 @@ Section IVT_Poly. (*#* ** IVT for polynomials *) -inline cic:/CoRN/reals/IVT/Civt_poly.con. +inline "cic:/CoRN/reals/IVT/Civt_poly.con". (* UNEXPORTED End IVT_Poly. diff --git a/matita/contribs/CoRN-Decl/reals/Intervals.ma b/matita/contribs/CoRN-Decl/reals/Intervals.ma index 3c04c2c23..0a53cc5d5 100644 --- a/matita/contribs/CoRN-Decl/reals/Intervals.ma +++ b/matita/contribs/CoRN-Decl/reals/Intervals.ma @@ -16,15 +16,13 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Intervals". +include "CoRN.ma". + (* $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. @@ -41,7 +39,7 @@ points less or equal than [b] and greater or equal than [a]. We 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]. @@ -51,32 +49,32 @@ As expected, both [a] and [b] are members of [[a,b]]. Also they are 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. *) -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. *) -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. @@ -88,7 +86,7 @@ and a well defined predicate [P] included in the domain of [F] and 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. @@ -102,15 +100,15 @@ Implicit Arguments Frestr [F P]. 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. *) -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. @@ -137,7 +135,7 @@ to come. The definition (equivalent to the classical one) states that 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 @@ -147,28 +145,28 @@ that we take the definition of totally bounded to be the relevant one 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. *) -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". (* begin hide *) -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". (* end hide *) @@ -176,17 +174,17 @@ inline cic:/CoRN/reals/Intervals/aux_seq_lub_prop.con. 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". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con. +inline "cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con". (* UNEXPORTED End Totally_Bounded. @@ -204,7 +202,7 @@ and explore some of its properties. 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 @@ -221,33 +219,33 @@ a positive real number. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/reals/Intervals/I.con. +inline "cic:/CoRN/reals/Intervals/I.con". (* end hide *) -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]. *) -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.*) -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 @@ -255,25 +253,25 @@ We now define a sequence on [n] points in [[a,b]] by 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].*) -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: *) -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: *) -inline cic:/CoRN/reals/Intervals/compact_elements.con. +inline "cic:/CoRN/reals/Intervals/compact_elements.con". (* UNEXPORTED Opaque Min Max. @@ -281,21 +279,21 @@ Opaque Min Max. (*#* 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. *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/Max_AbsIR.ma b/matita/contribs/CoRN-Decl/reals/Max_AbsIR.ma index 7a1e016b4..91cb3e481 100644 --- a/matita/contribs/CoRN-Decl/reals/Max_AbsIR.ma +++ b/matita/contribs/CoRN-Decl/reals/Max_AbsIR.ma @@ -16,15 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Max_AbsIR". +include "CoRN.ma". + (* $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. @@ -42,19 +42,19 @@ Let [x] and [y] be reals %\end{convention}% *) -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: @@ -70,19 +70,19 @@ With strong extensionality, we can make the binary operation [Max]. (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. *) -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. @@ -90,37 +90,37 @@ Section properties_of_Max. (*#* *** Maximum *) -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. @@ -144,55 +144,55 @@ The minimum is defined by the formula [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. @@ -208,67 +208,67 @@ Section Absolute. (*#* *** 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. @@ -291,21 +291,21 @@ Let [F,G:PartIR] and denote by [P] and [Q] their respective domains. %\end{convention}% *) -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". (* begin hide *) -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". (* end hide *) -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. @@ -315,33 +315,33 @@ End Part_Function_Max. 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". (* begin hide *) -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". (* end hide *) -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. *) -inline cic:/CoRN/reals/Max_AbsIR/FMin_char.con. +inline "cic:/CoRN/reals/Max_AbsIR/FMin_char.con". (* 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. @@ -351,9 +351,9 @@ End Part_Function_Abs. 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. @@ -363,15 +363,15 @@ Hint Resolve FAbs_char': algebra. Section Inclusion. *) -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". (* begin hide *) -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". (* end hide *) @@ -380,23 +380,23 @@ inline cic:/CoRN/reals/Max_AbsIR/Q.con. %\end{convention}% *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/NRootIR.ma b/matita/contribs/CoRN-Decl/reals/NRootIR.ma index 368848098..c82c1cde3 100644 --- a/matita/contribs/CoRN-Decl/reals/NRootIR.ma +++ b/matita/contribs/CoRN-Decl/reals/NRootIR.ma @@ -16,15 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/NRootIR". +include "CoRN.ma". + (* $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 *) @@ -39,21 +39,21 @@ Section NRoot. %\end{convention}% *) -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". (* begin hide *) -inline cic:/CoRN/reals/NRootIR/p.con. +inline "cic:/CoRN/reals/NRootIR/p.con". (* end hide *) -inline cic:/CoRN/reals/NRootIR/CnrootIR.con. +inline "cic:/CoRN/reals/NRootIR/CnrootIR.con". (* UNEXPORTED End NRoot. @@ -75,42 +75,42 @@ prove its main properties: Section Nth_Root. *) -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. *) -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}% *) -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. @@ -124,7 +124,7 @@ Implicit Arguments NRoot [x n]. 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". (*#**********************************) @@ -136,41 +136,41 @@ Section Square_root. (*#* ** Square root *) -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. *) -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. *) -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. *) -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. @@ -194,53 +194,53 @@ With the help of square roots, we can prove some more properties of absolute values in [IR]. *) -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. *) -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. *) -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. *) -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. @@ -257,11 +257,11 @@ Cauchy sequence that is never zero and whose Limit is not zero is also a Cauchy sequence. *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma b/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma index 21a487409..ae1943b24 100644 --- a/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma +++ b/matita/contribs/CoRN-Decl/reals/OddPolyRootIR.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/OddPolyRootIR". +include "CoRN.ma". + (* $Id: OddPolyRootIR.v,v 1.5 2004/04/23 10:01:05 lcf Exp $ *) -(* INCLUDE -IVT -*) +include "reals/IVT.ma". (*#* * Roots of polynomials of odd degree *) @@ -33,21 +33,21 @@ Section CPoly_Big. %\end{convention}% *) -inline cic:/CoRN/reals/OddPolyRootIR/R.var. +inline "cic:/CoRN/reals/OddPolyRootIR/R.var". (* begin hide *) -inline cic:/CoRN/reals/OddPolyRootIR/RX.con. +inline "cic:/CoRN/reals/OddPolyRootIR/RX.con". (* end hide *) -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. @@ -62,25 +62,25 @@ Section Flip_Poly. %\end{convention}% *) -inline cic:/CoRN/reals/OddPolyRootIR/R.var. +inline "cic:/CoRN/reals/OddPolyRootIR/R.var". (* begin hide *) -inline cic:/CoRN/reals/OddPolyRootIR/RX.con. +inline "cic:/CoRN/reals/OddPolyRootIR/RX.con". (* end hide *) -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. *) -inline cic:/CoRN/reals/OddPolyRootIR/flip_odd.con. +inline "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con". (* UNEXPORTED End Flip_Poly. @@ -99,19 +99,19 @@ Section OddPoly_Signs. %\end{convention}% *) -inline cic:/CoRN/reals/OddPolyRootIR/R.var. +inline "cic:/CoRN/reals/OddPolyRootIR/R.var". (* begin hide *) -inline cic:/CoRN/reals/OddPolyRootIR/RX.con. +inline "cic:/CoRN/reals/OddPolyRootIR/RX.con". (* end hide *) -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. @@ -127,21 +127,21 @@ this field. %\end{convention}% *) -inline cic:/CoRN/reals/OddPolyRootIR/R.var. +inline "cic:/CoRN/reals/OddPolyRootIR/R.var". (* begin hide *) -inline cic:/CoRN/reals/OddPolyRootIR/RX.con. +inline "cic:/CoRN/reals/OddPolyRootIR/RX.con". (* end hide *) -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. @@ -154,11 +154,11 @@ Section OddPoly_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. diff --git a/matita/contribs/CoRN-Decl/reals/Q_dense.ma b/matita/contribs/CoRN-Decl/reals/Q_dense.ma index 31b4b21a6..98b9247e7 100644 --- a/matita/contribs/CoRN-Decl/reals/Q_dense.ma +++ b/matita/contribs/CoRN-Decl/reals/Q_dense.ma @@ -16,35 +16,37 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Q_dense". +include "CoRN.ma". + (* begin hide *) -(* INCLUDE -Q_in_CReals -*) +include "reals/Q_in_CReals.ma". (*#***** 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. *) -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. *) -inline cic:/CoRN/reals/Q_dense/Rat_Interval.con. +inline "cic:/CoRN/reals/Q_dense/Rat_Interval.con". (* 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)) @@ -61,13 +63,13 @@ Qed. 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. @@ -77,85 +79,83 @@ End COrdField_extra. Section Rational_sequence. *) -(* INCLUDE -Opaque_algebra -*) +include "tactics/Opaque_algebra.ma". (*#*** 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. *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/Q_in_CReals.ma b/matita/contribs/CoRN-Decl/reals/Q_in_CReals.ma index 8a803f435..a9beac518 100644 --- a/matita/contribs/CoRN-Decl/reals/Q_in_CReals.ma +++ b/matita/contribs/CoRN-Decl/reals/Q_in_CReals.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Q_in_CReals". +include "CoRN.ma". + (* $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 @@ -26,17 +28,11 @@ rational numbers for which the real number lies betwen image of them; 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 -Nmonoid -*) +include "model/monoids/Nmonoid.ma". -(* INCLUDE -Zring -*) +include "model/rings/Zring.ma". (* UNEXPORTED Section Rational_sequence_prelogue. @@ -47,22 +43,24 @@ Section Rational_sequence_prelogue. %\end{convention}% *) -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 *) -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 *). + (* end hide *) (*#* @@ -72,21 +70,21 @@ inline cic:/CoRN/reals/Q_in_CReals/Archimedes'.con. 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]. *) -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: *) -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". (* begin hide *) @@ -98,53 +96,53 @@ Unset Printing Coercions. (*#* 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. *) -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] *) -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]. *) -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]: *) -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 @@ -157,14 +155,14 @@ because it can be used as an starting point for the typical "interval 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. *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/R_morphism.ma b/matita/contribs/CoRN-Decl/reals/R_morphism.ma index 24e1a144d..1118244b4 100644 --- a/matita/contribs/CoRN-Decl/reals/R_morphism.ma +++ b/matita/contribs/CoRN-Decl/reals/R_morphism.ma @@ -16,64 +16,66 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/R_morphism". +include "CoRN.ma". + (* 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 -CReals -*) +include "reals/CReals.ma". (* 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. *) -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. *) -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))). *) -inline cic:/CoRN/reals/R_morphism/fun_pres_Lim.con. +inline "cic:/CoRN/reals/R_morphism/fun_pres_Lim.con". (* 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:= @@ -84,39 +86,39 @@ 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 *) -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 *) -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 *) -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. @@ -126,29 +128,29 @@ End morphism. Section 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". -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. @@ -158,25 +160,25 @@ End composition. Section isomorphism. *) -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. *) -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. *) -inline cic:/CoRN/reals/R_morphism/Isomorphism.ind. +inline "cic:/CoRN/reals/R_morphism/Isomorphism.ind". (* UNEXPORTED End isomorphism. @@ -186,13 +188,13 @@ End isomorphism. 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. @@ -202,29 +204,29 @@ End surjective_map. 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. *) -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. @@ -234,13 +236,13 @@ End with_less. Section with_plus. *) -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. @@ -250,19 +252,19 @@ End with_plus. 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. *) -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. @@ -272,13 +274,13 @@ End surjectivity_helps. 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. diff --git a/matita/contribs/CoRN-Decl/reals/RealFuncts.ma b/matita/contribs/CoRN-Decl/reals/RealFuncts.ma index c717a91e2..ad7b03872 100644 --- a/matita/contribs/CoRN-Decl/reals/RealFuncts.ma +++ b/matita/contribs/CoRN-Decl/reals/RealFuncts.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/RealFuncts". +include "CoRN.ma". + (* $Id: RealFuncts.v,v 1.4 2004/04/07 15:08:10 lcf Exp $ *) -(* INCLUDE -CReals1 -*) +include "reals/CReals1.ma". (*#* * Continuity of Functions on Reals *) @@ -41,9 +41,9 @@ Unset Strict Implicit. Section Continuity. *) -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 @@ -60,15 +60,15 @@ Intervals like $[a,b]$#[a,b]# are defined for arbitrary reals [a,b] (being $\emptyset$#∅# 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: @@ -80,11 +80,11 @@ forall e [>] Zero, exists d [>] Zero, forall (x : IR) ]] *) -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. *) -inline cic:/CoRN/reals/RealFuncts/funLim_Cauchy.con. +inline "cic:/CoRN/reals/RealFuncts/funLim_Cauchy.con". (*#* The first definition implies the second one. *) @@ -113,40 +113,40 @@ forall e [>] Zero, exists d [>] Zero, forall (x : IR) ]] *) -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. *) -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). *) -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 *) -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. diff --git a/matita/contribs/CoRN-Decl/reals/RealLists.ma b/matita/contribs/CoRN-Decl/reals/RealLists.ma index ce7fbdc26..c3aba7338 100644 --- a/matita/contribs/CoRN-Decl/reals/RealLists.ma +++ b/matita/contribs/CoRN-Decl/reals/RealLists.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/RealLists". +include "CoRN.ma". + (* $Id: RealLists.v,v 1.4 2004/04/23 10:01:05 lcf Exp $ *) -(* INCLUDE -CReals1 -*) +include "reals/CReals1.ma". (* UNEXPORTED Section Lists. @@ -37,16 +37,16 @@ Notice that some of the properties listed below only make sense in the context w 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. *) -inline cic:/CoRN/reals/RealLists/length_leEq.con. +inline "cic:/CoRN/reals/RealLists/length_leEq.con". (*#* Length is preserved by mapping. *) @@ -54,7 +54,7 @@ inline cic:/CoRN/reals/RealLists/length_leEq.con. 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. *) @@ -63,42 +63,42 @@ Often we want to map partial functions through a list; this next operator provid 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: *) -inline cic:/CoRN/reals/RealLists/maxlist_greater.con. +inline "cic:/CoRN/reals/RealLists/maxlist_greater.con". (* begin hide *) -inline cic:/CoRN/reals/RealLists/maxlist_aux.con. +inline "cic:/CoRN/reals/RealLists/maxlist_aux.con". (* end hide *) -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". (* begin hide *) -inline cic:/CoRN/reals/RealLists/minlist_aux.con. +inline "cic:/CoRN/reals/RealLists/minlist_aux.con". (* end hide *) -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". (* UNEXPORTED End Lists. diff --git a/matita/contribs/CoRN-Decl/reals/Series.ma b/matita/contribs/CoRN-Decl/reals/Series.ma index ed331dbd1..50dd1005f 100644 --- a/matita/contribs/CoRN-Decl/reals/Series.ma +++ b/matita/contribs/CoRN-Decl/reals/Series.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Series". +include "CoRN.ma". + (* $Id: Series.v,v 1.6 2004/04/23 10:01:05 lcf Exp $ *) (*#* printing seq_part_sum %\ensuremath{\sum^n}% #∑n# *) @@ -24,13 +26,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Series". (*#* printing pi %\ensuremath{\pi}% #π *) -(* INCLUDE -CSumsReals -*) +include "reals/CSumsReals.ma". -(* INCLUDE -NRootIR -*) +include "reals/NRootIR.ma". (* UNEXPORTED Section Definitions. @@ -47,9 +45,9 @@ To each such sequence we can assign a sequence of partial sums. %\end{convention}% *) -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 @@ -57,15 +55,15 @@ difference between two arbitrary elements of the sequence of partial 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. *) -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 @@ -73,25 +71,25 @@ obvious fact that no sequence can be both convergent and divergent, whether 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. *) -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. @@ -101,11 +99,11 @@ End Definitions. Section More_Definitions. *) -inline cic:/CoRN/reals/Series/x.var. +inline "cic:/CoRN/reals/Series/x.var". (*#* 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. @@ -120,7 +118,7 @@ Section Power_Series. 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 @@ -131,19 +129,19 @@ we can also compute its sum. %\end{convention}% *) -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. @@ -159,9 +157,9 @@ Some operations with series preserve convergence. We start by defining 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. @@ -170,33 +168,33 @@ of two convergent series. %\end{convention}% *) -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. *) -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. @@ -206,15 +204,15 @@ End 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. *) -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. @@ -232,19 +230,19 @@ and derive an important corollary for series. 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. @@ -256,13 +254,13 @@ Section Cauchy_Almost_Everywhere. (*#* 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. @@ -278,27 +276,27 @@ Section Convergence_Criteria. %\end{convention}% *) -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. *) -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. *) -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. *) -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. @@ -308,11 +306,11 @@ End Convergence_Criteria. Section More_CC. *) -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. @@ -328,29 +326,29 @@ Alternate series are a special case. Suppose that [x] is nonnegative and 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". (* begin hide *) -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". (* end hide *) -inline cic:/CoRN/reals/Series/alternate_series_conv.con. +inline "cic:/CoRN/reals/Series/alternate_series_conv.con". (* UNEXPORTED End Alternate_Series. @@ -366,17 +364,17 @@ We end this chapter by defining two important numbers in mathematics: [pi] 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. diff --git a/matita/contribs/CoRN-Decl/reals/iso_CReals.ma b/matita/contribs/CoRN-Decl/reals/iso_CReals.ma index 5adaeb0c5..414856a30 100644 --- a/matita/contribs/CoRN-Decl/reals/iso_CReals.ma +++ b/matita/contribs/CoRN-Decl/reals/iso_CReals.ma @@ -16,108 +16,106 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/iso_CReals". +include "CoRN.ma". + (* 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 -Q_dense -*) +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 *) -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. *) -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 ********) -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 **********) -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 ***) -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. diff --git a/matita/contribs/CoRN-Decl/tactics/AlgReflection.ma b/matita/contribs/CoRN-Decl/tactics/AlgReflection.ma index 97fc1571b..fa4524743 100644 --- a/matita/contribs/CoRN-Decl/tactics/AlgReflection.ma +++ b/matita/contribs/CoRN-Decl/tactics/AlgReflection.ma @@ -16,39 +16,39 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/AlgReflection". +include "CoRN.ma". + (* $Id: AlgReflection.v,v 1.2 2004/03/26 16:07:03 lcf Exp $ *) (* begin hide *) -(* INCLUDE -CLogic -*) +include "algebra/CLogic.ma". (* 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. @@ -58,57 +58,57 @@ End Syntactic_Expressions. 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. @@ -118,11 +118,11 @@ End Normalization_Function. 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. diff --git a/matita/contribs/CoRN-Decl/tactics/DiffTactics1.ma b/matita/contribs/CoRN-Decl/tactics/DiffTactics1.ma index 2db26c9d9..a0457f8f7 100644 --- a/matita/contribs/CoRN-Decl/tactics/DiffTactics1.ma +++ b/matita/contribs/CoRN-Decl/tactics/DiffTactics1.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics1". +include "CoRN.ma". + (* begin hide *) (* UNEXPORTED diff --git a/matita/contribs/CoRN-Decl/tactics/DiffTactics2.ma b/matita/contribs/CoRN-Decl/tactics/DiffTactics2.ma index 3c3f0b200..9abd9ae08 100644 --- a/matita/contribs/CoRN-Decl/tactics/DiffTactics2.ma +++ b/matita/contribs/CoRN-Decl/tactics/DiffTactics2.ma @@ -16,27 +16,27 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics2". +include "CoRN.ma". + (* $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. *) -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. @@ -98,19 +98,19 @@ Ltac New_Contin := 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. diff --git a/matita/contribs/CoRN-Decl/tactics/DiffTactics3.ma b/matita/contribs/CoRN-Decl/tactics/DiffTactics3.ma index 658721890..11c2e5504 100644 --- a/matita/contribs/CoRN-Decl/tactics/DiffTactics3.ma +++ b/matita/contribs/CoRN-Decl/tactics/DiffTactics3.ma @@ -16,21 +16,17 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/DiffTactics3". +include "CoRN.ma". + (* $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 := @@ -41,7 +37,7 @@ Ltac Deriv_substR := end. *) -inline cic:/CoRN/tactics/DiffTactics3/symbPF.ind. +inline "cic:/CoRN/tactics/DiffTactics3/symbPF.ind". (* | ssum0 : nat->(nat->symbPF)->symbPF @@ -49,9 +45,9 @@ inline cic:/CoRN/tactics/DiffTactics3/symbPF.ind. | 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 := diff --git a/matita/contribs/CoRN-Decl/tactics/FieldReflection.ma b/matita/contribs/CoRN-Decl/tactics/FieldReflection.ma index 53d9f3dd0..df85a4f70 100644 --- a/matita/contribs/CoRN-Decl/tactics/FieldReflection.ma +++ b/matita/contribs/CoRN-Decl/tactics/FieldReflection.ma @@ -16,71 +16,67 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/FieldReflection". +include "CoRN.ma". + (* $Id: FieldReflection.v,v 1.4 2004/04/23 10:01:06 lcf Exp $ *) (* begin hide *) -(* INCLUDE -CFields -*) +include "algebra/CFields.ma". -(* INCLUDE -AlgReflection -*) +include "tactics/AlgReflection.ma". (* 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. @@ -90,15 +86,15 @@ End Field_Interpretation_Function. 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". (* four kinds of exprs: @@ -118,7 +114,7 @@ P: sorted on M, all M's not an I Opaque Zmult. *) -inline cic:/CoRN/tactics/FieldReflection/MI_mult_corr_F.con. +inline "cic:/CoRN/tactics/FieldReflection/MI_mult_corr_F.con". (* UNEXPORTED Transparent Zmult. @@ -128,7 +124,7 @@ Transparent Zmult. Opaque MI_mult. *) -inline cic:/CoRN/tactics/FieldReflection/MV_mult_corr_F.con. +inline "cic:/CoRN/tactics/FieldReflection/MV_mult_corr_F.con". (* UNEXPORTED Transparent MI_mult. @@ -138,7 +134,7 @@ Transparent 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. @@ -148,7 +144,7 @@ Transparent MV_mult MI_mult. Opaque MV_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. @@ -158,7 +154,7 @@ Transparent MV_mult. Opaque MM_plus. *) -inline cic:/CoRN/tactics/FieldReflection/PM_plus_corr_F.con. +inline "cic:/CoRN/tactics/FieldReflection/PM_plus_corr_F.con". (* UNEXPORTED Transparent MM_plus. @@ -168,7 +164,7 @@ Transparent MM_plus. Opaque PM_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. @@ -178,37 +174,37 @@ Transparent PM_plus. 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. *) -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. *) -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. *) -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. diff --git a/matita/contribs/CoRN-Decl/tactics/GroupReflection.ma b/matita/contribs/CoRN-Decl/tactics/GroupReflection.ma index 15858b6be..d065530ab 100644 --- a/matita/contribs/CoRN-Decl/tactics/GroupReflection.ma +++ b/matita/contribs/CoRN-Decl/tactics/GroupReflection.ma @@ -16,63 +16,61 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/GroupReflection". +include "CoRN.ma". + (* $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. *) -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. @@ -126,9 +124,9 @@ Opaque cg_inv. Opaque cg_minus. *) -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. @@ -138,15 +136,15 @@ End Group_Interpretation_Function. 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". (* four kinds of exprs: @@ -162,13 +160,13 @@ M: sorted on V 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. *) -inline cic:/CoRN/tactics/GroupReflection/MI_mult_corr_G.con. +inline "cic:/CoRN/tactics/GroupReflection/MI_mult_corr_G.con". (* UNEXPORTED Transparent Zmult. @@ -178,13 +176,13 @@ Transparent Zmult. Opaque MI_mult. *) -inline cic:/CoRN/tactics/GroupReflection/MV_mult_corr_G.con. +inline "cic:/CoRN/tactics/GroupReflection/MV_mult_corr_G.con". (* 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. @@ -194,7 +192,7 @@ Transparent MV_mult MI_mult. Opaque MV_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. @@ -204,7 +202,7 @@ Transparent MV_mult. Opaque MM_plus. *) -inline cic:/CoRN/tactics/GroupReflection/PM_plus_corr_G.con. +inline "cic:/CoRN/tactics/GroupReflection/PM_plus_corr_G.con". (* UNEXPORTED Transparent MM_plus. @@ -214,7 +212,7 @@ Transparent MM_plus. Opaque PM_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. @@ -224,17 +222,17 @@ Transparent PM_plus. 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. *) -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. diff --git a/matita/contribs/CoRN-Decl/tactics/Opaque_algebra.ma b/matita/contribs/CoRN-Decl/tactics/Opaque_algebra.ma index a5139538e..f614cbdac 100644 --- a/matita/contribs/CoRN-Decl/tactics/Opaque_algebra.ma +++ b/matita/contribs/CoRN-Decl/tactics/Opaque_algebra.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/Opaque_algebra". +include "CoRN.ma". + (* $Id: Opaque_algebra.v,v 1.1 2004/02/11 10:56:57 lcf Exp $ *) (* Opaque cs_crr. *) diff --git a/matita/contribs/CoRN-Decl/tactics/RingReflection.ma b/matita/contribs/CoRN-Decl/tactics/RingReflection.ma index bd8849850..c4d87d251 100644 --- a/matita/contribs/CoRN-Decl/tactics/RingReflection.ma +++ b/matita/contribs/CoRN-Decl/tactics/RingReflection.ma @@ -16,63 +16,61 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/RingReflection". +include "CoRN.ma". + (* $Id: RingReflection.v,v 1.4 2004/04/23 10:01:06 lcf Exp $ *) (* begin hide *) -(* INCLUDE -CRings -*) +include "algebra/CRings.ma". -(* INCLUDE -AlgReflection -*) +include "tactics/AlgReflection.ma". (* 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. @@ -142,9 +140,9 @@ Opaque cr_mult. Opaque nexp_op. *) -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. @@ -154,15 +152,15 @@ End Ring_Interpretation_Function. 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". (* four kinds of exprs: @@ -182,7 +180,7 @@ P: sorted on M, all M's not an I Opaque Zmult. *) -inline cic:/CoRN/tactics/RingReflection/MI_mult_corr_R.con. +inline "cic:/CoRN/tactics/RingReflection/MI_mult_corr_R.con". (* UNEXPORTED Transparent Zmult. @@ -192,7 +190,7 @@ Transparent Zmult. Opaque MI_mult. *) -inline cic:/CoRN/tactics/RingReflection/MV_mult_corr_R.con. +inline "cic:/CoRN/tactics/RingReflection/MV_mult_corr_R.con". (* UNEXPORTED Transparent MI_mult. @@ -202,7 +200,7 @@ Transparent 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. @@ -212,7 +210,7 @@ Transparent MV_mult MI_mult. Opaque MV_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. @@ -222,7 +220,7 @@ Transparent MV_mult. Opaque MM_plus. *) -inline cic:/CoRN/tactics/RingReflection/PM_plus_corr_R.con. +inline "cic:/CoRN/tactics/RingReflection/PM_plus_corr_R.con". (* UNEXPORTED Transparent MM_plus. @@ -232,7 +230,7 @@ Transparent MM_plus. Opaque PM_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. @@ -242,13 +240,13 @@ Transparent PM_plus. 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. *) -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. @@ -310,9 +308,9 @@ Step_final x2. Qed. *) -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. diff --git a/matita/contribs/CoRN-Decl/tactics/Step.ma b/matita/contribs/CoRN-Decl/tactics/Step.ma index 1008be2e4..4b922027a 100644 --- a/matita/contribs/CoRN-Decl/tactics/Step.ma +++ b/matita/contribs/CoRN-Decl/tactics/Step.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/Step". +include "CoRN.ma". + (* begin hide *) (* UNEXPORTED diff --git a/matita/contribs/CoRN-Decl/tactics/Transparent_algebra.ma b/matita/contribs/CoRN-Decl/tactics/Transparent_algebra.ma index 490ca4bb8..25fdc7e60 100644 --- a/matita/contribs/CoRN-Decl/tactics/Transparent_algebra.ma +++ b/matita/contribs/CoRN-Decl/tactics/Transparent_algebra.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/tactics/Transparent_algebra". +include "CoRN.ma". + (* $Id: Transparent_algebra.v,v 1.1 2004/02/11 10:56:58 lcf Exp $ *) (* UNEXPORTED diff --git a/matita/contribs/CoRN-Decl/transc/Exponential.ma b/matita/contribs/CoRN-Decl/transc/Exponential.ma index 8a1b637c6..434241caa 100644 --- a/matita/contribs/CoRN-Decl/transc/Exponential.ma +++ b/matita/contribs/CoRN-Decl/transc/Exponential.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/transc/Exponential". +include "CoRN.ma". + (* $Id: Exponential.v,v 1.7 2004/04/23 10:01:07 lcf Exp $ *) -(* INCLUDE -TaylorSeries -*) +include "transc/TaylorSeries.ma". (* UNEXPORTED Opaque Min Max. @@ -35,20 +35,20 @@ The main properties of the exponential and logarithmic functions. 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. *) -inline cic:/CoRN/transc/Exponential/Exp_zero.con. +inline "cic:/CoRN/transc/Exponential/Exp_zero.con". (*#* $e^1=e$#e1=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. @@ -58,13 +58,13 @@ Hint Resolve Exp_zero Exp_one: algebra. 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. *) -inline cic:/CoRN/transc/Exponential/Continuous_Exp.con. +inline "cic:/CoRN/transc/Exponential/Continuous_Exp.con". (* UNEXPORTED Hint Resolve Continuous_Exp: continuous. @@ -74,20 +74,20 @@ Hint Resolve Continuous_Exp: continuous. 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. *) -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. @@ -97,25 +97,25 @@ Opaque Expon. Transparent Expon. *) -inline cic:/CoRN/transc/Exponential/Exp_unique.con. +inline "cic:/CoRN/transc/Exponential/Exp_unique.con". (* 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. *) -inline cic:/CoRN/transc/Exponential/Exp_plus.con. +inline "cic:/CoRN/transc/Exponential/Exp_plus.con". (* 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. @@ -125,52 +125,52 @@ Hint Resolve Exp_inv_char: algebra. from zero. *) -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. *) -inline cic:/CoRN/transc/Exponential/Exp_inv.con. +inline "cic:/CoRN/transc/Exponential/Exp_inv.con". (* 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. *) -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. *) -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]. *) -inline cic:/CoRN/transc/Exponential/Derivative_Log.con. +inline "cic:/CoRN/transc/Exponential/Derivative_Log.con". (* 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. @@ -178,7 +178,7 @@ Hint Resolve Continuous_Log: continuous. (*#* 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. @@ -186,9 +186,9 @@ Hint Resolve Log_one: algebra. (*#* 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. @@ -204,17 +204,17 @@ Opaque 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. *) -inline cic:/CoRN/transc/Exponential/Log_mult'.con. +inline "cic:/CoRN/transc/Exponential/Log_mult'.con". (*#* 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. @@ -224,9 +224,9 @@ Opaque Expon Logarithm. 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. @@ -236,11 +236,11 @@ Transparent Logarithm. 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. *) -inline cic:/CoRN/transc/Exponential/Exp_Log.con. +inline "cic:/CoRN/transc/Exponential/Exp_Log.con". (* UNEXPORTED Hint Resolve Exp_Log: algebra. @@ -248,9 +248,9 @@ Hint Resolve Exp_Log: algebra. (*#* 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. @@ -258,9 +258,9 @@ Opaque Logarithm. (*#* 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. @@ -268,43 +268,43 @@ Hint Resolve Log_E: algebra. (*#* 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. *) -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. *) -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. *) -inline cic:/CoRN/transc/Exponential/Log_div'.con. +inline "cic:/CoRN/transc/Exponential/Log_div'.con". diff --git a/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma b/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma index 6ec5b90b4..7e6d8f719 100644 --- a/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma +++ b/matita/contribs/CoRN-Decl/transc/InvTrigonom.ma @@ -16,19 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/transc/InvTrigonom". +include "CoRN.ma". + (* $Id: InvTrigonom.v,v 1.9 2004/04/23 10:01:07 lcf Exp $ *) -(* INCLUDE -RealPowers -*) +include "transc/RealPowers.ma". -(* INCLUDE -TrigMon -*) +include "transc/TrigMon.ma". -(* INCLUDE -StrongIVT -*) +include "ftc/StrongIVT.ma". (*#* printing ArcSin %\ensuremath{\arcsin}% *) @@ -55,17 +51,17 @@ Arccosine is defined in terms of arcsine by the relation 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. @@ -78,28 +74,28 @@ Hint Resolve Continuous_ArcSin: continuous. (*#* ***Arccosine *) -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". (*#* ***Arctangent *) -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. @@ -120,59 +116,59 @@ We now prove that this functions are in fact inverses to the corresponding trigo ***Sine and Arcsine *) -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. *) -inline cic:/CoRN/transc/InvTrigonom/ArcSin_Sin.con. +inline "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin.con". (* UNEXPORTED Transparent ArcSin. *) -inline cic:/CoRN/transc/InvTrigonom/ArcSin_range.con. +inline "cic:/CoRN/transc/InvTrigonom/ArcSin_range.con". (* 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 *) -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. *) -inline cic:/CoRN/transc/InvTrigonom/ArcCos_resp_leEq.con. +inline "cic:/CoRN/transc/InvTrigonom/ArcCos_resp_leEq.con". (*#* ***Tangent and Arctangent *) -inline cic:/CoRN/transc/InvTrigonom/maps_Tan.con. +inline "cic:/CoRN/transc/InvTrigonom/maps_Tan.con". (* UNEXPORTED Opaque Tang. *) -inline cic:/CoRN/transc/InvTrigonom/ArcTan_Tan_inv.con. +inline "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan_inv.con". (* UNEXPORTED Transparent Tang. @@ -182,7 +178,7 @@ Transparent Tang. Opaque ArcTang. *) -inline cic:/CoRN/transc/InvTrigonom/ArcTan_Tan.con. +inline "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan.con". (* UNEXPORTED Opaque iprop. @@ -196,7 +192,7 @@ Transparent iprop. Opaque Cos. *) -inline cic:/CoRN/transc/InvTrigonom/Tan_ilim.con. +inline "cic:/CoRN/transc/InvTrigonom/Tan_ilim.con". (* UNEXPORTED Opaque Min. @@ -210,65 +206,65 @@ Transparent Cos. Section ArcTan_Range. *) -inline cic:/CoRN/transc/InvTrigonom/x.var. +inline "cic:/CoRN/transc/InvTrigonom/x.var". (* begin hide *) -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". (* end hide *) @@ -276,7 +272,7 @@ inline cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con. Transparent ArcTang. *) -inline cic:/CoRN/transc/InvTrigonom/ArcTan_range.con. +inline "cic:/CoRN/transc/InvTrigonom/ArcTan_range.con". (* UNEXPORTED End ArcTan_Range. @@ -286,13 +282,13 @@ End ArcTan_Range. Transparent ArcTang. *) -inline cic:/CoRN/transc/InvTrigonom/Tan_ArcTan.con. +inline "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan.con". (* UNEXPORTED Opaque ArcTang. *) -inline cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con. +inline "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con". (* UNEXPORTED End Inverses. diff --git a/matita/contribs/CoRN-Decl/transc/Pi.ma b/matita/contribs/CoRN-Decl/transc/Pi.ma index 0505c2794..3f077c443 100644 --- a/matita/contribs/CoRN-Decl/transc/Pi.ma +++ b/matita/contribs/CoRN-Decl/transc/Pi.ma @@ -16,9 +16,9 @@ set "baseuri" "cic:/matita/CoRN-Decl/transc/Pi". -(* INCLUDE -SinCos -*) +include "CoRN.ma". + +include "transc/SinCos.ma". (* UNEXPORTED Section Properties_of_Pi. @@ -31,7 +31,7 @@ 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. *) -inline cic:/CoRN/transc/Pi/pi_seq.con. +inline "cic:/CoRN/transc/Pi/pi_seq.con". (* UNEXPORTED Opaque Cosine. @@ -43,7 +43,7 @@ Opaque Cosine. Opaque Sine. *) -inline cic:/CoRN/transc/Pi/pi_seq_lemma.con. +inline "cic:/CoRN/transc/Pi/pi_seq_lemma.con". (* end hide *) @@ -53,64 +53,64 @@ This sequence is nonnegative and the cosine of any number between 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. *) -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". (* begin hide *) -inline cic:/CoRN/transc/Pi/pi_seq_gt_one.con. +inline "cic:/CoRN/transc/Pi/pi_seq_gt_one.con". (* 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. *) -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. *) -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#. *) -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. *) -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. @@ -139,45 +139,45 @@ A summary of what is being proved is simply: [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. @@ -210,23 +210,23 @@ We now move back to trigonometric identities: sine, cosine and tangent of the double. *) -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". (* begin hide *) -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]. *) -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. @@ -236,31 +236,31 @@ Hint Resolve Sin_QuarterPi Cos_QuarterPi: algebra. Opaque Sine Cosine. *) -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]. *) -inline cic:/CoRN/transc/Pi/Sin_HalfPi.con. +inline "cic:/CoRN/transc/Pi/Sin_HalfPi.con". (* 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. @@ -268,11 +268,11 @@ Hint Resolve Sin_plus_Pi Cos_plus_Pi: algebra. (*#* 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. diff --git a/matita/contribs/CoRN-Decl/transc/PowerSeries.ma b/matita/contribs/CoRN-Decl/transc/PowerSeries.ma index de37b5e48..ffd7d4720 100644 --- a/matita/contribs/CoRN-Decl/transc/PowerSeries.ma +++ b/matita/contribs/CoRN-Decl/transc/PowerSeries.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/transc/PowerSeries". +include "CoRN.ma". + (* $Id: PowerSeries.v,v 1.8 2004/04/23 10:01:08 lcf Exp $ *) (*#* printing Exp %\ensuremath{\exp}% *) @@ -28,9 +30,7 @@ set "baseuri" "cic:/matita/CoRN-Decl/transc/PowerSeries". (*#* printing Tan %\ensuremath{\tan}% *) -(* INCLUDE -FTC -*) +include "ftc/FTC.ma". (*#* *More on Power Series @@ -50,15 +50,15 @@ Let [a : nat -> IR]. %\end{convention}% *) -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 @@ -67,39 +67,39 @@ is the Dirichlet criterium. (* begin show *) -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". (* end show *) -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. *) -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. *) -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". (* begin show *) -inline cic:/CoRN/transc/PowerSeries/Ha'.var. +inline "cic:/CoRN/transc/PowerSeries/Ha'.var". (* end show *) -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. @@ -119,31 +119,31 @@ respectively by [a] and by [fun n => (a (S n))]. %\end{convention}% *) -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". (* begin hide *) -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 *) -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. *) -inline cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con. +inline "cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con". (*#* And a rule for differentiation. *) @@ -151,7 +151,7 @@ inline cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con. Opaque nring fac. *) -inline cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con. +inline "cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con". (* UNEXPORTED End More_on_PowerSeries. @@ -168,55 +168,55 @@ series, and prove their convergence. Tangent is defined as the 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. *) -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. *) -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. @@ -230,13 +230,13 @@ Hint Resolve included_Exp included_Sin included_Cos: included. 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". diff --git a/matita/contribs/CoRN-Decl/transc/RealPowers.ma b/matita/contribs/CoRN-Decl/transc/RealPowers.ma index 26a378354..5c4f4cbdd 100644 --- a/matita/contribs/CoRN-Decl/transc/RealPowers.ma +++ b/matita/contribs/CoRN-Decl/transc/RealPowers.ma @@ -16,15 +16,15 @@ set "baseuri" "cic:/matita/CoRN-Decl/transc/RealPowers". +include "CoRN.ma". + (* $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. @@ -39,7 +39,7 @@ $x^y=e^{y\times\log(x)}$#xy=ey*log(x)#, whenever [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 @@ -48,29 +48,29 @@ still has all the good properties of that operation; when [x [=] e] it 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. *) -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. *) -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. @@ -80,45 +80,45 @@ Hint Resolve power_zero power_one: algebra. Opaque nexp_op. *) -inline cic:/CoRN/transc/RealPowers/power_int.con. +inline "cic:/CoRN/transc/RealPowers/power_int.con". (* 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. *) -inline cic:/CoRN/transc/RealPowers/div_power.con. +inline "cic:/CoRN/transc/RealPowers/div_power.con". (* 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. *) -inline cic:/CoRN/transc/RealPowers/power_recip.con. +inline "cic:/CoRN/transc/RealPowers/power_recip.con". (* 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. @@ -137,17 +137,17 @@ on partial functions which preserves continuity. %\end{convention}% *) -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. @@ -163,7 +163,7 @@ Opaque Expon Logarithm. (*#* 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. *) @@ -175,9 +175,9 @@ Transparent Logarithm. Opaque Logarithm. *) -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. diff --git a/matita/contribs/CoRN-Decl/transc/SinCos.ma b/matita/contribs/CoRN-Decl/transc/SinCos.ma index b52f1f300..4a226195f 100644 --- a/matita/contribs/CoRN-Decl/transc/SinCos.ma +++ b/matita/contribs/CoRN-Decl/transc/SinCos.ma @@ -16,11 +16,11 @@ set "baseuri" "cic:/matita/CoRN-Decl/transc/SinCos". +include "CoRN.ma". + (* $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. @@ -32,19 +32,19 @@ Opaque Sine Cosine. (* begin hide *) -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". (* end hide *) -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. @@ -56,7 +56,7 @@ Hint Resolve Cos_plus Sin_plus: algebra. (*#* 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. @@ -64,9 +64,9 @@ Transparent Sine Cosine. (*#* 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. @@ -76,7 +76,7 @@ Opaque Sine Cosine. 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. @@ -90,7 +90,7 @@ The fundamental formulas of trigonometry: $\cos(x)^2+\sin(x)^2=1$#cos(x)2