module PEH = ProofEngineHelpers
module HEL = HExtlib
module DTI = DoubleTypeInference
+module NU = CicNotationUtil
module Cl = ProceduralClassify
module T = ProceduralTypes
and proc_bkd_proofs st synth names classes ts =
try
- let get_note =
- let names = ref (names, push st) in
- fun f ->
- match !names with
- | [], st -> fun _ -> f st
- | "" :: tl, st -> names := tl, st; fun _ -> f st
- | hd :: tl, st ->
- let note = case st hd in
- names := tl, inc st;
- fun b -> if b then T.Note note :: f st else f st
+ let get_names b = ref (names, if b then push st else st) in
+ let get_note f b names =
+ match !names with
+ | [], st -> f st
+ | "" :: tl, st -> names := tl, st; f st
+ | hd :: tl, st ->
+ let note = case st hd in
+ names := tl, inc st;
+ if b then T.Note note :: f st else f st
in
let _, dtext = test_depth st in
let aux (inv, _) v =
in
let ps = T.list_map2_filter aux classes ts in
let b = List.length ps > 1 in
- List.rev_map (fun f -> f b) ps
+ let names = get_names b in
+ List.rev_map (fun f -> f b names) ps
with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
(* object costruction *******************************************************)
-let is_theorem pars =
- pars = [] ||
- List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
- List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
-
-let is_definition pars =
- List.mem (`Flavour `Definition) pars
-
-let proc_obj st = function
- | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
- let ast = proc_proof st v in
- let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
- let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
- T.Statement (`Theorem, Some s, t, None, "") :: ast @ [T.Qed text]
- | C.AConstant (_, _, s, Some v, t, [], pars) when is_definition pars ->
- [T.Statement (`Definition, Some s, t, Some v, "")]
- | C.AConstant (_, _, s, None, t, [], pars) ->
+let th_flavours = [`Theorem; `Lemma; `Remark; `Fact]
+
+let def_flavours = [`Definition]
+
+let get_flavour ?flavour attrs =
+ let rec aux = function
+ | [] -> List.hd th_flavours
+ | `Flavour fl :: _ -> fl
+ | _ :: tl -> aux tl
+ in
+ match flavour with
+ | Some fl -> fl
+ | None -> aux attrs
+
+let proc_obj ?flavour st = function
+ | C.AConstant (_, _, s, Some v, t, [], attrs) ->
+ begin match get_flavour ?flavour attrs with
+ | flavour when List.mem flavour th_flavours ->
+ let ast = proc_proof st v in
+ let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
+ let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
+ T.Statement (flavour, Some s, t, None, "") :: ast @ [T.Qed text]
+ | flavour when List.mem flavour def_flavours ->
+ [T.Statement (flavour, Some s, t, Some v, "")]
+ | _ ->
+ failwith "not a theorem, definition, axiom or inductive type"
+ end
+ | C.AConstant (_, _, s, None, t, [], attrs) ->
[T.Statement (`Axiom, Some s, t, None, "")]
- | _ ->
- failwith "not a theorem, definition, axiom"
+ | C.AInductiveDefinition (_, types, [], lpsno, attrs) ->
+ [T.Inductive (types, lpsno, "")]
+ | _ ->
+ failwith "not a theorem, definition, axiom or inductive type"
(* interface functions ******************************************************)
case = []
} in
HLog.debug "Procedural: level 2 transformation";
- let steps = proc_obj st anobj in
+ let steps = proc_obj st ?flavour anobj in
HLog.debug "Procedural: grafite rendering";
List.rev (T.render_steps [] steps)
(****************************************************************************)
-type flavour = Cic.object_flavour
+type flavour = C.object_flavour
type name = string option
type hyp = string
-type what = Cic.annterm
+type what = C.annterm
type how = bool
-type using = Cic.annterm
+type using = C.annterm
type count = int
type note = string
type where = (hyp * name) option
-type inferred = Cic.annterm
-type pattern = Cic.annterm
-type body = Cic.annterm option
+type inferred = C.annterm
+type pattern = C.annterm
+type body = C.annterm option
+type types = C.anninductiveType list
+type lpsno = int
type step = Note of note
- | Statement of flavour * name * what * body * note
+ | Inductive of types * lpsno * note
+ | Statement of flavour * name * what * body * note
| Qed of note
| Id of note
| Intros of count option * name list * note
(* annterm constructors *****************************************************)
-let mk_arel i b = Cic.ARel ("", "", i, b)
+let mk_arel i b = C.ARel ("", "", i, b)
+
+(* FG: this is really awful !! *)
+let arel_of_name = function
+ | C.Name s -> mk_arel 0 s
+ | C.Anonymous -> mk_arel 0 "_"
+
+(* helper functions on left params for use with inductive types *************)
+
+let strip_lps lpsno arity =
+ let rec aux no lps = function
+ | C.AProd (_, name, w, t) when no > 0 ->
+ let lp = name, Some w in
+ aux (pred no) (lp :: lps) t
+ | t -> lps, t
+ in
+ aux lpsno [] arity
+
+let merge_lps lps1 lps2 =
+ let map (n1, w1) (n2, _) =
+ let n = match n1, n2 with
+ | C.Name _, _ -> n1
+ | _ -> n2
+ in
+ n, w1
+ in
+ if lps1 = [] then lps2 else
+ List.map2 map lps1 lps2
(* grafite ast constructors *************************************************)
let mk_thnote str a =
if str = "" then a else mk_note "" :: mk_note str :: a
+let mk_inductive types lpsno =
+ let map1 (lps1, cons) (name, arity) =
+ let lps2, arity = strip_lps lpsno arity in
+ merge_lps lps1 lps2, (name, arity) :: cons
+ in
+ let map2 (lps1, types) (_, name, kind, arity, cons) =
+ let lps2, arity = strip_lps lpsno arity in
+ let lps1, rev_cons = List.fold_left map1 (lps1, []) cons in
+ merge_lps lps1 lps2, (name, kind, arity, List.rev rev_cons) :: types
+ in
+ let map3 (name, xw) = arel_of_name name, xw in
+ let rev_lps, rev_types = List.fold_left map2 ([], []) types in
+ let lpars, types = List.rev_map map3 rev_lps, List.rev rev_types in
+ let obj = N.Inductive (lpars, types) in
+ G.Executable (floc, G.Command (floc, G.Obj (floc, obj)))
+
let mk_statement flavour name t v =
let name = match name with Some name -> name | None -> assert false in
let obj = N.Theorem (flavour, name, t, v) in
let rec render_step sep a = function
| Note s -> mk_notenote s a
| Statement (f, n, t, v, s) -> mk_statement f n t v :: mk_thnote s a
+ | Inductive (lps, ts, s) -> mk_inductive lps ts :: mk_thnote s a
| Qed s -> mk_qed :: mk_tacnote s a
| Id s -> mk_id sep :: mk_tacnote s a
| Intros (c, ns, s) -> mk_intros c ns sep :: mk_tacnote s a
let rec count_node a = function
| Note _
+ | Inductive _
| Statement _
| Qed _
| Id _
type inferred = Cic.annterm
type pattern = Cic.annterm
type body = Cic.annterm option
+type types = Cic.anninductiveType list
+type lpsno = int
type step = Note of note
+ | Inductive of types * lpsno * note
| Statement of flavour * name * what * body * note
| Qed of note
| Id of note
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 path = function
- | T.Inline (b, k, obj, p) ->
+ | T.Inline (b, k, obj, p, f) ->
let obj, p =
if b then Filename.concat (make_path path) obj, make_prefix path
else obj, p
in
let s = obj ^ G.string_of_inline_kind k in
- path, Some (T.Inline (b, k, Filename.concat in_base_uri s, p))
+ path, Some (T.Inline (b, k, Filename.concat in_base_uri s, p, f))
| T.Include s ->
begin
try path, Some (T.Include (List.assoc s st.requires))
let coercion value =
command_of_obj (G.Coercion (floc, UM.uri_of_string value, true, 0, 0))
-let inline (kind, uri, prefix) =
+let inline (kind, uri, prefix, flavour) =
let kind = match kind with
| T.Declarative -> G.Declarative
| T.Procedural -> G.Procedural None
in
- command_of_macro (G.Inline (floc, kind, uri, prefix, None))
+ command_of_macro (G.Inline (floc, kind, uri, prefix, flavour))
let out_alias och name uri =
Printf.fprintf och "alias id \"%s\" = \"%s\".\n\n" name uri
let commit kind och items =
let trd (_, _, x) = x in
- let trd_rth kind (_, _, x, y) = kind, x, y in
+ let trd_rth kind (_, _, x, y, z) = kind, x, y, z in
let commit = function
| T.Heading heading -> out_preamble och heading
| T.Line line -> out_line_comment och line
| T.Include script -> out_command och (require script)
| T.Coercion specs -> out_unexported och "COERCION" (snd specs)
| T.Notation specs -> out_unexported och "NOTATION" (snd specs) (**)
- | T.Inline (_, T.Var, src, _) -> out_alias och (UriManager.name_of_uri (UriManager.uri_of_string src)) src
+ | T.Inline (_, T.Var, src, _, _) -> out_alias och (UriManager.name_of_uri (UriManager.uri_of_string src)) src
| T.Inline specs -> out_command och (inline (trd_rth kind specs))
| T.Section specs -> out_unexported och "UNEXPORTED" (trd specs)
| T.Comment comment -> out_comment och comment
type prefix = string
+type flavour = Cic.object_flavour option
+
type item = Heading of (string * int)
| Line of string
| Comment of string
| Coercion of (local * string)
| Notation of (local * string)
| Section of (local * string * string)
- | Inline of (local * inline_kind * source * prefix)
+ | Inline of (local * inline_kind * source * prefix * flavour)
| Verbatim of string
| Discard of string
let cat x = String.concat " " x
let mk_vars local idents =
- let map ident = T.Inline (local, T.Var, trim ident, "") in
+ let map ident = T.Inline (local, T.Var, trim ident, "", None) in
List.map map idents
let strip2 s =
let notation str =
[T.Notation (false, str); T.Notation (true, str)]
+
+ let mk_flavour str =
+ match trim str with
+ | "Remark" -> Some `Remark
+ | "Lemma" -> Some `Lemma
+ | "Theorem" -> Some `Theorem
+ | "Definition" -> Some `Definition
+ | "Fixpoint" -> Some `Definition
+ | "Let" -> Some `Definition
+ | _ -> assert false
%}
%token <string> SPC STR IDENT INT EXTRA AC OP CP OC CC OQ CQ DEF FS COE CN SC
%token <string> ABBR IN LET TH PROOF QED VAR AX IND SEC END UNX REQ XP IP SET NOT LOAD ID COERC
macro_step:
| th ident restricts fs proof FS steps qed FS
- { out "TH" $2; $7 @ [T.Inline (false, T.Con, trim $2, "")] }
+ { out "TH" $2;
+ $7 @ [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)]
+ }
| th ident restricts fs proof restricts FS
- { out "TH" $2; [T.Inline (false, T.Con, trim $2, "")] }
+ { out "TH" $2;
+ [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)]
+ }
| th ident restricts fs steps qed FS
- { out "TH" $2; $5 @ [T.Inline (false, T.Con, trim $2, "")] }
+ { out "TH" $2;
+ $5 @ [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)]
+ }
| th ident restricts def restricts FS
- { out "TH" $2; [T.Inline (false, T.Con, trim $2, "")] }
+ { out "TH" $2;
+ [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)]
+ }
| th ident def restricts FS
- { out "TH" $2; [T.Inline (false, T.Con, trim $2, "")] }
+ { out "TH" $2;
+ [T.Inline (false, T.Con, trim $2, "", mk_flavour $1)]
+ }
| xlet ident restricts fs proof FS steps qed FS
- { out "LET" $2; $7 @ [T.Inline (true, T.Con, trim $2, "")] }
+ { out "LET" $2;
+ $7 @ [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)]
+ }
| xlet ident restricts fs proof restricts FS
- { out "LET" $2; [T.Inline (true, T.Con, trim $2, "")] }
+ { out "LET" $2;
+ [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)]
+ }
| xlet ident restricts fs steps qed FS
- { out "LET" $2; $5 @ [T.Inline (true, T.Con, trim $2, "")] }
+ { out "LET" $2;
+ $5 @ [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)]
+ }
| xlet ident restricts def restricts FS
- { out "LET" $2; [T.Inline (true, T.Con, trim $2, "")] }
+ { out "LET" $2;
+ [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)]
+ }
| xlet ident def restricts FS
- { out "LET" $2; [T.Inline (true, T.Con, trim $2, "")] }
+ { out "LET" $2;
+ [T.Inline (true, T.Con, trim $2, "", mk_flavour $1)]
+ }
| var idents xres FS
- { out "VAR" (cat $2); mk_vars true $2 }
+ { out "VAR" (cat $2); mk_vars true $2 }
| ax idents xres FS
- { out "AX" (cat $2); mk_vars false $2 }
+ { out "AX" (cat $2); mk_vars false $2 }
| ind ident unexports FS
- { out "IND" $2; T.Inline (false, T.Ind, trim $2, "") :: snd $3 }
+ { out "IND" $2;
+ T.Inline (false, T.Ind, trim $2, "", None) :: snd $3
+ }
| sec ident FS
- { out "SEC" $2; [T.Section (true, trim $2, $1 ^ $2)] }
+ { out "SEC" $2; [T.Section (true, trim $2, $1 ^ $2)] }
| xend ident FS
- { out "END" $2; [T.Section (false, trim $2, $1 ^ $2)] }
+ { out "END" $2; [T.Section (false, trim $2, $1 ^ $2)] }
| unx unexports FS
- { out "UNX" (fst $2); [T.Unexport ($1 ^ fst $2 ^ trim $3)] }
+ { out "UNX" (fst $2); [T.Unexport ($1 ^ fst $2 ^ trim $3)] }
| req xp ident FS
- { out "REQ" $3; [T.Include (trim $3)] }
+ { out "REQ" $3; [T.Include (trim $3)] }
| req ip ident FS
- { out "REQ" $3; [T.Include (trim $3)] }
+ { out "REQ" $3; [T.Include (trim $3)] }
| req ident FS
- { out "REQ" $2; [T.Include (trim $2)] }
+ { out "REQ" $2; [T.Include (trim $2)] }
| load str FS
- { out "REQ" $2; [T.Include (strip2 (trim $2))] }
+ { out "REQ" $2; [T.Include (strip2 (trim $2))] }
| coerc qid spcs cn unexports FS
- { out "COERCE" (hd $2); coercion (hd $2) }
+ { out "COERCE" (hd $2); coercion (hd $2) }
| id coerc qid spcs cn unexports FS
- { out "COERCE" (hd $3); coercion (hd $3) }
+ { out "COERCE" (hd $3); coercion (hd $3) }
| th ident error
- { out "ERROR" $2; failwith ("macro_step " ^ $2) }
+ { out "ERROR" $2; failwith ("macro_step " ^ $2) }
| ind ident error
- { out "ERROR" $2; failwith ("macro_step " ^ $2) }
+ { out "ERROR" $2; failwith ("macro_step " ^ $2) }
| var idents error
{ let vs = cat $2 in
- out "ERROR" vs; failwith ("macro_step " ^ vs) }
+ out "ERROR" vs; failwith ("macro_step " ^ vs) }
| ax idents error
{ let vs = cat $2 in
- out "ERROR" vs; failwith ("macro_step " ^ vs) }
+ out "ERROR" vs; failwith ("macro_step " ^ vs) }
;
item:
| OQ verbatims CQ { [T.Comment $2] }
in
let flavour_pp = function
| None -> ""
- | Some `Definition -> "as definition"
- | Some `MutualDefinition -> "as mutual"
- | Some `Fact -> "as fact"
- | Some `Lemma -> "as lemma"
- | Some `Remark -> "as remark"
- | Some `Theorem -> "as theorem"
- | Some `Variant -> "as variant"
- | Some `Axiom -> "as axiom"
+ | Some `Definition -> " as definition"
+ | Some `MutualDefinition -> " as mutual"
+ | Some `Fact -> " as fact"
+ | Some `Lemma -> " as lemma"
+ | Some `Remark -> " as remark"
+ | Some `Theorem -> " as theorem"
+ | Some `Variant -> " as variant"
+ | Some `Axiom -> " as axiom"
in
function
(* Whelp *)
This is random stuff that should be in the Coq basic library.
*)
-inline procedural "cic:/CoRN/algebra/Basics/lt_le_dec.con".
+inline procedural "cic:/CoRN/algebra/Basics/lt_le_dec.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/lt_z_two.con".
+inline procedural "cic:/CoRN/algebra/Basics/lt_z_two.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/le_pred.con".
+inline procedural "cic:/CoRN/algebra/Basics/le_pred.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/lt_mult_right.con".
+inline procedural "cic:/CoRN/algebra/Basics/lt_mult_right.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/le_mult_right.con".
+inline procedural "cic:/CoRN/algebra/Basics/le_mult_right.con" as lemma.
(*#* The power function does not exist in the standard library *)
-inline procedural "cic:/CoRN/algebra/Basics/power.con".
+inline procedural "cic:/CoRN/algebra/Basics/power.con" as definition.
(*#* Factorial function. Does not exist in Arith.
Needed for special operations on polynomials. *)
-inline procedural "cic:/CoRN/algebra/Basics/fac.con".
+inline procedural "cic:/CoRN/algebra/Basics/fac.con" as definition.
-inline procedural "cic:/CoRN/algebra/Basics/nat_fac_gtzero.con".
+inline procedural "cic:/CoRN/algebra/Basics/nat_fac_gtzero.con" as lemma.
(* needed for computational behavior of "Inversion" tactic *)
Qed.
*)
-inline procedural "cic:/CoRN/algebra/Basics/not_r_sumbool_rec.con".
+inline procedural "cic:/CoRN/algebra/Basics/not_r_sumbool_rec.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/not_l_sumbool_rec.con".
+inline procedural "cic:/CoRN/algebra/Basics/not_l_sumbool_rec.con" as lemma.
(* begin hide *)
(* end hide *)
-inline procedural "cic:/CoRN/algebra/Basics/POS_anti_convert.con".
+inline procedural "cic:/CoRN/algebra/Basics/POS_anti_convert.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/NEG_anti_convert.con".
+inline procedural "cic:/CoRN/algebra/Basics/NEG_anti_convert.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/lt_O_positive_to_nat.con".
+inline procedural "cic:/CoRN/algebra/Basics/lt_O_positive_to_nat.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/anti_convert_pred_convert.con".
+inline procedural "cic:/CoRN/algebra/Basics/anti_convert_pred_convert.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/p_is_some_anti_convert.con".
+inline procedural "cic:/CoRN/algebra/Basics/p_is_some_anti_convert.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/convert_is_POS.con".
+inline procedural "cic:/CoRN/algebra/Basics/convert_is_POS.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/min_convert_is_NEG.con".
+inline procedural "cic:/CoRN/algebra/Basics/min_convert_is_NEG.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/inject_nat_convert.con".
+inline procedural "cic:/CoRN/algebra/Basics/inject_nat_convert.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/Z_exh.con".
+inline procedural "cic:/CoRN/algebra/Basics/Z_exh.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/nats_Z_ind.con".
+inline procedural "cic:/CoRN/algebra/Basics/nats_Z_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/pred_succ_Z_ind.con".
+inline procedural "cic:/CoRN/algebra/Basics/pred_succ_Z_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/Zmult_minus_distr_r.con".
+inline procedural "cic:/CoRN/algebra/Basics/Zmult_minus_distr_r.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/Zodd_Zeven_min1.con".
+inline procedural "cic:/CoRN/algebra/Basics/Zodd_Zeven_min1.con" as lemma.
(* begin hide *)
(* end hide *)
-inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff.con".
+inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff.con" as definition.
(* begin hide *)
(* end hide *)
-inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_O.con".
+inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_O.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_Pos.con".
+inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_Pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_Neg.con".
+inline procedural "cic:/CoRN/algebra/Basics/caseZ_diff_Neg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/proper_caseZ_diff.con".
+inline procedural "cic:/CoRN/algebra/Basics/proper_caseZ_diff.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/diff_Z_ind.con".
+inline procedural "cic:/CoRN/algebra/Basics/diff_Z_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/Zlt_reg_mult_l.con".
+inline procedural "cic:/CoRN/algebra/Basics/Zlt_reg_mult_l.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/Zlt_opp.con".
+inline procedural "cic:/CoRN/algebra/Basics/Zlt_opp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/Zlt_conv_mult_l.con".
+inline procedural "cic:/CoRN/algebra/Basics/Zlt_conv_mult_l.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/Zgt_not_eq.con".
+inline procedural "cic:/CoRN/algebra/Basics/Zgt_not_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/Zmult_absorb.con".
+inline procedural "cic:/CoRN/algebra/Basics/Zmult_absorb.con" as lemma.
(* UNEXPORTED
Section Well_foundedT
alias id "A" = "cic:/CoRN/algebra/Basics/AccT/A.var".
-inline procedural "cic:/CoRN/algebra/Basics/well_founded.con".
+inline procedural "cic:/CoRN/algebra/Basics/well_founded.con" as definition.
(* UNEXPORTED
End AccT
alias id "F" = "cic:/CoRN/algebra/Basics/IndT/AccIter/F.var".
-inline procedural "cic:/CoRN/algebra/Basics/Acc_inv.con".
+inline procedural "cic:/CoRN/algebra/Basics/Acc_inv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Basics/Acc_iter.con".
+inline procedural "cic:/CoRN/algebra/Basics/Acc_iter.con" as definition.
(* UNEXPORTED
End AccIter
alias id "Rwf" = "cic:/CoRN/algebra/Basics/IndT/Rwf.var".
-inline procedural "cic:/CoRN/algebra/Basics/well_founded_induction_type.con".
+inline procedural "cic:/CoRN/algebra/Basics/well_founded_induction_type.con" as theorem.
(* UNEXPORTED
End IndT
alias id "f" = "cic:/CoRN/algebra/Basics/InductionT/f.var".
-inline procedural "cic:/CoRN/algebra/Basics/ltof.con".
+inline procedural "cic:/CoRN/algebra/Basics/ltof.con" as definition.
-inline procedural "cic:/CoRN/algebra/Basics/well_founded_ltof.con".
+inline procedural "cic:/CoRN/algebra/Basics/well_founded_ltof.con" as theorem.
-inline procedural "cic:/CoRN/algebra/Basics/induction_ltof2T.con".
+inline procedural "cic:/CoRN/algebra/Basics/induction_ltof2T.con" as theorem.
(* UNEXPORTED
End InductionT
Section InductionTT
*)
-inline procedural "cic:/CoRN/algebra/Basics/lt_wf_rect.con".
+inline procedural "cic:/CoRN/algebra/Basics/lt_wf_rect.con" as lemma.
(* UNEXPORTED
End InductionTT
Now we introduce commutativity and add some results.
*)
-inline procedural "cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con" as definition.
inline procedural "cic:/CoRN/algebra/CAbGroups/CAbGroup.ind".
%\end{convention}%
*)
-inline procedural "cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/cag_commutes.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/cag_commutes.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.con" as lemma.
(* UNEXPORTED
End AbGroup_Axioms
%\end{convention}%
*)
-inline procedural "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/subcrr.con" "Abelian_Groups__SubCAbGroups__".
+inline procedural "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/subcrr.con" "Abelian_Groups__SubCAbGroups__" as definition.
-inline procedural "cic:/CoRN/algebra/CAbGroups/isabgrp_scrr.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/isabgrp_scrr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con" as definition.
(* UNEXPORTED
End SubCAbGroups
%\end{convention}%
*)
-inline procedural "cic:/CoRN/algebra/CAbGroups/cag_op_inv.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/cag_op_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve cag_op_inv: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CAbGroups/assoc_1.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/assoc_1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/minus_plus.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/minus_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_lft.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_lft.con" as lemma.
(* UNEXPORTED
End Various
alias id "inv_inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var".
-inline procedural "cic:/CoRN/algebra/CAbGroups/plus_rext.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/plus_rext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/plus_runit.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/plus_runit.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/plus_is_fun.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/plus_is_fun.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/inv_inv'.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/inv_inv'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/plus_fun.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/plus_fun.con" as definition.
-inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con" as definition.
-inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con" as definition.
-inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con" as definition.
-inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con" as definition.
(* UNEXPORTED
End Nice_Char
alias id "G" = "cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var".
-inline procedural "cic:/CoRN/algebra/CAbGroups/nmult.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/nmult.con" as definition.
-inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_wd.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_one.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_Zero.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_Zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_plus.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_mult.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_inv.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_inv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_plus'.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/nmult_plus'.con" as lemma.
(* UNEXPORTED
Hint Resolve nmult_wd nmult_Zero nmult_inv nmult_plus nmult_plus': algebra.
*)
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult.con" as definition.
(*
Lemma Zeq_imp_nat_eq : forall m n:nat, m = n -> m = n.
Qed.
*)
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_char.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_char.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_wd.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_one.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_min_one.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_min_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_zero.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_Zero.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_Zero.con" as lemma.
(* UNEXPORTED
Hint Resolve zmult_zero: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_plus.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_mult.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_plus'.con".
+inline procedural "cic:/CoRN/algebra/CAbGroups/zmult_plus'.con" as lemma.
(* UNEXPORTED
End Group_Extras
Now we introduce commutativity and add some results.
*)
-inline procedural "cic:/CoRN/algebra/CAbMonoids/is_CAbMonoid.con".
+inline procedural "cic:/CoRN/algebra/CAbMonoids/is_CAbMonoid.con" as definition.
inline procedural "cic:/CoRN/algebra/CAbMonoids/CAbMonoid.ind".
%\end{convention}%
*)
-inline procedural "cic:/CoRN/algebra/CAbMonoids/CAbMonoid_is_CAbMonoid.con".
+inline procedural "cic:/CoRN/algebra/CAbMonoids/CAbMonoid_is_CAbMonoid.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes.con".
+inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con" as lemma.
(* UNEXPORTED
End AbMonoid_Axioms
%\end{convention}%
*)
-inline procedural "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/subcrr.con" "Abelian_Monoids__SubCAbMonoids__".
+inline procedural "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/subcrr.con" "Abelian_Monoids__SubCAbMonoids__" as definition.
-inline procedural "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con".
+inline procedural "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con".
+inline procedural "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con" as definition.
(* UNEXPORTED
End SubCAbMonoids
** Definition of the notion Field
*)
-inline procedural "cic:/CoRN/algebra/CFields/is_CField.con".
+inline procedural "cic:/CoRN/algebra/CFields/is_CField.con" as definition.
inline procedural "cic:/CoRN/algebra/CFields/CField.ind".
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl'.con".
+inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl'.con" as definition.
-inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl.con".
+inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl.con" as definition.
(* UNEXPORTED
Implicit Arguments f_rcpcl [F].
we have a proof of [y [#] Zero].
*)
-inline procedural "cic:/CoRN/algebra/CFields/cf_div.con".
+inline procedural "cic:/CoRN/algebra/CFields/cf_div.con" as definition.
(* UNEXPORTED
Implicit Arguments cf_div [F].
alias id "F" = "cic:/CoRN/algebra/CFields/Field_axioms/F.var".
-inline procedural "cic:/CoRN/algebra/CFields/CField_is_CField.con".
+inline procedural "cic:/CoRN/algebra/CFields/CField_is_CField.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse.con".
+inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse.con" as lemma.
(* UNEXPORTED
End Field_axioms
alias id "F" = "cic:/CoRN/algebra/CFields/Field_basics/F.var".
-inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/field_mult_inv.con".
+inline procedural "cic:/CoRN/algebra/CFields/field_mult_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve field_mult_inv: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CFields/field_mult_inv_op.con".
+inline procedural "cic:/CoRN/algebra/CFields/field_mult_inv_op.con" as lemma.
(* UNEXPORTED
End Field_basics
alias id "F" = "cic:/CoRN/algebra/CFields/Field_multiplication/F.var".
-inline procedural "cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/mult_lft_resp_ap.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_lft_resp_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/mult_rht_resp_ap.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_rht_resp_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/mult_resp_neq_zero.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_resp_neq_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/mult_resp_neq.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_resp_neq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/mult_eq_zero.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_eq_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_lft.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_rht.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/square_eq_aux.con".
+inline procedural "cic:/CoRN/algebra/CFields/square_eq_aux.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/square_eq_weak.con".
+inline procedural "cic:/CoRN/algebra/CFields/square_eq_weak.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/cond_square_eq.con".
+inline procedural "cic:/CoRN/algebra/CFields/cond_square_eq.con" as lemma.
(* UNEXPORTED
End Field_multiplication
Section x_square
*)
-inline procedural "cic:/CoRN/algebra/CFields/x_xminone.con".
+inline procedural "cic:/CoRN/algebra/CFields/x_xminone.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/square_id.con".
+inline procedural "cic:/CoRN/algebra/CFields/square_id.con" as lemma.
(* UNEXPORTED
End x_square
alias id "F" = "cic:/CoRN/algebra/CFields/Rcpcl_properties/F.var".
-inline procedural "cic:/CoRN/algebra/CFields/inv_one.con".
+inline procedural "cic:/CoRN/algebra/CFields/inv_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_wd.con".
+inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_mult.con".
+inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_resp_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_resp_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_f_rcpcl.con".
+inline procedural "cic:/CoRN/algebra/CFields/f_rcpcl_f_rcpcl.con" as lemma.
(* UNEXPORTED
End Rcpcl_properties
The multiplicative monoid of NonZeros.
*)
-inline procedural "cic:/CoRN/algebra/CFields/NonZeroMonoid.con".
+inline procedural "cic:/CoRN/algebra/CFields/NonZeroMonoid.con" as definition.
-inline procedural "cic:/CoRN/algebra/CFields/fmg_cs_inv.con".
+inline procedural "cic:/CoRN/algebra/CFields/fmg_cs_inv.con" as definition.
-inline procedural "cic:/CoRN/algebra/CFields/plus_nonzeros_eq_mult_dom.con".
+inline procedural "cic:/CoRN/algebra/CFields/plus_nonzeros_eq_mult_dom.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/cfield_to_mult_cgroup.con".
+inline procedural "cic:/CoRN/algebra/CFields/cfield_to_mult_cgroup.con" as lemma.
(* UNEXPORTED
End MultipGroup
alias id "F" = "cic:/CoRN/algebra/CFields/Div_properties/F.var".
-inline procedural "cic:/CoRN/algebra/CFields/div_prop.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_prop.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/div_1.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/div_1'.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_1'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/div_1''.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_1''.con" as lemma.
(* UNEXPORTED
Hint Resolve div_1: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CFields/x_div_x.con".
+inline procedural "cic:/CoRN/algebra/CFields/x_div_x.con" as lemma.
(* UNEXPORTED
Hint Resolve x_div_x: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CFields/x_div_one.con".
+inline procedural "cic:/CoRN/algebra/CFields/x_div_one.con" as lemma.
(*#*
The next lemma says $x\cdot\frac{y}{z} = \frac{x\cdot y}{z}$
#x.(y/z) = (x.y)/z#.
*)
-inline procedural "cic:/CoRN/algebra/CFields/x_mult_y_div_z.con".
+inline procedural "cic:/CoRN/algebra/CFields/x_mult_y_div_z.con" as lemma.
(* UNEXPORTED
Hint Resolve x_mult_y_div_z: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CFields/div_wd.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_wd.con" as lemma.
(* UNEXPORTED
Hint Resolve div_wd: algebra_c.
#[(x/y)/z = x/(y.z)]#
*)
-inline procedural "cic:/CoRN/algebra/CFields/div_div.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_div.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/div_resp_ap_zero_rev.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_resp_ap_zero_rev.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/div_resp_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_resp_ap_zero.con" as lemma.
(*#*
The next lemma says $\frac{x}{\frac{y}{z}} = \frac{x\cdot z}{y}$
#[x/(y/z) = (x.z)/y]#
*)
-inline procedural "cic:/CoRN/algebra/CFields/div_div2.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_div2.con" as lemma.
(*#*
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 procedural "cic:/CoRN/algebra/CFields/mult_of_divs.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_of_divs.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/div_dist.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_dist.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/div_dist'.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_dist'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/div_semi_sym.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_semi_sym.con" as lemma.
(* UNEXPORTED
Hint Resolve div_semi_sym: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CFields/eq_div.con".
+inline procedural "cic:/CoRN/algebra/CFields/eq_div.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/div_strext.con".
+inline procedural "cic:/CoRN/algebra/CFields/div_strext.con" as lemma.
(* UNEXPORTED
End Div_properties
alias id "F" = "cic:/CoRN/algebra/CFields/Mult_Cancel_Ap_Zero/F.var".
-inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_rht.con".
+inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/recip_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CFields/recip_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/recip_resp_ap.con".
+inline procedural "cic:/CoRN/algebra/CFields/recip_resp_ap.con" as lemma.
(* UNEXPORTED
End Mult_Cancel_Ap_Zero
(* begin hide *)
-inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/P.con" "CField_Ops__".
+inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/P.con" "CField_Ops__" as definition.
-inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Q.con" "CField_Ops__".
+inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Q.con" "CField_Ops__" as definition.
(* end hide *)
Some auxiliary notions are helpful in defining the domain.
*)
-inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/R.con" "CField_Ops__Part_Function_Recip__".
+inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/R.con" "CField_Ops__Part_Function_Recip__" as definition.
-inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/Ext2R.con" "CField_Ops__Part_Function_Recip__".
+inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/Ext2R.con" "CField_Ops__Part_Function_Recip__" as definition.
-inline procedural "cic:/CoRN/algebra/CFields/part_function_recip_strext.con".
+inline procedural "cic:/CoRN/algebra/CFields/part_function_recip_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/part_function_recip_pred_wd.con".
+inline procedural "cic:/CoRN/algebra/CFields/part_function_recip_pred_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/Frecip.con".
+inline procedural "cic:/CoRN/algebra/CFields/Frecip.con" as definition.
(* UNEXPORTED
End Part_Function_Recip
For division things work out almost in the same way.
*)
-inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/R.con" "CField_Ops__Part_Function_Div__".
+inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/R.con" "CField_Ops__Part_Function_Div__" as definition.
-inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/Ext2R.con" "CField_Ops__Part_Function_Div__".
+inline procedural "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/Ext2R.con" "CField_Ops__Part_Function_Div__" as definition.
-inline procedural "cic:/CoRN/algebra/CFields/part_function_div_strext.con".
+inline procedural "cic:/CoRN/algebra/CFields/part_function_div_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/part_function_div_pred_wd.con".
+inline procedural "cic:/CoRN/algebra/CFields/part_function_div_pred_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/Fdiv.con".
+inline procedural "cic:/CoRN/algebra/CFields/Fdiv.con" as definition.
(* UNEXPORTED
End Part_Function_Div
alias id "R" = "cic:/CoRN/algebra/CFields/CField_Ops/R.var".
-inline procedural "cic:/CoRN/algebra/CFields/included_FRecip.con".
+inline procedural "cic:/CoRN/algebra/CFields/included_FRecip.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/included_FRecip'.con".
+inline procedural "cic:/CoRN/algebra/CFields/included_FRecip'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/included_FDiv.con".
+inline procedural "cic:/CoRN/algebra/CFields/included_FDiv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/included_FDiv'.con".
+inline procedural "cic:/CoRN/algebra/CFields/included_FDiv'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CFields/included_FDiv''.con".
+inline procedural "cic:/CoRN/algebra/CFields/included_FDiv''.con" as lemma.
(* UNEXPORTED
End CField_Ops
** Definition of the notion of Group
*)
-inline procedural "cic:/CoRN/algebra/CGroups/is_inverse.con".
+inline procedural "cic:/CoRN/algebra/CGroups/is_inverse.con" as definition.
(* UNEXPORTED
Implicit Arguments is_inverse [S].
*)
-inline procedural "cic:/CoRN/algebra/CGroups/is_CGroup.con".
+inline procedural "cic:/CoRN/algebra/CGroups/is_CGroup.con" as definition.
inline procedural "cic:/CoRN/algebra/CGroups/CGroup.ind".
Notation "[--] x" := (cg_inv x) (at level 2, right associativity).
*)
-inline procedural "cic:/CoRN/algebra/CGroups/cg_minus.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_minus.con" as definition.
(*#*
%\begin{nameconvention}%
alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_axioms/G.var".
-inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse.con" as lemma.
(* UNEXPORTED
End CGroup_axioms
alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_basics/G.var".
-inline procedural "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_lft_inv_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_lft_inv_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_correct.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_correct.con" as lemma.
(* UNEXPORTED
Hint Resolve cg_rht_inv_unfolded cg_lft_inv_unfolded cg_minus_correct:
algebra.
*)
-inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse'.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse'.con" as lemma.
(* Hints for Auto *)
-inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_unfolded.con" as lemma.
(* UNEXPORTED
Hint Resolve cg_minus_unfolded: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_wd.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_wd.con" as lemma.
(* UNEXPORTED
Hint Resolve cg_minus_wd: algebra_c.
*)
-inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_strext.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_is_csetoid_bin_op.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_minus_is_csetoid_bin_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CGroups/grp_inv_assoc.con".
+inline procedural "cic:/CoRN/algebra/CGroups/grp_inv_assoc.con" as lemma.
(* UNEXPORTED
Hint Resolve grp_inv_assoc: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_inv.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve cg_inv_inv: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_lft.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_rht.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique'.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique_2.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_unique_2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_zero_inv.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_zero_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve cg_zero_inv: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_zero.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_op.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_inv_op.con" as lemma.
(*#*
Useful for interactive proof development.
*)
-inline procedural "cic:/CoRN/algebra/CGroups/x_minus_x.con".
+inline procedural "cic:/CoRN/algebra/CGroups/x_minus_x.con" as lemma.
(*#*
** Sub-groups
alias id "inv_pres_P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/inv_pres_P.var".
-inline procedural "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subcrr.con" "CGroup_basics__SubCGroups__".
+inline procedural "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subcrr.con" "CGroup_basics__SubCGroups__" as definition.
-inline procedural "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subinv.con" "CGroup_basics__SubCGroups__".
+inline procedural "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subinv.con" "CGroup_basics__SubCGroups__" as definition.
-inline procedural "cic:/CoRN/algebra/CGroups/isgrp_scrr.con".
+inline procedural "cic:/CoRN/algebra/CGroups/isgrp_scrr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/Build_SubCGroup.con".
+inline procedural "cic:/CoRN/algebra/CGroups/Build_SubCGroup.con" as definition.
(* UNEXPORTED
End SubCGroups
alias id "G" = "cic:/CoRN/algebra/CGroups/Assoc_properties/G.var".
-inline procedural "cic:/CoRN/algebra/CGroups/assoc_2.con".
+inline procedural "cic:/CoRN/algebra/CGroups/assoc_2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/zero_minus.con".
+inline procedural "cic:/CoRN/algebra/CGroups/zero_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_mixed.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_cancel_mixed.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/plus_resp_eq.con".
+inline procedural "cic:/CoRN/algebra/CGroups/plus_resp_eq.con" as lemma.
(* UNEXPORTED
End Assoc_properties
alias id "G" = "cic:/CoRN/algebra/CGroups/cgroups_apartness/G.var".
-inline procedural "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/op_rht_resp_ap.con".
+inline procedural "cic:/CoRN/algebra/CGroups/op_rht_resp_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/cg_ap_cancel_rht.con".
+inline procedural "cic:/CoRN/algebra/CGroups/cg_ap_cancel_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/plus_cancel_ap_rht.con".
+inline procedural "cic:/CoRN/algebra/CGroups/plus_cancel_ap_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/minus_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CGroups/minus_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/zero_minus_apart.con".
+inline procedural "cic:/CoRN/algebra/CGroups/zero_minus_apart.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/inv_resp_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CGroups/inv_resp_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/inv_resp_ap.con".
+inline procedural "cic:/CoRN/algebra/CGroups/inv_resp_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/minus_resp_ap_rht.con".
+inline procedural "cic:/CoRN/algebra/CGroups/minus_resp_ap_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/minus_resp_ap_lft.con".
+inline procedural "cic:/CoRN/algebra/CGroups/minus_resp_ap_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con".
+inline procedural "cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con" as lemma.
(* UNEXPORTED
End cgroups_apartness
(* begin hide *)
-inline procedural "cic:/CoRN/algebra/CGroups/CGroup_Ops/P.con" "CGroup_Ops__".
+inline procedural "cic:/CoRN/algebra/CGroups/CGroup_Ops/P.con" "CGroup_Ops__" as definition.
-inline procedural "cic:/CoRN/algebra/CGroups/CGroup_Ops/Q.con" "CGroup_Ops__".
+inline procedural "cic:/CoRN/algebra/CGroups/CGroup_Ops/Q.con" "CGroup_Ops__" as definition.
(* end hide *)
Section Part_Function_Inv
*)
-inline procedural "cic:/CoRN/algebra/CGroups/part_function_inv_strext.con".
+inline procedural "cic:/CoRN/algebra/CGroups/part_function_inv_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/Finv.con".
+inline procedural "cic:/CoRN/algebra/CGroups/Finv.con" as definition.
(* UNEXPORTED
End Part_Function_Inv
Section Part_Function_Minus
*)
-inline procedural "cic:/CoRN/algebra/CGroups/part_function_minus_strext.con".
+inline procedural "cic:/CoRN/algebra/CGroups/part_function_minus_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/Fminus.con".
+inline procedural "cic:/CoRN/algebra/CGroups/Fminus.con" as definition.
(* UNEXPORTED
End Part_Function_Minus
alias id "R" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/R.var".
-inline procedural "cic:/CoRN/algebra/CGroups/included_FInv.con".
+inline procedural "cic:/CoRN/algebra/CGroups/included_FInv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/included_FInv'.con".
+inline procedural "cic:/CoRN/algebra/CGroups/included_FInv'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus.con".
+inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus'.con".
+inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus''.con".
+inline procedural "cic:/CoRN/algebra/CGroups/included_FMinus''.con" as lemma.
(* UNEXPORTED
End CGroup_Ops
version.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/CProp.con".
+inline procedural "cic:/CoRN/algebra/CLogic/CProp.con" as definition.
(* UNEXPORTED
Section Basics
and some basic connectives in [CProp].
*)
-inline procedural "cic:/CoRN/algebra/CLogic/Not.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Not.con" as definition.
inline procedural "cic:/CoRN/algebra/CLogic/CAnd.ind".
-inline procedural "cic:/CoRN/algebra/CLogic/Iff.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Iff.con" as definition.
inline procedural "cic:/CoRN/algebra/CLogic/CFalse.ind".
inline procedural "cic:/CoRN/algebra/CLogic/CTrue.ind".
-inline procedural "cic:/CoRN/algebra/CLogic/proj1_sigT.con".
+inline procedural "cic:/CoRN/algebra/CLogic/proj1_sigT.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/proj2_sigT.con".
+inline procedural "cic:/CoRN/algebra/CLogic/proj2_sigT.con" as definition.
inline procedural "cic:/CoRN/algebra/CLogic/sig2T.ind".
-inline procedural "cic:/CoRN/algebra/CLogic/proj1_sig2T.con".
+inline procedural "cic:/CoRN/algebra/CLogic/proj1_sig2T.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/proj2a_sig2T.con".
+inline procedural "cic:/CoRN/algebra/CLogic/proj2a_sig2T.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/proj2b_sig2T.con".
+inline procedural "cic:/CoRN/algebra/CLogic/proj2b_sig2T.con" as definition.
inline procedural "cic:/CoRN/algebra/CLogic/toCProp.ind".
-inline procedural "cic:/CoRN/algebra/CLogic/toCProp_e.con".
+inline procedural "cic:/CoRN/algebra/CLogic/toCProp_e.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/CNot.con".
+inline procedural "cic:/CoRN/algebra/CLogic/CNot.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/Ccontrapos'.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Ccontrapos'.con" as lemma.
inline procedural "cic:/CoRN/algebra/CLogic/COr.ind".
Infix "IFF" := Iff (at level 60, right associativity).
*)
-inline procedural "cic:/CoRN/algebra/CLogic/Iff_left.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Iff_left.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Iff_right.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Iff_right.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Iff_refl.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Iff_refl.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Iff_sym.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Iff_sym.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Iff_trans.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Iff_trans.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Iff_imp_imp.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Iff_imp_imp.con" as lemma.
(* UNEXPORTED
Declare Right Step Iff_right.
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CLogic/not_r_cor_rect.con".
+inline procedural "cic:/CoRN/algebra/CLogic/not_r_cor_rect.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/not_l_cor_rect.con".
+inline procedural "cic:/CoRN/algebra/CLogic/not_l_cor_rect.con" as lemma.
(* begin hide *)
alias id "P" = "cic:/CoRN/algebra/CLogic/Choice/P.var".
-inline procedural "cic:/CoRN/algebra/CLogic/choice.con".
+inline procedural "cic:/CoRN/algebra/CLogic/choice.con" as lemma.
(* UNEXPORTED
End Choice
when [A], [B] and [C] are non trivial.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/CNot_Not_or.con".
+inline procedural "cic:/CoRN/algebra/CLogic/CNot_Not_or.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/CdeMorgan_ex_all.con".
+inline procedural "cic:/CoRN/algebra/CLogic/CdeMorgan_ex_all.con" as lemma.
(* UNEXPORTED
End Logical_Remarks
alias id "A" = "cic:/CoRN/algebra/CLogic/CRelation_Definition/A.var".
-inline procedural "cic:/CoRN/algebra/CLogic/Crelation.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Crelation.con" as definition.
alias id "R" = "cic:/CoRN/algebra/CLogic/CRelation_Definition/R.var".
-inline procedural "cic:/CoRN/algebra/CLogic/Creflexive.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Creflexive.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/Ctransitive.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Ctransitive.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/Csymmetric.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Csymmetric.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/Cequiv.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Cequiv.con" as definition.
(* UNEXPORTED
End CRelation_Definition
alias id "A" = "cic:/CoRN/algebra/CLogic/TRelation_Definition/A.var".
-inline procedural "cic:/CoRN/algebra/CLogic/Trelation.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Trelation.con" as definition.
alias id "R" = "cic:/CoRN/algebra/CLogic/TRelation_Definition/R.var".
-inline procedural "cic:/CoRN/algebra/CLogic/Treflexive.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Treflexive.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/Ttransitive.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Ttransitive.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/Tsymmetric.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Tsymmetric.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/Tequiv.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Tequiv.con" as definition.
(* UNEXPORTED
End TRelation_Definition
inline procedural "cic:/CoRN/algebra/CLogic/Cle.ind".
-inline procedural "cic:/CoRN/algebra/CLogic/Cnat_double_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Cnat_double_ind.con" as theorem.
-inline procedural "cic:/CoRN/algebra/CLogic/my_Cle_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/my_Cle_ind.con" as theorem.
-inline procedural "cic:/CoRN/algebra/CLogic/Cle_n_S.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Cle_n_S.con" as theorem.
-inline procedural "cic:/CoRN/algebra/CLogic/toCle.con".
+inline procedural "cic:/CoRN/algebra/CLogic/toCle.con" as lemma.
(* UNEXPORTED
Hint Resolve toCle.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/Cle_to.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Cle_to.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Clt.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Clt.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/toCProp_lt.con".
+inline procedural "cic:/CoRN/algebra/CLogic/toCProp_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Clt_to.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Clt_to.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Cle_le_S_eq.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Cle_le_S_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Cnat_total_order.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Cnat_total_order.con" as lemma.
inline procedural "cic:/CoRN/algebra/CLogic/Codd.ind".
-inline procedural "cic:/CoRN/algebra/CLogic/Codd_even_to.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Codd_even_to.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Codd_to.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Codd_to.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Ceven_to.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Ceven_to.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/to_Codd_even.con".
+inline procedural "cic:/CoRN/algebra/CLogic/to_Codd_even.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/to_Codd.con".
+inline procedural "cic:/CoRN/algebra/CLogic/to_Codd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/to_Ceven.con".
+inline procedural "cic:/CoRN/algebra/CLogic/to_Ceven.con" as lemma.
(* UNEXPORTED
End le_odd
(*#* **Miscellaneous
*)
-inline procedural "cic:/CoRN/algebra/CLogic/CZ_exh.con".
+inline procedural "cic:/CoRN/algebra/CLogic/CZ_exh.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Cnats_Z_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Cnats_Z_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Cdiff_Z_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Cdiff_Z_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Cpred_succ_Z_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Cpred_succ_Z_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/not_r_sum_rec.con".
+inline procedural "cic:/CoRN/algebra/CLogic/not_r_sum_rec.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/not_l_sum_rec.con".
+inline procedural "cic:/CoRN/algebra/CLogic/not_l_sum_rec.con" as lemma.
(* UNEXPORTED
End Misc
setoid equality.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/nat_less_n_pred.con".
+inline procedural "cic:/CoRN/algebra/CLogic/nat_less_n_pred.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/nat_less_n_pred'.con".
+inline procedural "cic:/CoRN/algebra/CLogic/nat_less_n_pred'.con" as definition.
(* UNEXPORTED
Implicit Arguments nat_less_n_pred [n].
Next, we prove the usual results about sums of even and odd numbers:
*)
-inline procedural "cic:/CoRN/algebra/CLogic/even_plus_n_n.con".
+inline procedural "cic:/CoRN/algebra/CLogic/even_plus_n_n.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/even_or_odd_plus.con".
+inline procedural "cic:/CoRN/algebra/CLogic/even_or_odd_plus.con" as lemma.
(*#* Finally, we prove that an arbitrary natural number can be written in some canonical way.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/even_or_odd_plus_gt.con".
+inline procedural "cic:/CoRN/algebra/CLogic/even_or_odd_plus_gt.con" as lemma.
(* UNEXPORTED
End Odd_and_Even
definitions keeping conciseness.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/Clt_le_weak.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Clt_le_weak.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/lt_5.con".
+inline procedural "cic:/CoRN/algebra/CLogic/lt_5.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/lt_8.con".
+inline procedural "cic:/CoRN/algebra/CLogic/lt_8.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/pred_lt.con".
+inline procedural "cic:/CoRN/algebra/CLogic/pred_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/lt_10.con".
+inline procedural "cic:/CoRN/algebra/CLogic/lt_10.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/lt_pred'.con".
+inline procedural "cic:/CoRN/algebra/CLogic/lt_pred'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/le_1.con".
+inline procedural "cic:/CoRN/algebra/CLogic/le_1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/le_2.con".
+inline procedural "cic:/CoRN/algebra/CLogic/le_2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/plus_eq_one_imp_eq_zero.con".
+inline procedural "cic:/CoRN/algebra/CLogic/plus_eq_one_imp_eq_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/not_not_lt.con".
+inline procedural "cic:/CoRN/algebra/CLogic/not_not_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/plus_pred_pred_plus.con".
+inline procedural "cic:/CoRN/algebra/CLogic/plus_pred_pred_plus.con" as lemma.
(*#* We now prove some properties of functions on the natural numbers.
holds for weak monotonicity.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon.con".
+inline procedural "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon_le.con".
+inline procedural "cic:/CoRN/algebra/CLogic/nat_local_mon_imp_mon_le.con" as lemma.
(*#* A strictly increasing function is injective: *)
-inline procedural "cic:/CoRN/algebra/CLogic/nat_mon_imp_inj.con".
+inline procedural "cic:/CoRN/algebra/CLogic/nat_mon_imp_inj.con" as lemma.
(*#* And (not completely trivial) a function that preserves [lt] also preserves [le]. *)
-inline procedural "cic:/CoRN/algebra/CLogic/nat_mon_imp_mon'.con".
+inline procedural "cic:/CoRN/algebra/CLogic/nat_mon_imp_mon'.con" as lemma.
(*#*
The last lemmas in this section state that a monotonous function in the
These are useful for integration.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/mon_fun_covers.con".
+inline procedural "cic:/CoRN/algebra/CLogic/mon_fun_covers.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/weird_mon_covers.con".
+inline procedural "cic:/CoRN/algebra/CLogic/weird_mon_covers.con" as lemma.
(* UNEXPORTED
End Natural_Numbers
Useful for the Fundamental Theorem of Algebra.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/kseq_prop.con".
+inline procedural "cic:/CoRN/algebra/CLogic/kseq_prop.con" as lemma.
(* UNEXPORTED
Section Predicates_to_CProp
results for [CProp]-valued predicates:
*)
-inline procedural "cic:/CoRN/algebra/CLogic/even_induction.con".
+inline procedural "cic:/CoRN/algebra/CLogic/even_induction.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/odd_induction.con".
+inline procedural "cic:/CoRN/algebra/CLogic/odd_induction.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/four_induction.con".
+inline procedural "cic:/CoRN/algebra/CLogic/four_induction.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/nat_complete_double_induction.con".
+inline procedural "cic:/CoRN/algebra/CLogic/nat_complete_double_induction.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/odd_double_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/odd_double_ind.con" as lemma.
(*#* For subsetoid predicates in the natural numbers we can eliminate
disjunction (and existential quantification) as follows.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/finite_or_elim.con".
+inline procedural "cic:/CoRN/algebra/CLogic/finite_or_elim.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/str_finite_or_elim.con".
+inline procedural "cic:/CoRN/algebra/CLogic/str_finite_or_elim.con" as lemma.
(* UNEXPORTED
End Predicates_to_CProp
completeness's sake.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/even_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/even_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/odd_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/odd_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/nat_complete_double_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/nat_complete_double_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/four_ind.con".
+inline procedural "cic:/CoRN/algebra/CLogic/four_ind.con" as lemma.
(* UNEXPORTED
End Predicates_to_Prop
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CLogic/Zlts.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Zlts.con" as definition.
-inline procedural "cic:/CoRN/algebra/CLogic/toCProp_Zlt.con".
+inline procedural "cic:/CoRN/algebra/CLogic/toCProp_Zlt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/CZlt_to.con".
+inline procedural "cic:/CoRN/algebra/CLogic/CZlt_to.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_1.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_2.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_3.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_3.con" as lemma.
(*#* The following have unusual names, in line with the series of lemmata in
fast_integers.v.
*)
-inline procedural "cic:/CoRN/algebra/CLogic/ZL4'.con".
+inline procedural "cic:/CoRN/algebra/CLogic/ZL4'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/ZL9.con".
+inline procedural "cic:/CoRN/algebra/CLogic/ZL9.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_4.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_4.con" as theorem.
-inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_5.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Zsgn_5.con" as theorem.
-inline procedural "cic:/CoRN/algebra/CLogic/nat_nat_pos.con".
+inline procedural "cic:/CoRN/algebra/CLogic/nat_nat_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/S_predn.con".
+inline procedural "cic:/CoRN/algebra/CLogic/S_predn.con" as theorem.
-inline procedural "cic:/CoRN/algebra/CLogic/absolu_1.con".
+inline procedural "cic:/CoRN/algebra/CLogic/absolu_1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/absolu_2.con".
+inline procedural "cic:/CoRN/algebra/CLogic/absolu_2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Zgt_mult_conv_absorb_l.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Zgt_mult_conv_absorb_l.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Zgt_mult_reg_absorb_l.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Zgt_mult_reg_absorb_l.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CLogic/Zmult_Sm_Sn.con".
+inline procedural "cic:/CoRN/algebra/CLogic/Zmult_Sm_Sn.con" as lemma.
(* NOTATION
Notation ProjT1 := (proj1_sigT _ _).
** Definition of monoids
*)
-inline procedural "cic:/CoRN/algebra/CMonoids/is_rht_unit.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/is_rht_unit.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CMonoids/is_lft_unit.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/is_lft_unit.con" as definition.
(* UNEXPORTED
Implicit Arguments is_lft_unit [S].
Notation Zero := (cm_unit _).
*)
-inline procedural "cic:/CoRN/algebra/CMonoids/nonZeroP.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/nonZeroP.con" as definition.
(* End_SpecReals *)
alias id "M" = "cic:/CoRN/algebra/CMonoids/CMonoid_axioms/M.var".
-inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CMonoids/cm_lft_unit.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/cm_lft_unit.con" as lemma.
(* UNEXPORTED
End CMonoid_axioms
alias id "M" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/M.var".
-inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CMonoids/cm_lft_unit_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/cm_lft_unit_unfolded.con" as lemma.
(* UNEXPORTED
Hint Resolve cm_rht_unit_unfolded cm_lft_unit_unfolded: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CMonoids/cm_unit_unique_lft.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/cm_unit_unique_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CMonoids/cm_unit_unique_rht.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/cm_unit_unique_rht.con" as lemma.
(* Begin_SpecReals *)
The proof component of the monoid is irrelevant.
*)
-inline procedural "cic:/CoRN/algebra/CMonoids/is_CMonoid_proof_irr.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/is_CMonoid_proof_irr.con" as lemma.
(* End_SpecReals *)
alias id "op_pres_P" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/op_pres_P.var".
-inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/subcrr.con" "CMonoid_basics__SubCMonoids__".
+inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/subcrr.con" "CMonoid_basics__SubCMonoids__" as definition.
-inline procedural "cic:/CoRN/algebra/CMonoids/ismon_scrr.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/ismon_scrr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CMonoids/Build_SubCMonoid.con".
+inline procedural "cic:/CoRN/algebra/CMonoids/Build_SubCMonoid.con" as definition.
(* UNEXPORTED
End SubCMonoids
(* Begin_SpecReals *)
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall.con" as definition.
(* UNEXPORTED
Implicit Arguments AbsSmall [R].
alias id "R" = "cic:/CoRN/algebra/COrdAbs/AbsSmall_properties/R.var".
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr_unfolded.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl_unfolded.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl_unfolded.con" as lemma.
(* UNEXPORTED
Declare Left Step AbsSmall_wdl_unfolded.
(* end hide *)
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_leEq_trans.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_leEq_trans.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/zero_AbsSmall.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/zero_AbsSmall.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_trans.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_trans.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/leEq_imp_AbsSmall.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/leEq_imp_AbsSmall.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/inv_resp_AbsSmall.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/inv_resp_AbsSmall.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_minus.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_plus.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div_two.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div_two.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_delta.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_delta.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_delta.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_delta.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_eps_div2.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_eps_div2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_eps_div2.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_eps_div2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_intermediate.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_intermediate.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div2.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_nonneg.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_mult.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_cancel_mult.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_cancel_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con" as lemma.
(* UNEXPORTED
End AbsSmall_properties
(*#* ** Properties of [AbsBig] *)
-inline procedural "cic:/CoRN/algebra/COrdAbs/absBig.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/absBig.con" as definition.
(* NOTATION
Notation AbsBig := (absBig _).
*)
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con" as lemma.
(* UNEXPORTED
Section absBig_wd_properties
alias id "R" = "cic:/CoRN/algebra/COrdAbs/absBig_wd_properties/R.var".
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr_unfolded.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con".
+inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con" as lemma.
(* UNEXPORTED
End absBig_wd_properties
(* end hide *)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/Cauchy_prop.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/Cauchy_prop.con" as definition.
(* begin hide *)
cic:/matita/CoRN-Procedural/algebra/COrdCauchy/CS_seq.con
*)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/SeqLimit.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/SeqLimit.con" as definition.
(* End_SpecReals *)
%\end{convention}%
*)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_bounded.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_bounded.con" as theorem.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_const.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_const.con" as lemma.
(*#*
%\begin{convention}% Assume [f] and [g] are Cauchy sequences on [R].
alias id "Hg" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hg.var".
-inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_inv.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_inv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_mult.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_mult.con" as lemma.
(*#*
We now assume that [f] is, from some point onwards, greater than
alias id "f_bnd" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f_bnd.var".
-inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_seq.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_seq.con" as definition.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip.con" as lemma.
(* UNEXPORTED
End OrdField_Cauchy
well here anyway.
*)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con" as lemma.
(* UNEXPORTED
Section Mult_AbsSmall
%\end{convention}%
*)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall'_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall'_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_lft.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall.con" as lemma.
(* UNEXPORTED
End Mult_AbsSmall
%\end{convention}%
*)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/smaller.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/smaller.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/estimate_abs.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/estimate_abs.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_contin.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mult_contin.con" as lemma.
(*#* Addition is also continuous. *)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/plus_contin.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/plus_contin.con" as lemma.
(* UNEXPORTED
End Mult_Continuous
in terms of preservation of less or equal (less).
*)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_less_char'.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_less_char'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_less_char.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_less_char.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char'.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/resp_leEq_char.con" as lemma.
(*#*
Next, we see different characterizations of monotonous functions from
Also, strictly monotonous functions are injective.
*)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_lt.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_lt.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_lt.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_lt.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_lt.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_lt.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_le.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_le.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon_imp_mon'_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_le.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_le.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/local_mon'_imp_mon'2_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_le.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_mon'_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_le.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/mon_imp_inj_le.con" as lemma.
(*#*
A similar result for %{\em %partial%}% functions.
*)
-inline procedural "cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con".
+inline procedural "cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con" as lemma.
(* UNEXPORTED
End Monotonous_functions
Infix "[<]" := cof_less (at level 70, no associativity).
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/greater.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/greater.con" as definition.
(* UNEXPORTED
Implicit Arguments greater [F].
Less or equal is defined as ``not greater than''.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/leEq.con" as definition.
(*#*
%\begin{nameconvention}%
alias id "F" = "cic:/CoRN/algebra/COrdFields/COrdField_axioms/F.var".
-inline procedural "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_strorder.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_strorder.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_transitive_unfolded.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_transitive_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_antisymmetric_unfolded.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_antisymmetric_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_irreflexive.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_irreflexive_unfolded.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_irreflexive_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_conf_ap.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_conf_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_wdr.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_wdr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_wdl.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_wdl.con" as lemma.
(* UNEXPORTED
End COrdField_axioms
alias id "R" = "cic:/CoRN/algebra/COrdFields/OrdField_basics/R.var".
-inline procedural "cic:/CoRN/algebra/COrdFields/less_imp_ap.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_imp_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/Greater_imp_ap.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/Greater_imp_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/ap_imp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/ap_imp_less.con" as lemma.
(*#*
Now properties which can be derived.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/less_cotransitive.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_cotransitive.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_cotransitive_unfolded.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_cotransitive_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_ap_zero.con" as lemma.
(* Main characterization of less *)
-inline procedural "cic:/CoRN/algebra/COrdFields/leEq_not_eq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/leEq_not_eq.con" as lemma.
(* UNEXPORTED
End OrdField_basics
alias id "R" = "cic:/CoRN/algebra/COrdFields/Basic_Properties_of_leEq/R.var".
-inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdr.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdl.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdl.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/leEq_reflexive.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/leEq_reflexive.con" as lemma.
(* UNEXPORTED
Declare Left Step leEq_wdl.
Declare Right Step leEq_wdr.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/eq_imp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/eq_imp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/leEq_imp_eq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/leEq_imp_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/lt_equiv_imp_eq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/lt_equiv_imp_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_leEq_trans.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_leEq_trans.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/leEq_less_trans.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/leEq_less_trans.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/leEq_transitive.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/leEq_transitive.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_leEq.con" as lemma.
(* UNEXPORTED
End Basic_Properties_of_leEq
alias id "R" = "cic:/CoRN/algebra/COrdFields/infinity_of_cordfields/R.var".
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_one.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nring_less_succ.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nring_less_succ.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nring_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nring_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nring_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nring_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nring_apart.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nring_apart.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero_imp.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nring_ap_zero_imp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/Snring.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/Snring.con" as definition.
include "tactics/Transparent_algebra.ma".
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_Snring.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_Snring.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nringS_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nringS_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nring_fac_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nring_fac_ap_zero.con" as lemma.
include "tactics/Opaque_algebra.ma".
%\end{nameconvention}%
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/less_plusOne.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_plusOne.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/zero_lt_posplus1.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/zero_lt_posplus1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/plus_one_ext_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/plus_one_ext_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/one_less_two.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/one_less_two.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/two_less_three.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/two_less_three.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/three_less_four.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/three_less_four.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_two.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_two.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/one_less_three.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/one_less_three.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/two_less_four.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/two_less_four.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_three.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_three.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/one_less_four.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/one_less_four.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_four.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_four.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/two_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/two_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/three_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/three_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/four_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/four_ap_zero.con" as lemma.
(* UNEXPORTED
End up_to_four
(*#* *** Properties of some other numbers *)
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_six.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_six.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_eight.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_eight.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_nine.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_nine.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_twelve.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_twelve.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_sixteen.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_sixteen.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_eighteen.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_eighteen.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_twentyfour.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_twentyfour.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_fortyeight.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_fortyeight.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/six_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/six_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/eight_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/eight_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/nine_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nine_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/twelve_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/twelve_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/sixteen_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/sixteen_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/eighteen_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/eighteen_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/twentyfour_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/twentyfour_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con" as lemma.
(* UNEXPORTED
End More_than_four
alias id "F" = "cic:/CoRN/algebra/COrdFields/consequences_of_infinity/F.var".
-inline procedural "cic:/CoRN/algebra/COrdFields/square_eq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/square_eq.con" as lemma.
(*#*
Ordered fields have characteristic zero.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/char0_OrdField.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/char0_OrdField.con" as lemma.
(* UNEXPORTED
End consequences_of_infinity
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_lft.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/inv_resp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/inv_resp_less.con" as lemma.
(* UNEXPORTED
Transparent cg_minus.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/minus_resp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/minus_resp_less.con" as lemma.
(* UNEXPORTED
Transparent cg_minus.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/minus_resp_less_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/minus_resp_less_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_both.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/plus_resp_less_both.con" as lemma.
(*#*
For versions of [plus_resp_less_both] where one [ [<] ] in the
Cancellation laws
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/plus_cancel_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/plus_cancel_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/inv_cancel_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/inv_cancel_less.con" as lemma.
(*#*
Coq%(see the Coq shortcoming in Section~\ref{section:setoid-basics})%.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_plus.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_plus'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_plus'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_minus.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_minus'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_minus'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_plus_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_plus_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_plus_less'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_plus_less'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_minus_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_minus_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_minus_less'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_minus_less'.con" as lemma.
(*#*
Some special cases of laws for shifting.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_zero_less_minus'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/qltone.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/qltone.con" as lemma.
(* UNEXPORTED
End addition
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/recip_resp_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/recip_resp_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_less_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_less_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less_lft.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less_both.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/mult_resp_less_both.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/recip_resp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/recip_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/div_resp_less.con" as lemma.
(*#* Cancellation laws
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/mult_cancel_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/mult_cancel_less.con" as lemma.
(*#*
Laws for shifting
on plus and minus.%
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_div_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_div_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_div_less'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_div_less'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_div.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_div.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_mult.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_mult'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_less_mult'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/shift_mult_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/shift_mult_less.con" as lemma.
(*#* Other properties of multiplication and division
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/minusOne_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/minusOne_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/swap_div.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/swap_div.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/eps_div_less_eps.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/eps_div_less_eps.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_two.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_two.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_two'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_two'.con" as lemma.
(*
Apply mult_cancel_less with (Two::R).
Qed.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_three.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_three.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_three'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_three'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_four.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_four.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_four'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_four'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_six.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_six.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_eight.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_eight.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_nine.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_nine.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_twelve.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_twelve.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_sixteen.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_sixteen.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_eighteen.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_eighteen.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_twentyfour.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_twentyfour.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con" as lemma.
(* UNEXPORTED
End multiplication
*** Miscellaneous properties
*)
-inline procedural "cic:/CoRN/algebra/COrdFields/nring_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/nring_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/less_nring.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/less_nring.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/pos_nring_fac.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/pos_nring_fac.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/Smallest_less_Average.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/Smallest_less_Average.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/Average_less_Greatest.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/Average_less_Greatest.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/Sum_resp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/Sum_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/Sumx_resp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/Sumx_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/positive_Sum_two.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/positive_Sum_two.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/positive_Sumx.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/positive_Sumx.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields/negative_Sumx.con".
+inline procedural "cic:/CoRN/algebra/COrdFields/negative_Sumx.con" as lemma.
(* UNEXPORTED
End misc
*** Addition and subtraction%\label{section:leEq-plus-minus}%
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_lft.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/inv_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/inv_resp_leEq.con" as lemma.
(* UNEXPORTED
Transparent cg_minus.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_both.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_both.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_less_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_less_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_leEq_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_less_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_less_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_both.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/minus_resp_leEq_both.con" as lemma.
(*#* Cancellation properties
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/plus_cancel_leEq_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/plus_cancel_leEq_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/inv_cancel_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/inv_cancel_leEq.con" as lemma.
(*#* Laws for shifting
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_plus_leEq'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_plus'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_lft.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_minus_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_minus_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_minus'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con" as lemma.
(* UNEXPORTED
End addition
Multiplication and division respect [[<=]]
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_lft.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_both.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_leEq_both.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/recip_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/recip_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/div_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/div_resp_leEq.con" as lemma.
(* UNEXPORTED
Hint Resolve recip_resp_leEq: algebra.
(*#* Cancellation properties
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_leEq.con" as lemma.
(*#* Laws for shifting
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_mult_leEq'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_mult'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_mult'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_div_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_div_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_div_leEq'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_div_leEq'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_div.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/shift_leEq_div.con" as lemma.
(* UNEXPORTED
Hint Resolve shift_leEq_div: algebra.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/eps_div_leEq_eps.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/eps_div_leEq_eps.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_two.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_two.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_two'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_two'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_three.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_three.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_three'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_three'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_four.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_four.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con" as lemma.
(* UNEXPORTED
End multiplication
*** Miscellaneous Properties
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/sqr_nonneg.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/sqr_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/nring_nonneg.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nring_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/suc_leEq_dub.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/suc_leEq_dub.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/leEq_nring.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/leEq_nring.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/cc_abs_aid.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/cc_abs_aid.con" as lemma.
include "tactics/Transparent_algebra.ma".
-inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_pos.con" as lemma.
include "tactics/Opaque_algebra.ma".
-inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_nonneg.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/mult_resp_nonneg.con" as lemma.
include "tactics/Transparent_algebra.ma".
-inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_nonneg.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/power_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/power_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nexp_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/power_cancel_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/power_cancel_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/power_cancel_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/power_cancel_less.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/nat_less_bin_nexp.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/nat_less_bin_nexp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/Sum_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/Sum_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/Sumx_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/Sumx_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/Sum2_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/Sum2_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/approach_zero.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/approach_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con" as lemma.
(* UNEXPORTED
End misc
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con" as lemma.
(* UNEXPORTED
End Properties_of_leEq
(* end hide *)
-inline procedural "cic:/CoRN/algebra/COrdFields2/mult_pos_imp.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/mult_pos_imp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_pos_nonneg.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_pos_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_nonneg_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_nonneg_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/pos_square.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/pos_square.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_rht.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_lft.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/mult_cancel_pos_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/pos_wd.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/pos_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/even_power_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/even_power_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/odd_power_cancel_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/odd_power_cancel_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/plus_resp_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/pos_nring_S.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/pos_nring_S.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/square_eq_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/square_eq_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/square_eq_neg.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/square_eq_neg.con" as lemma.
(* UNEXPORTED
End PosP_properties
%\end{convention}%
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ.con" as definition.
(* UNEXPORTED
Implicit Arguments one_div_succ [R].
alias id "R" = "cic:/CoRN/algebra/COrdFields2/One_div_succ_properties/R.var".
-inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_pos.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_pos.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con" as lemma.
(* UNEXPORTED
End One_div_succ_properties
** Properties of [Half]
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/Half.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/Half.con" as definition.
(* UNEXPORTED
Implicit Arguments Half [R].
alias id "R" = "cic:/CoRN/algebra/COrdFields2/Half_properties/R.var".
-inline procedural "cic:/CoRN/algebra/COrdFields2/half_1.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/half_1.con" as lemma.
(* UNEXPORTED
Hint Resolve half_1: algebra.
*)
-inline procedural "cic:/CoRN/algebra/COrdFields2/pos_half.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/pos_half.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/half_1'.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/half_1'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/half_2.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/half_2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/half_lt1.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/half_lt1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/COrdFields2/half_3.con".
+inline procedural "cic:/CoRN/algebra/COrdFields2/half_3.con" as lemma.
(* UNEXPORTED
End Half_properties
(*#* * Polynomials apart from zero *)
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/distinct1.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/distinct1.con" as definition.
(* UNEXPORTED
Implicit Arguments distinct1 [A].
include "tactics/Transparent_algebra.ma".
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_shifted.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_shifted.con" as lemma.
include "tactics/Opaque_algebra.ma".
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_factor.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_factor.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/zero_poly.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/zero_poly.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/identical_poly.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/identical_poly.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_degree.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_degree.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_zero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_apzero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_apzero.con" as lemma.
(* UNEXPORTED
Hint Resolve poly_01_factor'_zero.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_degree.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_degree.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_zero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_one.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_one.con" as lemma.
(* UNEXPORTED
Hint Resolve poly_01_factor_zero poly_01_factor_one: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree'.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_zero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_one.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_01_one.con" as lemma.
(* UNEXPORTED
Hint Resolve poly_01_zero poly_01_one: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation''.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation''.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation'.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_representation.con" as lemma.
(* UNEXPORTED
Hint Resolve poly_representation: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con" as lemma.
(* UNEXPORTED
End Poly_Representation
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_apzero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_apzero.con" as lemma.
(*#*
Also, in this situation polynomials are extensional functions.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con" as lemma.
(* UNEXPORTED
End Characteristic_zero
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con".
+inline procedural "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con" as lemma.
(* UNEXPORTED
End Poly_ApZero_Interval
coefficient is [[#]Zero])!
*)
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/lth_of_poly.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/lth_of_poly.con" as definition.
(*#*
When dealing with constructive polynomials, notably over the reals or
that the `degree is at most [j]'.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/odd_cpoly.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/odd_cpoly.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/even_cpoly.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/even_cpoly.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/regular.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/regular.con" as definition.
(* UNEXPORTED
End Degree_def
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_wd.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_wd.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_wd.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_imp_degree_le.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_imp_degree_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_c_.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_c_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_c_.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_c_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_c_one.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_c_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_x_.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_x_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_x_.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_x_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_x_.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_x_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mon.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mon.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_inv.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_inv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_plus.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_minus.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/Sum_degree_le.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/Sum_degree_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_inv.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_inv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_plus_rht.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_plus_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_minus_lft.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_minus_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_plus.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_minus.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult_aux.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult_aux.con" as lemma.
(* UNEXPORTED
Hint Resolve degree_mult_aux: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_mult.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_nexp.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_nexp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_nexp.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_nexp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/lt_i_lth_of_poly.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/lt_i_lth_of_poly.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_degree_lth.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_degree_lth.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/Cpoly_ex_degree.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/Cpoly_ex_degree.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum''.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum''.con" as lemma.
(* UNEXPORTED
Hint Resolve poly_as_sum'': algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum'.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_zero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_1_imp.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_1_imp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_cpoly_linear.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_cpoly_linear.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_cpoly_linear.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_cpoly_linear.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_one.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con" as lemma.
(* UNEXPORTED
End Degree_props
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_nexp.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_nexp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult_imp.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult_imp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con".
+inline procedural "cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con" as lemma.
(* UNEXPORTED
End degree_props_Field
+ ... + an X^n#, the [Zero]-th coefficient is $a_0$#a0#, the first
is $a_1$#a1# etcetera. *)
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_strext.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_wd.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_fun.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_fun.con" as definition.
(*#*
%\begin{shortcoming}%
%\end{shortcoming}%
*)
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nonConst.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nonConst.con" as definition.
(*#*
The following is probably NOT needed. These functions are
NOT extensional, that is, they are not CSetoid functions.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ok.con" as definition.
(* The in_coeff predicate*)
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/in_coeff.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/in_coeff.con" as definition.
(*#*
The [cpoly_zero] case should be [c [=] Zero] in order to be extensional.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con" as lemma.
(* UNEXPORTED
End NthCoeff_def
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_zero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_lin.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_lin.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_c_.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_c_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_x_mult.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_O_x_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_x_mult.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_x_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_mult_x_.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/coeff_Sm_mult_x_.con" as lemma.
(* 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 procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ap_zero_imp.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_ap_zero_imp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_plus.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve nth_coeff_inv: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_c_mult_p.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_c_mult_p.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_p_mult_c_.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_p_mult_c_.con" as lemma.
(* UNEXPORTED
Hint Resolve nth_coeff_c_mult_p nth_coeff_p_mult_c_ nth_coeff_plus: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_complicated.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_complicated.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/all_nth_coeff_eq_imp.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/all_nth_coeff_eq_imp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/poly_at_zero.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/poly_at_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv'.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_inv'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_minus.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_minus.con" as lemma.
(* UNEXPORTED
Hint Resolve nth_coeff_minus: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum0.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum0.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_sum.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_eq.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_neq.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_nexp_neq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con".
+inline procedural "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con" as lemma.
(* UNEXPORTED
End NthCoeff_props
inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly.ind".
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_one.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_one.con" as definition.
(*#*
Some useful induction lemmas for doubly quantified propositions.
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0'.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0'.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0'.con" as lemma.
(*#* *** The polynomials form a setoid
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq_zero.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq_p_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_eq_p_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_p_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_p_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/irreflexive_cpoly_ap.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/irreflexive_cpoly_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/symmetric_cpoly_ap.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/symmetric_cpoly_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cotransitive_cpoly_ap.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cotransitive_cpoly_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/tight_apart_cpoly_ap.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/tight_apart_cpoly_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_is_CSetoid.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_is_CSetoid.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid.con" as definition.
(*#*
Now that we know that the polynomials form a setoid, we can use the
in terms of these generators.
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_zero_cs.con" "CPoly_CRing__".
+inline procedural "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_zero_cs.con" "CPoly_CRing__" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_linear_cs.con" "CPoly_CRing__".
+inline procedural "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_linear_cs.con" "CPoly_CRing__" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_ind_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_ind_cs.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_ind0_cs.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind0_cs.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ind_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ind_cs.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind0_cs.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind0_cs.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_zero_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_zero_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_eq_lin_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_eq_lin_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_eq_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_eq_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_lin_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_eq_lin_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_eq_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_ap_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_zero_ap_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_ap_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_cpoly_lin_ap_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_ap_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_strext.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_wd.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_comp_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_comp_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_triple_comp_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_triple_comp_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_comp_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_comp_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_triple_comp_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_triple_comp_ind.con" as lemma.
(*#*
*** The polynomials form a semi-group and a monoid
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_cs.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_plus.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_plus_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_plus_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_commutative.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_commutative.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_q_ap_q.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_q_ap_q.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_p_plus_ap_p.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_p_plus_ap_p.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero_plus.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_ap_zero_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_wd.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_associative.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_plus_associative.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csemi_grp.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csemi_grp.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cm_proof.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cm_proof.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cmonoid.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cmonoid.con" as definition.
(*#* *** The polynomials form a group
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_cs.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_wd.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_inv_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cg_proof.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cg_proof.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cgroup.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cgroup.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cag_proof.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cag_proof.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cabgroup.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cabgroup.con" as definition.
(*#* *** The polynomials form a ring
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_cs.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult_cr.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult_cr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult_cr.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult_cr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_strext.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_wd.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cs.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cs.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_zero_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_wd.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_dist.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_dist.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cr_dist.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cr_dist.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult_cr.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult_cr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_assoc_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_lin.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_commutative.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_commutative.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_dist_rht.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_dist_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_assoc.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_assoc.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_one.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_cr_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_one_mult.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_one_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_one.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_monoid.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_mult_monoid.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cr_non_triv.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cr_non_triv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_is_CRing.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_is_CRing.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cring.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_cring.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant_strext.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant_wd.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_constant_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_C_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_C_.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_X_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_X_.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_strext.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_wd.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_wd.con" as lemma.
(* UNEXPORTED
End CPoly_CRing
Implicit Arguments _X_ [CR].
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun'.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_linear_fun'.con" as definition.
(* UNEXPORTED
Implicit Arguments cpoly_linear_fun' [CR].
alias id "d" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/d.var".
-inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_eq_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_eq_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/zero_eq_linear_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/zero_eq_linear_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_zero_eq_linear.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_zero_eq_linear.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_linear_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_linear_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_eq_linear.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_eq_linear.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_zero_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_zero_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/zero_ap_linear_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/zero_ap_linear_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_zero_ap_linear.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_zero_ap_linear.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/zero_ap_linear.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/zero_ap_linear.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_linear_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_linear_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_ap_linear.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_linear_ap_linear.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_linear.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/linear_ap_linear.con" as lemma.
(* UNEXPORTED
End helpful_section
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_induc.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_induc.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Ccpoly_double_sym_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Cpoly_double_comp_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Cpoly_double_comp_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Cpoly_triple_comp_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Cpoly_triple_comp_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_induc.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_induc.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_sym_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/poly_double_comp_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/poly_double_comp_ind.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/poly_triple_comp_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/poly_triple_comp_ind.con" as lemma.
(* UNEXPORTED
Transparent cpoly_cring.
Transparent cpoly_csetoid.
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_strext.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_wd.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_fun.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_apply_fun.con" as definition.
(* UNEXPORTED
End CPoly_CRing_ctd
*** Constant and identity
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_X_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_X_.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_C_.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_C_.con" as lemma.
(* UNEXPORTED
Hint Resolve cpoly_X_ cpoly_C_: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_const_eq.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_const_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_c_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_c_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_c_one.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_c_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_lin.con" as lemma.
(* UNEXPORTED
Hint Resolve cpoly_lin: algebra.
(* SUPERFLUOUS *)
-inline procedural "cic:/CoRN/algebra/CPolynomials/poly_linear.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/poly_linear.con" as lemma.
(* UNEXPORTED
Hint Resolve _c_zero: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/poly_c_apzero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/poly_c_apzero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult_lin.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult_lin.con" as lemma.
(* SUPERFLUOUS ? *)
-inline procedural "cic:/CoRN/algebra/CPolynomials/lin_mult.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/lin_mult.con" as lemma.
(* UNEXPORTED
Hint Resolve lin_mult: algebra.
(*#* *** Application of polynomials
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/poly_eq_zero.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/poly_eq_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/apply_wd.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/apply_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpolyap_pres_eq.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpolyap_pres_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpolyap_strext.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpolyap_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid_op.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_csetoid_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_c_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_c_apply.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_x_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_x_apply.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/plus_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/plus_apply.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/inv_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/inv_apply.con" as lemma.
(* UNEXPORTED
Hint Resolve plus_apply inv_apply: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/minus_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/minus_apply.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/_c_mult_apply.con" as lemma.
(* UNEXPORTED
Hint Resolve _c_mult_apply: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/mult_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/mult_apply.con" as lemma.
(* UNEXPORTED
Hint Resolve mult_apply: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/one_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/one_apply.con" as lemma.
(* UNEXPORTED
Hint Resolve one_apply: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/nexp_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/nexp_apply.con" as lemma.
(* SUPERFLUOUS *)
-inline procedural "cic:/CoRN/algebra/CPolynomials/poly_inv_apply.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/poly_inv_apply.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Sum0_cpoly_ap.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Sum0_cpoly_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CPolynomials/Sum_cpoly_ap.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/Sum_cpoly_ap.con" as lemma.
(* UNEXPORTED
End Poly_properties
Notation Cpoly_cring := (cpoly_cring CR).
*)
-inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind.con".
+inline procedural "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind.con" as lemma.
(* UNEXPORTED
End Poly_Prop_Induction
** Definition of the notion of Ring
*)
-inline procedural "cic:/CoRN/algebra/CRings/distributive.con".
+inline procedural "cic:/CoRN/algebra/CRings/distributive.con" as definition.
(* UNEXPORTED
Implicit Arguments distributive [S].
cic:/matita/CoRN-Procedural/algebra/CRings/cr_crr.con
*)
-inline procedural "cic:/CoRN/algebra/CRings/cr_plus.con".
+inline procedural "cic:/CoRN/algebra/CRings/cr_plus.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/cr_inv.con".
+inline procedural "cic:/CoRN/algebra/CRings/cr_inv.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/cr_minus.con".
+inline procedural "cic:/CoRN/algebra/CRings/cr_minus.con" as definition.
(* NOTATION
Notation One := (cr_one _).
alias id "R" = "cic:/CoRN/algebra/CRings/CRing_axioms/R.var".
-inline procedural "cic:/CoRN/algebra/CRings/CRing_is_CRing.con".
+inline procedural "cic:/CoRN/algebra/CRings/CRing_is_CRing.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/mult_assoc.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_assoc.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/mult_commutes.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_commutes.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/mult_mon.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_mon.con" as lemma.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CRings/dist.con".
+inline procedural "cic:/CoRN/algebra/CRings/dist.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/ring_non_triv.con".
+inline procedural "cic:/CoRN/algebra/CRings/ring_non_triv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/mult_wd.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/mult_wdl.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_wdl.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/mult_wdr.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_wdr.con" as lemma.
(* Begin_SpecReals *)
The multiplicative monoid of a ring is defined as follows.
*)
-inline procedural "cic:/CoRN/algebra/CRings/Build_multCMonoid.con".
+inline procedural "cic:/CoRN/algebra/CRings/Build_multCMonoid.con" as definition.
(* UNEXPORTED
End Ring_constructions
(* begin hide *)
-inline procedural "cic:/CoRN/algebra/CRings/Ring_unfolded/mmR.con" "Ring_unfolded__".
+inline procedural "cic:/CoRN/algebra/CRings/Ring_unfolded/mmR.con" "Ring_unfolded__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CRings/mult_assoc_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_assoc_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/mult_commut_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_commut_unfolded.con" as lemma.
(* UNEXPORTED
Hint Resolve mult_commut_unfolded: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/mult_one.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/one_mult.con".
+inline procedural "cic:/CoRN/algebra/CRings/one_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/ring_dist_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CRings/ring_dist_unfolded.con" as lemma.
(* UNEXPORTED
Hint Resolve ring_dist_unfolded: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con" as lemma.
(* UNEXPORTED
End Ring_unfolded
alias id "R" = "cic:/CoRN/algebra/CRings/Ring_basics/R.var".
-inline procedural "cic:/CoRN/algebra/CRings/one_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CRings/one_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/is_zero_rht.con".
+inline procedural "cic:/CoRN/algebra/CRings/is_zero_rht.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/is_zero_lft.con".
+inline procedural "cic:/CoRN/algebra/CRings/is_zero_lft.con" as definition.
(* UNEXPORTED
Implicit Arguments is_zero_rht [S].
Implicit Arguments is_zero_lft [S].
*)
-inline procedural "cic:/CoRN/algebra/CRings/cring_mult_zero.con".
+inline procedural "cic:/CoRN/algebra/CRings/cring_mult_zero.con" as lemma.
(* UNEXPORTED
Hint Resolve cring_mult_zero: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/x_mult_zero.con".
+inline procedural "cic:/CoRN/algebra/CRings/x_mult_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/cring_mult_zero_op.con".
+inline procedural "cic:/CoRN/algebra/CRings/cring_mult_zero_op.con" as lemma.
(* UNEXPORTED
Hint Resolve cring_mult_zero_op: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/cring_inv_mult_lft.con".
+inline procedural "cic:/CoRN/algebra/CRings/cring_inv_mult_lft.con" as lemma.
(* UNEXPORTED
Hint Resolve cring_inv_mult_lft: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/cring_inv_mult_rht.con".
+inline procedural "cic:/CoRN/algebra/CRings/cring_inv_mult_rht.con" as lemma.
(* UNEXPORTED
Hint Resolve cring_inv_mult_rht: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/cring_mult_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CRings/cring_mult_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/cring_mult_ap_zero_op.con".
+inline procedural "cic:/CoRN/algebra/CRings/cring_mult_ap_zero_op.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/inv_mult_invol.con".
+inline procedural "cic:/CoRN/algebra/CRings/inv_mult_invol.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/ring_dist_minus.con".
+inline procedural "cic:/CoRN/algebra/CRings/ring_dist_minus.con" as lemma.
(* UNEXPORTED
Hint Resolve ring_dist_minus: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/ring_distl_minus.con".
+inline procedural "cic:/CoRN/algebra/CRings/ring_distl_minus.con" as lemma.
(* UNEXPORTED
Hint Resolve ring_distl_minus: algebra.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CRings/nexp.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/nexp_well_def.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_well_def.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/nexp_strong_ext.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_strong_ext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/nexp_op.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_op.con" as definition.
(* Begin_SpecReals *)
to have characteristic [0].
*)
-inline procedural "cic:/CoRN/algebra/CRings/nring.con".
+inline procedural "cic:/CoRN/algebra/CRings/nring.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/Char0.con".
+inline procedural "cic:/CoRN/algebra/CRings/Char0.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CRings/nring_comm_plus.con".
+inline procedural "cic:/CoRN/algebra/CRings/nring_comm_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/nring_comm_mult.con".
+inline procedural "cic:/CoRN/algebra/CRings/nring_comm_mult.con" as lemma.
(* Begin_SpecReals *)
Notation FortyEight := (nring 48).
*)
-inline procedural "cic:/CoRN/algebra/CRings/one_plus_one.con".
+inline procedural "cic:/CoRN/algebra/CRings/one_plus_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/x_plus_x.con".
+inline procedural "cic:/CoRN/algebra/CRings/x_plus_x.con" as lemma.
(* UNEXPORTED
Hint Resolve one_plus_one x_plus_x: algebra.
In a ring of characteristic zero, [nring] is really an injection.
*)
-inline procedural "cic:/CoRN/algebra/CRings/nring_different.con".
+inline procedural "cic:/CoRN/algebra/CRings/nring_different.con" as lemma.
(* UNEXPORTED
Section int_injection
one. It is kept to avoid having to redo all the proofs.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_zero.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_zero.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_old_zero: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_diff.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_diff.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_old_diff.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_plus_nat.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_plus_nat.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_old_plus_nat: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv_nat.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv_nat.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_old_inv_nat: algebra.
Hint Resolve zring_old_diff: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_plus.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_plus.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_old_plus: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_old_inv: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_minus.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_minus.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_old_minus: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_mult.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_mult.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_old_mult: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_one.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_one.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_old_one: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv_one.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_old_inv_one.con" as lemma.
(*#************** new def of zring. ***********************)
(*#* The [zring] function can be defined directly. This is done here.
*)
-inline procedural "cic:/CoRN/algebra/CRings/pring_aux.con".
+inline procedural "cic:/CoRN/algebra/CRings/pring_aux.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/pring.con".
+inline procedural "cic:/CoRN/algebra/CRings/pring.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/zring.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/pring_aux_lemma.con".
+inline procedural "cic:/CoRN/algebra/CRings/pring_aux_lemma.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/double_nring.con".
+inline procedural "cic:/CoRN/algebra/CRings/double_nring.con" as lemma.
(* UNEXPORTED
Hint Resolve pring_aux_lemma double_nring: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/pring_aux_nring.con".
+inline procedural "cic:/CoRN/algebra/CRings/pring_aux_nring.con" as lemma.
(* UNEXPORTED
Hint Resolve pring_aux_nring: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/pring_convert.con".
+inline procedural "cic:/CoRN/algebra/CRings/pring_convert.con" as lemma.
(* UNEXPORTED
Hint Resolve pring_convert: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_zring_old.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_zring_old.con" as lemma.
(* UNEXPORTED
Hint Resolve zring_zring_old: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zring_zero.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/zring_diff.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_diff.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/zring_plus_nat.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_plus_nat.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/zring_inv_nat.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_inv_nat.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/zring_plus.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/zring_inv.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_inv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/zring_minus.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/zring_mult.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_mult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/zring_one.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/zring_inv_one.con".
+inline procedural "cic:/CoRN/algebra/CRings/zring_inv_one.con" as lemma.
(* UNEXPORTED
End int_injection
Section infinite_ring_sums
*)
-inline procedural "cic:/CoRN/algebra/CRings/Sum_upto.con".
+inline procedural "cic:/CoRN/algebra/CRings/Sum_upto.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/sum_upto_O.con".
+inline procedural "cic:/CoRN/algebra/CRings/sum_upto_O.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/Sum_from_upto.con".
+inline procedural "cic:/CoRN/algebra/CRings/Sum_from_upto.con" as definition.
(*#*
Here's an alternative def of [Sum_from_upto], with a lemma that
it's equivalent to the original.
*)
-inline procedural "cic:/CoRN/algebra/CRings/seq_from.con".
+inline procedural "cic:/CoRN/algebra/CRings/seq_from.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/Sum_from_upto_alt.con".
+inline procedural "cic:/CoRN/algebra/CRings/Sum_from_upto_alt.con" as definition.
(* UNEXPORTED
End infinite_ring_sums
(*#* *** Ring Sums over Lists
*)
-inline procedural "cic:/CoRN/algebra/CRings/RList_Mem.con".
+inline procedural "cic:/CoRN/algebra/CRings/RList_Mem.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/List_Sum_upto.con".
+inline procedural "cic:/CoRN/algebra/CRings/List_Sum_upto.con" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/list_sum_upto_O.con".
+inline procedural "cic:/CoRN/algebra/CRings/list_sum_upto_O.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/List_Sum_from_upto.con".
+inline procedural "cic:/CoRN/algebra/CRings/List_Sum_from_upto.con" as definition.
(* UNEXPORTED
End ring_sums_over_lists
alias id "R" = "cic:/CoRN/algebra/CRings/Dist_properties/R.var".
-inline procedural "cic:/CoRN/algebra/CRings/dist_1b.con".
+inline procedural "cic:/CoRN/algebra/CRings/dist_1b.con" as lemma.
(* UNEXPORTED
Hint Resolve dist_1b: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/dist_2a.con".
+inline procedural "cic:/CoRN/algebra/CRings/dist_2a.con" as lemma.
(* UNEXPORTED
Hint Resolve dist_2a: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/dist_2b.con".
+inline procedural "cic:/CoRN/algebra/CRings/dist_2b.con" as lemma.
(* UNEXPORTED
Hint Resolve dist_2b: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum0_lft.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum0_lft.con" as lemma.
(* UNEXPORTED
Hint Resolve mult_distr_sum0_lft.
*)
-inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum_lft.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum_lft.con" as lemma.
(* UNEXPORTED
Hint Resolve mult_distr_sum_lft: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_distr_sum_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/sumx_const.con".
+inline procedural "cic:/CoRN/algebra/CRings/sumx_const.con" as lemma.
(* UNEXPORTED
End Dist_properties
alias id "R" = "cic:/CoRN/algebra/CRings/NExp_properties/R.var".
-inline procedural "cic:/CoRN/algebra/CRings/nexp_wd.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/nexp_strext.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/nexp_Sn.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_Sn.con" as lemma.
(* UNEXPORTED
Hint Resolve nexp_wd nexp_Sn: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/nexp_plus.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_plus.con" as lemma.
(* UNEXPORTED
Hint Resolve nexp_plus: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/one_nexp.con".
+inline procedural "cic:/CoRN/algebra/CRings/one_nexp.con" as lemma.
(* UNEXPORTED
Hint Resolve one_nexp: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/mult_nexp.con".
+inline procedural "cic:/CoRN/algebra/CRings/mult_nexp.con" as lemma.
(* UNEXPORTED
Hint Resolve mult_nexp: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/nexp_mult.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_mult.con" as lemma.
(* UNEXPORTED
Hint Resolve nexp_mult: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/zero_nexp.con".
+inline procedural "cic:/CoRN/algebra/CRings/zero_nexp.con" as lemma.
(* UNEXPORTED
Hint Resolve zero_nexp: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_even.con".
+inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_even.con" as lemma.
(* UNEXPORTED
Hint Resolve inv_nexp_even: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_two.con".
+inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_two.con" as lemma.
(* UNEXPORTED
Hint Resolve inv_nexp_two: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_odd.con".
+inline procedural "cic:/CoRN/algebra/CRings/inv_nexp_odd.con" as lemma.
(* UNEXPORTED
Hint Resolve inv_nexp_odd: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/nexp_one.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_one.con" as lemma.
(* UNEXPORTED
Hint Resolve nexp_one: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/nexp_two.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_two.con" as lemma.
(* UNEXPORTED
Hint Resolve nexp_two: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/inv_one_even_nexp.con".
+inline procedural "cic:/CoRN/algebra/CRings/inv_one_even_nexp.con" as lemma.
(* UNEXPORTED
Hint Resolve inv_one_even_nexp: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/inv_one_odd_nexp.con".
+inline procedural "cic:/CoRN/algebra/CRings/inv_one_odd_nexp.con" as lemma.
(* UNEXPORTED
Hint Resolve inv_one_odd_nexp: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/square_plus.con".
+inline procedural "cic:/CoRN/algebra/CRings/square_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/square_minus.con".
+inline procedural "cic:/CoRN/algebra/CRings/square_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/nexp_funny.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_funny.con" as lemma.
(* UNEXPORTED
Hint Resolve nexp_funny: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CRings/nexp_funny'.con".
+inline procedural "cic:/CoRN/algebra/CRings/nexp_funny'.con" as lemma.
(* UNEXPORTED
Hint Resolve nexp_funny': algebra.
(* begin hide *)
-inline procedural "cic:/CoRN/algebra/CRings/CRing_Ops/P.con" "CRing_Ops__".
+inline procedural "cic:/CoRN/algebra/CRings/CRing_Ops/P.con" "CRing_Ops__" as definition.
-inline procedural "cic:/CoRN/algebra/CRings/CRing_Ops/Q.con" "CRing_Ops__".
+inline procedural "cic:/CoRN/algebra/CRings/CRing_Ops/Q.con" "CRing_Ops__" as definition.
(* end hide *)
Section Part_Function_Mult
*)
-inline procedural "cic:/CoRN/algebra/CRings/part_function_mult_strext.con".
+inline procedural "cic:/CoRN/algebra/CRings/part_function_mult_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/Fmult.con".
+inline procedural "cic:/CoRN/algebra/CRings/Fmult.con" as definition.
(* UNEXPORTED
End Part_Function_Mult
alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var".
-inline procedural "cic:/CoRN/algebra/CRings/part_function_nth_strext.con".
+inline procedural "cic:/CoRN/algebra/CRings/part_function_nth_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/Fnth.con".
+inline procedural "cic:/CoRN/algebra/CRings/Fnth.con" as definition.
(* UNEXPORTED
End Part_Function_Nth_Power
alias id "R'" = "cic:/CoRN/algebra/CRings/CRing_Ops/R'.var".
-inline procedural "cic:/CoRN/algebra/CRings/included_FMult.con".
+inline procedural "cic:/CoRN/algebra/CRings/included_FMult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/included_FMult'.con".
+inline procedural "cic:/CoRN/algebra/CRings/included_FMult'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/included_FMult''.con".
+inline procedural "cic:/CoRN/algebra/CRings/included_FMult''.con" as lemma.
alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/n.var".
-inline procedural "cic:/CoRN/algebra/CRings/included_FNth.con".
+inline procedural "cic:/CoRN/algebra/CRings/included_FNth.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/included_FNth'.con".
+inline procedural "cic:/CoRN/algebra/CRings/included_FNth'.con" as lemma.
(* UNEXPORTED
End CRing_Ops
*)
-inline procedural "cic:/CoRN/algebra/CRings/Fscalmult.con".
+inline procedural "cic:/CoRN/algebra/CRings/Fscalmult.con" as definition.
(* UNEXPORTED
Implicit Arguments Fmult [R].
(* begin hide *)
-inline procedural "cic:/CoRN/algebra/CRings/ScalarMultiplication/P.con" "ScalarMultiplication__".
+inline procedural "cic:/CoRN/algebra/CRings/ScalarMultiplication/P.con" "ScalarMultiplication__" as definition.
(* end hide *)
alias id "R'" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var".
-inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult.con".
+inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult'.con".
+inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult'.con" as lemma.
(* UNEXPORTED
End ScalarMultiplication
**Definition of the notion of semigroup
*)
-inline procedural "cic:/CoRN/algebra/CSemiGroups/is_CSemiGroup.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/is_CSemiGroup.con" as definition.
inline procedural "cic:/CoRN/algebra/CSemiGroups/CSemiGroup.ind".
alias id "G" = "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_axioms/G.var".
-inline procedural "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSemiGroups/plus_assoc.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/plus_assoc.con" as lemma.
(* UNEXPORTED
End CSemiGroup_axioms
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con" as lemma.
(* UNEXPORTED
End CSemiGroup_basics
(* begin hide *)
-inline procedural "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/P.con" "Part_Function_Plus__".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/P.con" "Part_Function_Plus__" as definition.
-inline procedural "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/Q.con" "Part_Function_Plus__".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/Q.con" "Part_Function_Plus__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CSemiGroups/part_function_plus_strext.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/part_function_plus_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSemiGroups/Fplus.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/Fplus.con" as definition.
(*#*
%\begin{convention}% Let [R:G->CProp].
alias id "R" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/R.var".
-inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus'.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con" as lemma.
(* UNEXPORTED
End Part_Function_Plus
alias id "op_pres_P" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/op_pres_P.var".
-inline procedural "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/subcrr.con" "SubCSemiGroups__".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/subcrr.con" "SubCSemiGroups__" as definition.
-inline procedural "cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con".
+inline procedural "cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con" as definition.
(* UNEXPORTED
End SubCSemiGroups
alias id "g" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/g.var".
-inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con" as definition.
(* UNEXPORTED
End unary_function_composition
Section unary_and_binary_function_composition
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_un_fun.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_un_fun.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_fun.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_fun.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_un_bin_fun.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_un_bin_fun.con" as definition.
(* UNEXPORTED
End unary_and_binary_function_composition
Section function_projection
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/proj_bin_fun.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/proj_bin_fun.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/projected_bin_fun.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/projected_bin_fun.con" as definition.
(* UNEXPORTED
End function_projection
alias id "S" = "cic:/CoRN/algebra/CSetoidFun/BinProj/S.var".
-inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/cs_binproj1.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/cs_binproj1.con" as definition.
(* UNEXPORTED
End BinProj
alias id "op" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/op.var".
-inline procedural "cic:/CoRN/algebra/CSetoidFun/opOnFun.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/opOnFun.con" as definition.
(* UNEXPORTED
End CombiningUnaryOperations
alias id "Q" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/Q.var".
-inline procedural "cic:/CoRN/algebra/CSetoidFun/conjP.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/conjP.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/prj1.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/prj1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/prj2.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/prj2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/conj_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/conj_wd.con" as lemma.
(* UNEXPORTED
End Conjunction
Although at this stage we never use it, for completeness's sake we also treat disjunction (corresponding to union of subsets).
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/disj.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/disj.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/inj1.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/inj1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/inj2.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/inj2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/disj_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/disj_wd.con" as lemma.
(* UNEXPORTED
End Disjunction
alias id "R" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/R.var".
-inline procedural "cic:/CoRN/algebra/CSetoidFun/extend.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/extend.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/ext1.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/ext1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/ext2_a.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/ext2_a.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/ext2.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/ext2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/extension_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/extension_wd.con" as lemma.
(* UNEXPORTED
End Extension
The next lemma states that every partial function is well defined.
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/bpfwdef.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/bpfwdef.con" as lemma.
(*#* Similar for automorphisms. *)
The next lemma states that every partial function is well defined.
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/pfwdef.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/pfwdef.con" as lemma.
(*#*
A few characteristics of this definition should be explained:
To begin with, we want to be able to ``see'' each total function as a partial function.
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/total_eq_part.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/total_eq_part.con" as definition.
(* UNEXPORTED
Section Part_Function_Const
alias id "c" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Const/c.var".
-inline procedural "cic:/CoRN/algebra/CSetoidFun/Fconst.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/Fconst.con" as definition.
(* UNEXPORTED
End Part_Function_Const
Section Part_Function_Id
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/Fid.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/Fid.con" as definition.
(* UNEXPORTED
End Part_Function_Id
(* begin hide *)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/P.con" "CSetoid_Ops__Part_Function_Composition__".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/P.con" "CSetoid_Ops__Part_Function_Composition__" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/Q.con" "CSetoid_Ops__Part_Function_Composition__".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/Q.con" "CSetoid_Ops__Part_Function_Composition__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/R.con" "CSetoid_Ops__Part_Function_Composition__".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/R.con" "CSetoid_Ops__Part_Function_Composition__" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/part_function_comp_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/part_function_comp_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/part_function_comp_dom_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/part_function_comp_dom_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/Fcomp.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/Fcomp.con" as definition.
(* UNEXPORTED
End Part_Function_Composition
(* begin hide *)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/P.con" "BinPart_Function_Composition__".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/P.con" "BinPart_Function_Composition__" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/Q.con" "BinPart_Function_Composition__".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/Q.con" "BinPart_Function_Composition__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/R.con" "BinPart_Function_Composition__".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/R.con" "BinPart_Function_Composition__" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_dom_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_dom_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/BinFcomp.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/BinFcomp.con" as definition.
(* UNEXPORTED
End BinPart_Function_Composition
(*#* **Bijections *)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/injective.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/injective.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/injective_weak.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/injective_weak.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/surjective.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/surjective.con" as definition.
(* UNEXPORTED
Implicit Arguments injective [A B].
Implicit Arguments surjective [A B].
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/injective_imp_injective_weak.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/injective_imp_injective_weak.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/bijective.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/bijective.con" as definition.
(* UNEXPORTED
Implicit Arguments bijective [A B].
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/id_is_bij.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/id_is_bij.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/comp_resp_bij.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/comp_resp_bij.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/inv.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/inv.con" as lemma.
(* UNEXPORTED
Implicit Arguments inv [A B].
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/invfun.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/invfun.con" as definition.
(* UNEXPORTED
Implicit Arguments invfun [A B].
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/inv1.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/inv1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/inv2.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/inv2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/inv_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/inv_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidFun/Inv.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/Inv.con" as definition.
(* UNEXPORTED
Implicit Arguments Inv [A B].
*)
-inline procedural "cic:/CoRN/algebra/CSetoidFun/Inv_bij.con".
+inline procedural "cic:/CoRN/algebra/CSetoidFun/Inv_bij.con" as definition.
(* UNEXPORTED
End bijections
alias id "S" = "cic:/CoRN/algebra/CSetoidInc/inclusion/S.var".
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included.con" as definition.
(* UNEXPORTED
Section Basics
alias id "R" = "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var".
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_refl.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_refl.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_trans.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_trans.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj'.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj''.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj''.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_lft.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_rht.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_conj_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_extend.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_extend.con" as lemma.
(* UNEXPORTED
End Basics
(* begin hide *)
-inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/P.con" "inclusion__".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/P.con" "inclusion__" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/Q.con" "inclusion__".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/inclusion/Q.con" "inclusion__" as definition.
(* end hide *)
alias id "R" = "cic:/CoRN/algebra/CSetoidInc/inclusion/R.var".
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp'.con".
+inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp'.con" as lemma.
(* UNEXPORTED
End inclusion
include "tactics/Step.ma".
-inline procedural "cic:/CoRN/algebra/CSetoids/Relation.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Relation.con" as definition.
(* End_SpecReals *)
alias id "A" = "cic:/CoRN/algebra/CSetoids/Properties_of_relations/A.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/irreflexive.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/irreflexive.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/cotransitive.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/cotransitive.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/tight_apart.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/tight_apart.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/antisymmetric.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/antisymmetric.con" as definition.
(* UNEXPORTED
End Properties_of_relations
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/cs_neq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/cs_neq.con" as definition.
(* UNEXPORTED
Implicit Arguments cs_neq [S].
alias id "S" = "cic:/CoRN/algebra/CSetoids/CSetoid_axioms/S.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_irreflexive.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_symmetric.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_cotransitive.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_cotransitive.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_tight.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_tight.con" as lemma.
(* UNEXPORTED
End CSetoid_axioms
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 procedural "cic:/CoRN/algebra/CSetoids/ex_unq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ex_unq.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/eq_reflexive.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/eq_reflexive.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/eq_symmetric.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/eq_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/eq_transitive.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/eq_transitive.con" as lemma.
(*#*
%\begin{shortcoming}%
%\end{nameconvention}%
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/eq_reflexive_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/eq_reflexive_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/eq_symmetric_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/eq_symmetric_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/eq_transitive_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/eq_transitive_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/eq_wdl.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/eq_wdl.con" as lemma.
(* Begin_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_irreflexive_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_irreflexive_unfolded.con" as lemma.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_cotransitive_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_cotransitive_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_symmetric_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_symmetric_unfolded.con" as lemma.
(*#*
%\begin{shortcoming}%
%\end{shortcoming}%
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/eq_imp_not_ap.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/eq_imp_not_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/not_ap_imp_eq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/not_ap_imp_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/neq_imp_notnot_ap.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/neq_imp_notnot_ap.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/notnot_ap_imp_neq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/notnot_ap_imp_neq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_imp_neq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_imp_neq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/not_neq_imp_eq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/not_neq_imp_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/eq_imp_not_neq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/eq_imp_not_neq.con" as lemma.
(* Begin_SpecReals *)
(*#* **The product of setoids *)
-inline procedural "cic:/CoRN/algebra/CSetoids/prod_ap.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/prod_ap.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/prod_eq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/prod_eq.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/prodcsetoid_is_CSetoid.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/prodcsetoid_is_CSetoid.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ProdCSetoid.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ProdCSetoid.con" as definition.
(* UNEXPORTED
End product_csetoid
alias id "P" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPredicates/P.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/pred_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/pred_wd.con" as definition.
(* UNEXPORTED
End CSetoidPredicates
cic:/matita/CoRN-Procedural/algebra/CSetoids/csp_pred.con
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/csp_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csp_wd.con" as lemma.
(*#* Similar, with [Prop] instead of [CProp]. *)
alias id "P" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPPredicates/P.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/pred_wd'.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/pred_wd'.con" as definition.
(* UNEXPORTED
End CSetoidPPredicates
cic:/matita/CoRN-Procedural/algebra/CSetoids/csp'_pred.con
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/csp'_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csp'_wd.con" as lemma.
(* Begin_SpecReals *)
alias id "R" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CsetoidRelations/R.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdr.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdr.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdl.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdl.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_lft.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_lft.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_rht.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_rht.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_imp_lftarg.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_imp_lftarg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_imp_rhtarg.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/rel_strext_imp_rhtarg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/rel_strextarg_imp_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/rel_strextarg_imp_strext.con" as lemma.
(* Begin_SpecReals *)
alias id "R" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CCsetoidRelations/R.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdr.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdr.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdl.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdl.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_lft.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_lft.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_rht.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_rht.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_lftarg.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_lftarg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_rhtarg.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strext_imp_rhtarg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strextarg_imp_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Crel_strextarg_imp_strext.con" as lemma.
(* Begin_SpecReals *)
cic:/matita/CoRN-Procedural/algebra/CSetoids/Ccsr_rel.con
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/Ccsr_wdr.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Ccsr_wdr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/Ccsr_wdl.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Ccsr_wdl.con" as lemma.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdr.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdr.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdl.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdl.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdr_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdr_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdl_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_wdl_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/ap_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/ap_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/predS_well_def.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/predS_well_def.con" as definition.
(* Begin_SpecReals *)
alias id "f" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/unary_functions/f.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/fun_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/fun_wd.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/fun_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/fun_strext.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/fun_strext_imp_wd.con" as lemma.
(* Begin_SpecReals *)
cic:/matita/CoRN-Procedural/algebra/CSetoids/csf_fun.con
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/csf_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csf_wd.con" as lemma.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/Const_CSetoid_fun.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Const_CSetoid_fun.con" as definition.
(* Begin_SpecReals *)
alias id "f" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/binary_functions/f.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_wd.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_strext.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_strext_imp_wd.con" as lemma.
(* Begin_SpecReals *)
cic:/matita/CoRN-Procedural/algebra/CSetoids/csbf_fun.con
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/csbf_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csbf_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/csf_wd_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csf_wd_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/csf_strext_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csf_strext_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/csbf_wd_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csbf_wd_unfolded.con" as lemma.
(* UNEXPORTED
End CSetoid_functions
(*#* Properties of binary operations *)
-inline procedural "cic:/CoRN/algebra/CSetoids/commutes.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/commutes.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/associative.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/associative.con" as definition.
(*#* Well-defined unary operations on a setoid. *)
-inline procedural "cic:/CoRN/algebra/CSetoids/un_op_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/un_op_wd.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/un_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/un_op_strext.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_un_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_un_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_un_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_un_op.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/id_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/id_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/id_pres_eq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/id_pres_eq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/id_un_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/id_un_op.con" as definition.
(* begin hide *)
(* Begin_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/cs_un_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/cs_un_op_strext.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/un_op_wd_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/un_op_wd_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/un_op_strext_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/un_op_strext_unfolded.con" as lemma.
(*#* Well-defined binary operations on a setoid. *)
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_wd.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_strext.con" as definition.
(* Begin_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_bin_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_bin_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_bin_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_bin_op.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/cs_bin_op_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/cs_bin_op_wd.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/cs_bin_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/cs_bin_op_strext.con" as definition.
(* Begin_SpecReals *)
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_wd_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_wd_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_strext_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_strext_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_lft.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_rht.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_wd_un_op_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_lft.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_lft.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_rht.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_is_strext_un_op_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op2un_op_rht.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op2un_op_rht.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op2un_op_lft.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op2un_op_lft.con" as definition.
(* Begin_SpecReals *)
Well-defined outer operations on a setoid.
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/outer_op_well_def.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/outer_op_well_def.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/outer_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/outer_op_strext.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_outer_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_outer_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_outer_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Build_CSetoid_outer_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/csoo_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csoo_wd.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/csoo_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csoo_strext.con" as definition.
(* begin hide *)
(* end hide *)
-inline procedural "cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con" as lemma.
(* UNEXPORTED
End csetoid_outer_ops
also not be printed, which is handy.
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/restrict_relation.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/restrict_relation.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/Crestrict_relation.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Crestrict_relation.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_eq.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_eq.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_ap.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_ap.con" as definition.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_equiv.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_equiv.con" as remark.
(* Begin_SpecReals *)
-inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_is_CSetoid.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_is_CSetoid.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid.con" as definition.
(* End_SpecReals *)
alias id "f" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/f.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con" as definition.
(*#*
%\begin{convention}%
alias id "pr" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/pr.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op_wd.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_un_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_un_op.con" as definition.
(* UNEXPORTED
End SubCSetoid_unary_operations
alias id "f" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/f.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con" as definition.
(*#*
%\begin{convention}%
alias id "pr" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/pr.var".
-inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op_well_def.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op_well_def.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op_strext.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_bin_op.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_bin_op.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/restr_f_assoc.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/restr_f_assoc.con" as lemma.
(* UNEXPORTED
End SubCSetoid_binary_operations
(*#* **Miscellaneous
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/proper_caseZ_diff_CS.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/proper_caseZ_diff_CS.con" as lemma.
(*#*
Finally, we characterize functions defined on the natural numbers also as setoid functions, similarly to what we already did for predicates.
*)
-inline procedural "cic:/CoRN/algebra/CSetoids/nat_less_n_fun.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/nat_less_n_fun.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSetoids/nat_less_n_fun'.con".
+inline procedural "cic:/CoRN/algebra/CSetoids/nat_less_n_fun'.con" as definition.
(* UNEXPORTED
Implicit Arguments nat_less_n_fun [S n].
(* Sum1 and Sum use subtraction *)
-inline procedural "cic:/CoRN/algebra/CSums/Sumlist.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sumlist.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSums/Sumx.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sumx.con" as definition.
(*#*
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 procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun.con".
+inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch1.con".
+inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch2.con".
+inline procedural "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch2.con" as lemma.
(*#* [Sum0] defines the sum for [i=0..(n-1)] *)
-inline procedural "cic:/CoRN/algebra/CSums/Sum0.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum0.con" as definition.
(*#* [Sum1] defines the sum for [i=m..(n-1)] *)
-inline procedural "cic:/CoRN/algebra/CSums/Sum1.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum1.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSums/Sum.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum.con" as definition.
(* 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 procedural "cic:/CoRN/algebra/CSums/Sum2.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum2.con" as definition.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_one.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_one.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum_one: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CSums/Sum_empty.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_empty.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum_empty: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CSums/Sum_Sum.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_Sum.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum_Sum: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CSums/Sum_first.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_first.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_last.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_last.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum_last: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CSums/Sum_last'.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_last'.con" as lemma.
(*#*
We add some extensionality results which will be quite useful
when working with integration.
*)
-inline procedural "cic:/CoRN/algebra/CSums/Sum0_strext.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum0_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_strext.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sumx_strext.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sumx_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum0_strext'.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum0_strext'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_strext'.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_strext'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum0_wd.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum0_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_wd.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sumx_wd.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sumx_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_wd'.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_wd'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum2_wd.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum2_wd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum0_plus_Sum0.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum0_plus_Sum0.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum0_plus_Sum0: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CSums/Sum_plus_Sum.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_plus_Sum.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sumx_plus_Sumx.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sumx_plus_Sumx.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum2_plus_Sum2.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum2_plus_Sum2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/inv_Sum0.con".
+inline procedural "cic:/CoRN/algebra/CSums/inv_Sum0.con" as lemma.
(* UNEXPORTED
Hint Resolve inv_Sum0: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CSums/inv_Sum.con".
+inline procedural "cic:/CoRN/algebra/CSums/inv_Sum.con" as lemma.
(* UNEXPORTED
Hint Resolve inv_Sum: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CSums/inv_Sumx.con".
+inline procedural "cic:/CoRN/algebra/CSums/inv_Sumx.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/inv_Sum2.con".
+inline procedural "cic:/CoRN/algebra/CSums/inv_Sum2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_minus_Sum.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_minus_Sum.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum_minus_Sum: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CSums/Sumx_minus_Sumx.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sumx_minus_Sumx.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum2_minus_Sum2.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum2_minus_Sum2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_apzero.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_apzero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_zero.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_term.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_term.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum0_shift.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum0_shift.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum0_shift: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CSums/Sum_shift.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_shift.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sum_big_shift.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sum_big_shift.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sumx_Sum0.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sumx_Sum0.con" as lemma.
(* UNEXPORTED
End Sums
alias id "G" = "cic:/CoRN/algebra/CSums/More_Sums/G.var".
-inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum.con".
+inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum_gen.con".
+inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum_gen.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/str_Mengolli_Sum_gen.con".
+inline procedural "cic:/CoRN/algebra/CSums/str_Mengolli_Sum_gen.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CSums/Sumx_to_Sum.con".
+inline procedural "cic:/CoRN/algebra/CSums/Sumx_to_Sum.con" as lemma.
(* UNEXPORTED
End More_Sums
alias id "V" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var".
-inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CVectorSpace/zero_vs_op.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/zero_vs_op.con" as lemma.
(* UNEXPORTED
Hint Resolve vs_op_zero zero_vs_op: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_V.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_V.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_S.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_inv_S.con" as lemma.
(* UNEXPORTED
Hint Resolve vs_op_inv_V vs_op_inv_S: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_inv_assoc.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_inv_assoc.con" as lemma.
(* UNEXPORTED
Hint Resolve vs_inv_assoc: algebra.
*)
-inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_l.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_l.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_r.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/ap_zero_vs_op_r.con" as lemma.
(* note this is the same proof as mult_resp_ap_zero *)
-inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_rht.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_rht.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con".
+inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con" as lemma.
(* UNEXPORTED
End VS_basics
than the other, equality is the negation of the apartness.
*)
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_Set.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_Set.con" as definition.
(* UNEXPORTED
Section CSetoid_Structure
*)
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_eq.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_eq.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_cotrans.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_cotrans.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_cotrans.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_cotrans.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_symmetric.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_irreflexive.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_irreflexive.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_eq_tight.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_eq_tight.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con" as definition.
(* UNEXPORTED
End CSetoid_Structure
are specifically proved are just the necessary ones to get the group axioms.
*)
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_zero.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_zero.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_lft_ext.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_lft_ext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_assoc.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_assoc.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_zero_lft_unit.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_zero_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_comm.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_comm.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv_is_inv.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv_is_inv.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv_ext.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_inv_ext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rinv.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rinv.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CAbGroup.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CAbGroup.con" as definition.
(* UNEXPORTED
End Group_Structure
Same comments as previously.
*)
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_plus.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_plus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_minus.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_minus.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_rht_unit.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_comm.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_comm.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_ap_zero'.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_ap_zero'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_lft_ext.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_lft_ext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_rht_ext.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_rht_ext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_strext.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rmult.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rmult.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_assoc.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_assoc.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_lft_unit.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_one_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CRing.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CRing.con" as definition.
(* UNEXPORTED
End Ring_Structure
quite straightforwardly.
*)
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_integral_domain.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_integral_domain.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_strext.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse'.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CField.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_CField.con" as definition.
(* UNEXPORTED
End Field_Structure
defined at the beginning.
*)
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_strext.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_lt_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt.con" as definition.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_transitive.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_transitive.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_strict.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_strict.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_resp_lt.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_plus_resp_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_resp_lt.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_mult_resp_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_COrdField.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_COrdField.con" as definition.
(* UNEXPORTED
End Order
Section Auxiliary
*)
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_1.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_2.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_1.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_1.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_2.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_2.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_1.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_1.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con".
+inline procedural "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con" as lemma.
(* UNEXPORTED
End Auxiliary
alias id "R" = "cic:/CoRN/algebra/Expon/More_Nexp/R.var".
-inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con" as lemma.
(* UNEXPORTED
Hint Resolve nexp_resp_ap_zero: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div'.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_div'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_lt.con".
+inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_lt.con".
+inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_lt.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_le.con".
+inline procedural "cic:/CoRN/algebra/Expon/small_nexp_resp_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_le.con".
+inline procedural "cic:/CoRN/algebra/Expon/great_nexp_resp_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_one.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_one.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_even.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_even.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_odd.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_leEq_neg_odd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_recip.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_distr_recip.con" as lemma.
(* UNEXPORTED
Hint Resolve nexp_distr_recip: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/nexp_even_nonneg.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_even_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le'.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le'.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le.con".
+inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_le.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/bin_less_un.con".
+inline procedural "cic:/CoRN/algebra/Expon/bin_less_un.con" as lemma.
(* UNEXPORTED
End More_Nexp
have most properties now.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp.con" as definition.
(* UNEXPORTED
End Zexp_def
alias id "R" = "cic:/CoRN/algebra/Expon/Zexp_properties/R.var".
-inline procedural "cic:/CoRN/algebra/Expon/zexp_zero.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_zero.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_zero: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_nexp.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_nexp.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_nexp: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_inv_nexp: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp'.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_inv_nexp'.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_inv_nexp': algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_strext.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_strext.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/zexp_wd.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_wd.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_wd: algebra_c.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_plus1.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_plus1.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_plus1: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_resp_ap_zero.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_resp_ap_zero.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_resp_ap_zero: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_inv.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_inv: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_inv1.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_inv1.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_inv1: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_plus.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_plus.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_plus: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_minus.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_minus.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_minus: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/one_zexp.con".
+inline procedural "cic:/CoRN/algebra/Expon/one_zexp.con" as lemma.
(* UNEXPORTED
Hint Resolve one_zexp: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/mult_zexp.con".
+inline procedural "cic:/CoRN/algebra/Expon/mult_zexp.con" as lemma.
(* UNEXPORTED
Hint Resolve mult_zexp: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_mult.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_mult.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_mult: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_two.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_two.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_two: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_even.con".
+inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_even.con" as lemma.
(* UNEXPORTED
Hint Resolve inv_zexp_even: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_two.con".
+inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_two.con" as lemma.
(* UNEXPORTED
Hint Resolve inv_zexp_two: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_odd.con".
+inline procedural "cic:/CoRN/algebra/Expon/inv_zexp_odd.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/zexp_one.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_one.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_one: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_funny.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_funny.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_funny: algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_funny'.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_funny'.con" as lemma.
(* UNEXPORTED
Hint Resolve zexp_funny': algebra.
*)
-inline procedural "cic:/CoRN/algebra/Expon/zexp_pos.con".
+inline procedural "cic:/CoRN/algebra/Expon/zexp_pos.con" as lemma.
(* UNEXPORTED
End Zexp_properties
alias id "R" = "cic:/CoRN/algebra/Expon/Root_Unique/R.var".
-inline procedural "cic:/CoRN/algebra/Expon/root_unique.con".
+inline procedural "cic:/CoRN/algebra/Expon/root_unique.con" as lemma.
-inline procedural "cic:/CoRN/algebra/Expon/root_one.con".
+inline procedural "cic:/CoRN/algebra/Expon/root_one.con" as lemma.
(* UNEXPORTED
End Root_Unique
inline procedural "cic:/CoRN/algebra/ListType/list.ind".
-inline procedural "cic:/CoRN/algebra/ListType/app.con".
+inline procedural "cic:/CoRN/algebra/ListType/app.con" as definition.
-inline procedural "cic:/CoRN/algebra/ListType/app_nil_end.con".
+inline procedural "cic:/CoRN/algebra/ListType/app_nil_end.con" as lemma.
(* UNEXPORTED
Hint Resolve app_nil_end: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/app_ass.con".
+inline procedural "cic:/CoRN/algebra/ListType/app_ass.con" as lemma.
(* UNEXPORTED
Hint Resolve app_ass: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/ass_app.con".
+inline procedural "cic:/CoRN/algebra/ListType/ass_app.con" as lemma.
(* UNEXPORTED
Hint Resolve ass_app: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/tail.con".
+inline procedural "cic:/CoRN/algebra/ListType/tail.con" as definition.
-inline procedural "cic:/CoRN/algebra/ListType/nil_cons.con".
+inline procedural "cic:/CoRN/algebra/ListType/nil_cons.con" as lemma.
(*#***************************************)
(*#***************************************)
-inline procedural "cic:/CoRN/algebra/ListType/length.con".
+inline procedural "cic:/CoRN/algebra/ListType/length.con" as definition.
(*#*****************************)
Section length_order
*)
-inline procedural "cic:/CoRN/algebra/ListType/lel.con".
+inline procedural "cic:/CoRN/algebra/ListType/lel.con" as definition.
(* UNEXPORTED
Hint Unfold lel: list.
alias id "n" = "cic:/CoRN/algebra/ListType/List/length_order/n.var".
-inline procedural "cic:/CoRN/algebra/ListType/lel_refl.con".
+inline procedural "cic:/CoRN/algebra/ListType/lel_refl.con" as lemma.
-inline procedural "cic:/CoRN/algebra/ListType/lel_trans.con".
+inline procedural "cic:/CoRN/algebra/ListType/lel_trans.con" as lemma.
-inline procedural "cic:/CoRN/algebra/ListType/lel_cons_cons.con".
+inline procedural "cic:/CoRN/algebra/ListType/lel_cons_cons.con" as lemma.
-inline procedural "cic:/CoRN/algebra/ListType/lel_cons.con".
+inline procedural "cic:/CoRN/algebra/ListType/lel_cons.con" as lemma.
-inline procedural "cic:/CoRN/algebra/ListType/lel_tail.con".
+inline procedural "cic:/CoRN/algebra/ListType/lel_tail.con" as lemma.
-inline procedural "cic:/CoRN/algebra/ListType/lel_nil.con".
+inline procedural "cic:/CoRN/algebra/ListType/lel_nil.con" as lemma.
(* UNEXPORTED
End length_order
v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/In.con".
+inline procedural "cic:/CoRN/algebra/ListType/In.con" as definition.
-inline procedural "cic:/CoRN/algebra/ListType/in_eq.con".
+inline procedural "cic:/CoRN/algebra/ListType/in_eq.con" as lemma.
(* UNEXPORTED
Hint Resolve in_eq: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/in_cons.con".
+inline procedural "cic:/CoRN/algebra/ListType/in_cons.con" as lemma.
(* UNEXPORTED
Hint Resolve in_cons: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/in_app_or.con".
+inline procedural "cic:/CoRN/algebra/ListType/in_app_or.con" as lemma.
(* UNEXPORTED
Hint Immediate in_app_or: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/in_or_app.con".
+inline procedural "cic:/CoRN/algebra/ListType/in_or_app.con" as lemma.
(* UNEXPORTED
Hint Resolve in_or_app: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/incl.con".
+inline procedural "cic:/CoRN/algebra/ListType/incl.con" as definition.
(* UNEXPORTED
Hint Unfold incl: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/incl_refl.con".
+inline procedural "cic:/CoRN/algebra/ListType/incl_refl.con" as lemma.
(* UNEXPORTED
Hint Resolve incl_refl: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/incl_tl.con".
+inline procedural "cic:/CoRN/algebra/ListType/incl_tl.con" as lemma.
(* UNEXPORTED
Hint Immediate incl_tl: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/incl_tran.con".
+inline procedural "cic:/CoRN/algebra/ListType/incl_tran.con" as lemma.
-inline procedural "cic:/CoRN/algebra/ListType/incl_appl.con".
+inline procedural "cic:/CoRN/algebra/ListType/incl_appl.con" as lemma.
(* UNEXPORTED
Hint Immediate incl_appl: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/incl_appr.con".
+inline procedural "cic:/CoRN/algebra/ListType/incl_appr.con" as lemma.
(* UNEXPORTED
Hint Immediate incl_appr: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/incl_cons.con".
+inline procedural "cic:/CoRN/algebra/ListType/incl_cons.con" as lemma.
(* UNEXPORTED
Hint Resolve incl_cons: list v62.
*)
-inline procedural "cic:/CoRN/algebra/ListType/incl_app.con".
+inline procedural "cic:/CoRN/algebra/ListType/incl_app.con" as lemma.
(* UNEXPORTED
End List
alias id "f" = "cic:/CoRN/algebra/ListType/Map/f.var".
-inline procedural "cic:/CoRN/algebra/ListType/map.con".
+inline procedural "cic:/CoRN/algebra/ListType/map.con" as definition.
(* UNEXPORTED
End Map
Section AbsCC_properties
*)
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero_imp_pos.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero_imp_pos.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_wd.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_wd.con" as lemma.
(* UNEXPORTED
Hint Resolve AbsCC_wd: algebra_c.
*)
-inline procedural "cic:/CoRN/complex/AbsCC/cc_inv_abs.con".
+inline procedural "cic:/CoRN/complex/AbsCC/cc_inv_abs.con" as lemma.
(* UNEXPORTED
Hint Resolve cc_inv_abs: algebra.
*)
-inline procedural "cic:/CoRN/complex/AbsCC/cc_minus_abs.con".
+inline procedural "cic:/CoRN/complex/AbsCC/cc_minus_abs.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/cc_mult_abs.con".
+inline procedural "cic:/CoRN/complex/AbsCC/cc_mult_abs.con" as lemma.
(* UNEXPORTED
Hint Resolve cc_mult_abs: algebra.
*)
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_minzero.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_minzero.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_IR.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_IR.con" as lemma.
(* UNEXPORTED
Hint Resolve AbsCC_IR: algebra.
*)
-inline procedural "cic:/CoRN/complex/AbsCC/cc_div_abs.con".
+inline procedural "cic:/CoRN/complex/AbsCC/cc_div_abs.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/cc_div_abs'.con".
+inline procedural "cic:/CoRN/complex/AbsCC/cc_div_abs'.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_zero.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_zero.con" as lemma.
(* UNEXPORTED
Hint Resolve AbsCC_zero: algebra.
*)
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_one.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_one.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/cc_pow_abs.con".
+inline procedural "cic:/CoRN/complex/AbsCC/cc_pow_abs.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_pos.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_pos.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_small_imp_eq.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_small_imp_eq.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_1_2.con" "AbsCC_properties__".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_1_2.con" "AbsCC_properties__" as definition.
(* end hide *)
Hint Resolve l_1_1_2: algebra.
*)
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_square_Re_Im.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_square_Re_Im.con" as lemma.
(* UNEXPORTED
Hint Resolve AbsCC_square_Re_Im: algebra.
(* begin hide *)
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_2_3_CC.con" "AbsCC_properties__".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_2_3_CC.con" "AbsCC_properties__" as definition.
(* end hide *)
Hint Resolve l_1_2_3_CC: algebra.
*)
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_mult_conj.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_mult_conj.con" as lemma.
(* UNEXPORTED
Hint Resolve CC_conj_mult: algebra.
(* begin hide *)
-inline procedural "cic:/CoRN/complex/AbsCC/l_2_1_2.con".
+inline procedural "cic:/CoRN/complex/AbsCC/l_2_1_2.con" as lemma.
(* UNEXPORTED
Hint Resolve l_2_1_2: algebra.
(* end hide *)
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_mult_square.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_mult_square.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_square_ap_zero.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_square_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/cc_recip_char.con".
+inline procedural "cic:/CoRN/complex/AbsCC/cc_recip_char.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_strext.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_strext.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsSmallCC.con".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsSmallCC.con" as definition.
-inline procedural "cic:/CoRN/complex/AbsCC/Cexis_AFS_CC.con".
+inline procedural "cic:/CoRN/complex/AbsCC/Cexis_AFS_CC.con" as lemma.
(* The following lemmas are just auxiliary results *)
(* begin hide *)
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_1_2.con" "AbsCC_properties__".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_1_2.con" "AbsCC_properties__" as definition.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_2_3.con" "AbsCC_properties__".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_2_3.con" "AbsCC_properties__" as definition.
-inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_3_4.con" "AbsCC_properties__".
+inline procedural "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_3_4.con" "AbsCC_properties__" as definition.
(* end hide *)
(*#* ** The triangle inequality *)
-inline procedural "cic:/CoRN/complex/AbsCC/triangle.con".
+inline procedural "cic:/CoRN/complex/AbsCC/triangle.con" as lemma.
-inline procedural "cic:/CoRN/complex/AbsCC/triangle_Sum.con".
+inline procedural "cic:/CoRN/complex/AbsCC/triangle_Sum.con" as lemma.
inline procedural "cic:/CoRN/complex/CComplex/CC_set.ind".
-inline procedural "cic:/CoRN/complex/CComplex/cc_ap.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_ap.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_eq.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_eq.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_is_CSetoid.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_is_CSetoid.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_csetoid.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_csetoid.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_plus.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_plus.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_mult.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_mult.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_zero.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_zero.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_one.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_one.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_i.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_i.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_inv.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_inv.con" as definition.
(* not needed anymore
Lemma cc_plus_op_proof : (bin_op_wd cc_csetoid cc_plus).
Qed.
*)
-inline procedural "cic:/CoRN/complex/CComplex/cc_inv_strext.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_inv_strext.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_plus_strext.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_plus_strext.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_mult_strext.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_mult_strext.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_inv_op.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_inv_op.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_plus_op.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_plus_op.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_mult_op.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_mult_op.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_csg_associative.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_csg_associative.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cr_mult_associative.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cr_mult_associative.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_csemi_grp.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_csemi_grp.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cm_proof.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cm_proof.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cmonoid.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cmonoid.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cg_proof.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cg_proof.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cr_dist.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cr_dist.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cr_non_triv.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cr_non_triv.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cgroup.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cgroup.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cabgroup.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cabgroup.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cr_mult_mon.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cr_mult_mon.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_mult_commutes.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_mult_commutes.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_isCRing.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_isCRing.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cring.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cring.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_ap_zero.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_inv_aid.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_inv_aid.con" as lemma.
(*#*
If [x [~=] Zero] or [y [~=] Zero], then [x [/] x[^]2 [+] y[^]2 [~=] Zero] or
[[--]y[/]x[^]2[+]y[^]2 [~=] Zero].
*)
-inline procedural "cic:/CoRN/complex/CComplex/cc_inv_aid2.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_inv_aid2.con" as lemma.
(*
REMARK KEPT FOR SENTIMENTAL REASONS...
actual function.
*)
-inline procedural "cic:/CoRN/complex/CComplex/cc_recip.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_recip.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_cfield_proof.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cfield_proof.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_Recip_proof.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_Recip_proof.con" as lemma.
(* UNEXPORTED
Opaque cc_recip.
Opaque cc_inv.
*)
-inline procedural "cic:/CoRN/complex/CComplex/cc_cfield.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_cfield.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/CC.con".
+inline procedural "cic:/CoRN/complex/CComplex/CC.con" as definition.
(*#*
Maps from reals to complex and vice-versa are defined, as well as conjugate,
absolute value and the imaginary unit [I] *)
-inline procedural "cic:/CoRN/complex/CComplex/cc_set_CC.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_set_CC.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/CC_conj.con".
+inline procedural "cic:/CoRN/complex/CComplex/CC_conj.con" as definition.
(* 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 procedural "cic:/CoRN/complex/CComplex/AbsCC.con".
+inline procedural "cic:/CoRN/complex/CComplex/AbsCC.con" as definition.
-inline procedural "cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con".
+inline procedural "cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con" as lemma.
(* UNEXPORTED
End Complex_Numbers
(* end hide *)
-inline procedural "cic:/CoRN/complex/CComplex/II.con".
+inline procedural "cic:/CoRN/complex/CComplex/II.con" as definition.
(* NOTATION
Infix "[+I*]" := cc_set_CC (at level 48, no associativity).
Section I_properties
*)
-inline procedural "cic:/CoRN/complex/CComplex/I_square.con".
+inline procedural "cic:/CoRN/complex/CComplex/I_square.con" as lemma.
(* UNEXPORTED
Hint Resolve I_square: algebra.
*)
-inline procedural "cic:/CoRN/complex/CComplex/I_square'.con".
+inline procedural "cic:/CoRN/complex/CComplex/I_square'.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/I_recip_lft.con".
+inline procedural "cic:/CoRN/complex/CComplex/I_recip_lft.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/I_recip_rht.con".
+inline procedural "cic:/CoRN/complex/CComplex/I_recip_rht.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/mult_I.con".
+inline procedural "cic:/CoRN/complex/CComplex/mult_I.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/I_wd.con".
+inline procedural "cic:/CoRN/complex/CComplex/I_wd.con" as lemma.
(*#* ** Properties of [Re] and [Im] *)
-inline procedural "cic:/CoRN/complex/CComplex/calculate_norm.con".
+inline procedural "cic:/CoRN/complex/CComplex/calculate_norm.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/calculate_Re.con".
+inline procedural "cic:/CoRN/complex/CComplex/calculate_Re.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/calculate_Im.con".
+inline procedural "cic:/CoRN/complex/CComplex/calculate_Im.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/Re_wd.con".
+inline procedural "cic:/CoRN/complex/CComplex/Re_wd.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/Im_wd.con".
+inline procedural "cic:/CoRN/complex/CComplex/Im_wd.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/Re_resp_plus.con".
+inline procedural "cic:/CoRN/complex/CComplex/Re_resp_plus.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/Re_resp_inv.con".
+inline procedural "cic:/CoRN/complex/CComplex/Re_resp_inv.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/Im_resp_plus.con".
+inline procedural "cic:/CoRN/complex/CComplex/Im_resp_plus.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/Im_resp_inv.con".
+inline procedural "cic:/CoRN/complex/CComplex/Im_resp_inv.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_calculate_square.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_calculate_square.con" as lemma.
(* UNEXPORTED
End I_properties
Section Conj_properties
*)
-inline procedural "cic:/CoRN/complex/CComplex/CC_conj_plus.con".
+inline procedural "cic:/CoRN/complex/CComplex/CC_conj_plus.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/CC_conj_mult.con".
+inline procedural "cic:/CoRN/complex/CComplex/CC_conj_mult.con" as lemma.
(* UNEXPORTED
Hint Resolve CC_conj_mult: algebra.
*)
-inline procedural "cic:/CoRN/complex/CComplex/CC_conj_strext.con".
+inline procedural "cic:/CoRN/complex/CComplex/CC_conj_strext.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/CC_conj_conj.con".
+inline procedural "cic:/CoRN/complex/CComplex/CC_conj_conj.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/CC_conj_zero.con".
+inline procedural "cic:/CoRN/complex/CComplex/CC_conj_zero.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/CC_conj_one.con".
+inline procedural "cic:/CoRN/complex/CComplex/CC_conj_one.con" as lemma.
(* UNEXPORTED
Hint Resolve CC_conj_one: algebra.
*)
-inline procedural "cic:/CoRN/complex/CComplex/CC_conj_nexp.con".
+inline procedural "cic:/CoRN/complex/CComplex/CC_conj_nexp.con" as lemma.
(* UNEXPORTED
End Conj_properties
Section cc_IR_properties
*)
-inline procedural "cic:/CoRN/complex/CComplex/Re_cc_IR.con".
+inline procedural "cic:/CoRN/complex/CComplex/Re_cc_IR.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/Im_cc_IR.con".
+inline procedural "cic:/CoRN/complex/CComplex/Im_cc_IR.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_wd.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_wd.con" as lemma.
(* UNEXPORTED
Hint Resolve cc_IR_wd: algebra_c.
*)
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_resp_ap.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_resp_ap.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult.con" as lemma.
(* UNEXPORTED
Hint Resolve cc_IR_mult: algebra.
*)
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult_lft.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult_lft.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult_rht.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_mult_rht.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_plus.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_plus.con" as lemma.
(* UNEXPORTED
Hint Resolve cc_IR_plus: algebra.
*)
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_minus.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_minus.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_zero.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_zero.con" as lemma.
(* UNEXPORTED
Hint Resolve cc_IR_zero: algebra.
*)
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_one.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_one.con" as lemma.
(* UNEXPORTED
Hint Resolve cc_IR_one: algebra.
*)
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_nring.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_nring.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/cc_IR_nexp.con".
+inline procedural "cic:/CoRN/complex/CComplex/cc_IR_nexp.con" as lemma.
(* UNEXPORTED
End cc_IR_properties
include "tactics/Transparent_algebra.ma".
-inline procedural "cic:/CoRN/complex/CComplex/char0_CC.con".
+inline procedural "cic:/CoRN/complex/CComplex/char0_CC.con" as lemma.
include "tactics/Opaque_algebra.ma".
-inline procedural "cic:/CoRN/complex/CComplex/poly_apzero_CC.con".
+inline procedural "cic:/CoRN/complex/CComplex/poly_apzero_CC.con" as lemma.
-inline procedural "cic:/CoRN/complex/CComplex/poly_CC_extensional.con".
+inline procedural "cic:/CoRN/complex/CComplex/poly_CC_extensional.con" as lemma.
(*#* ** The Complex Exponential *)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC.con" as definition.
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_wd.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_wd.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_1.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_1.con" as lemma.
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_2.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_2.con" as lemma.
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_3.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_3.con" as lemma.
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_4.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_equation_aid_4.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_plus.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_plus.con" as lemma.
(* UNEXPORTED
Hint Resolve ExpCC_plus: algebra.
*)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Zero.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Zero.con" as lemma.
(* UNEXPORTED
Hint Resolve ExpCC_Zero: algebra.
*)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv_aid.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv_aid.con" as lemma.
(* UNEXPORTED
Hint Resolve ExpCC_inv_aid: algebra.
*)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_ap_zero.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve ExpCC_inv: algebra.
*)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_pow.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_pow.con" as lemma.
(* UNEXPORTED
Hint Resolve ExpCC_pow: algebra.
*)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/AbsCC_ExpCC.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/AbsCC_ExpCC.con" as lemma.
(* UNEXPORTED
Hint Resolve AbsCC_ExpCC: algebra.
*)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Periodic.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Periodic.con" as lemma.
(* UNEXPORTED
Hint Resolve ExpCC_Periodic: algebra.
*)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Exp.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/ExpCC_Exp.con" as lemma.
(* UNEXPORTED
Hint Resolve ExpCC_Exp: algebra.
Opaque Sin Cos Exp.
*)
-inline procedural "cic:/CoRN/complex/Complex_Exponential/Euler.con".
+inline procedural "cic:/CoRN/complex/Complex_Exponential/Euler.con" as theorem.
Section CC_ap_zero
*)
-inline procedural "cic:/CoRN/complex/NRootCC/cc_ap_zero.con".
+inline procedural "cic:/CoRN/complex/NRootCC/cc_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/C_cc_ap_zero.con".
+inline procedural "cic:/CoRN/complex/NRootCC/C_cc_ap_zero.con" as lemma.
(* UNEXPORTED
End CC_ap_zero
Section Imag_to_Real
*)
-inline procedural "cic:/CoRN/complex/NRootCC/imag_to_real.con".
+inline procedural "cic:/CoRN/complex/NRootCC/imag_to_real.con" as lemma.
(* UNEXPORTED
End Imag_to_Real
Section NRootI
*)
-inline procedural "cic:/CoRN/complex/NRootCC/sqrt_Half.con".
+inline procedural "cic:/CoRN/complex/NRootCC/sqrt_Half.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/sqrt_I.con".
+inline procedural "cic:/CoRN/complex/NRootCC/sqrt_I.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/sqrt_I_nexp.con".
+inline procedural "cic:/CoRN/complex/NRootCC/sqrt_I_nexp.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nroot_I_nexp_aux.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nroot_I_nexp_aux.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nroot_I.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nroot_I.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/nroot_I_nexp.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nroot_I_nexp.con" as lemma.
(* UNEXPORTED
Hint Resolve nroot_I_nexp: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nroot_minus_I.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nroot_minus_I.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/nroot_minus_I_nexp.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nroot_minus_I_nexp.con" as lemma.
(* UNEXPORTED
End NRootI
(* begin hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c2.con" "NRootCC_1__NRootCC_1_ap_real__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c2.con" "NRootCC_1__NRootCC_1_ap_real__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_c2pos.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_c2pos.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c.con" "NRootCC_1__NRootCC_1_ap_real__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c.con" "NRootCC_1__NRootCC_1_ap_real__" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'2.con" "NRootCC_1__NRootCC_1_ap_real__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'2.con" "NRootCC_1__NRootCC_1_ap_real__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a'2pos.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a'2pos.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'.con" "NRootCC_1__NRootCC_1_ap_real__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'.con" "NRootCC_1__NRootCC_1_ap_real__" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'2.con" "NRootCC_1__NRootCC_1_ap_real__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'2.con" "NRootCC_1__NRootCC_1_ap_real__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_b'2pos.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_b'2pos.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'.con" "NRootCC_1__NRootCC_1_ap_real__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'.con" "NRootCC_1__NRootCC_1_ap_real__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a3.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a3.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a4.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a4.con" as lemma.
(* UNEXPORTED
Hint Resolve nrCC1_a4: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a5.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a5.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a6.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a6.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a6'.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a6'.con" as lemma.
(* UNEXPORTED
Hint Resolve nrCC1_a5: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a7_upper.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a7_upper.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a7_lower.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC1_a7_lower.con" as lemma.
(* UNEXPORTED
Hint Resolve nrCC1_a3 nrCC1_a7_upper nrCC1_a7_lower: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_upper.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_upper.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_lower.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_lower.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_real.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_real.con" as lemma.
(* UNEXPORTED
End NRootCC_1_ap_real
(* begin hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/c'.con" "NRootCC_1__NRootCC_1_ap_imag__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/c'.con" "NRootCC_1__NRootCC_1_ap_imag__" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a'.con" "NRootCC_1__NRootCC_1_ap_imag__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a'.con" "NRootCC_1__NRootCC_1_ap_imag__" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b'.con" "NRootCC_1__NRootCC_1_ap_imag__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b'.con" "NRootCC_1__NRootCC_1_ap_imag__" as definition.
(* end hide *)
Hint Resolve sqrt_I_nexp: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_imag.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_imag.con" as lemma.
(* UNEXPORTED
End NRootCC_1_ap_imag
(*#* We now define the roots of arbitrary non zero complex numbers. *)
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_1.con" as lemma.
(* UNEXPORTED
End NRootCC_1
alias id "c_" = "cic:/CoRN/complex/NRootCC/NRootCC_2/c_.var".
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2'.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2'.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2.con" as lemma.
(* UNEXPORTED
End NRootCC_2
Section NRootCC_3
*)
-inline procedural "cic:/CoRN/complex/NRootCC/Im_poly.con".
+inline procedural "cic:/CoRN/complex/NRootCC/Im_poly.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a1.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a1.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a2.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a2.con" as lemma.
(*#*
%\begin{convention}% Let [a,b : IR], [b_ : (b [#] Zero)] and [n : nat].
alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_3/n.var".
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly''.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly''.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a3.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a3.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a4.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a4.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a5.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a5.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a6.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a6.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly'.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly'.con" as definition.
(* UNEXPORTED
Hint Resolve nrCC3_a3: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a7.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a7.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a8.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a8.con" as lemma.
(* UNEXPORTED
Hint Resolve nth_coeff_p_mult_c_: algebra.
Hint Resolve nrCC3_a6: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a9.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_a9.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_poly.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_poly.con" as definition.
(* UNEXPORTED
Hint Resolve nrCC3_a1 nrCC3_a7: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_.con" as lemma.
(* UNEXPORTED
Hint Resolve nrootCC_3_: algebra.
Hint Resolve calculate_Im: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3.con" as lemma.
(* UNEXPORTED
Hint Resolve nrCC3_a2: algebra.
Hint Resolve nrCC3_a9: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_degree.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3_degree.con" as lemma.
(* UNEXPORTED
End NRootCC_3
alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_3'/n_.var".
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_degree.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_degree.con" as lemma.
(* UNEXPORTED
End NRootCC_3'
(* begin hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/c.con" "NRootCC_4__NRootCC_4_ap_real__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/c.con" "NRootCC_4__NRootCC_4_ap_real__" as definition.
(* end hide *)
Hint Resolve nrootCC_3: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a1.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a1.con" as lemma.
(*#*
%\begin{convention}% Let [r2',c2 : IR] and [r2'_ : (r2' [#] Zero)].
Hint Resolve nrootCC_3': algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a1'.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a1'.con" as lemma.
(* UNEXPORTED
End NRootCC_4_solutions
alias id "y2_property" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2_property.var".
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a2.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a2.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a3.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a3.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a4.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a4.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_y.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_y.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_x.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_x.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/x.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/x.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a5.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a5.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a6.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a6.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_z.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_z.con" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/z.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/z.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a7.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a7.con" as lemma.
(* UNEXPORTED
Hint Resolve nrCC4_a6: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a8.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a8.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a9.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a9.con" as lemma.
(* UNEXPORTED
End NRootCC_4_equations
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a10.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC4_a10.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real.con" as lemma.
(* UNEXPORTED
End NRootCC_4_ap_real
(* begin hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/c'.con" "NRootCC_4__NRootCC_4_ap_imag__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/c'.con" "NRootCC_4__NRootCC_4_ap_imag__" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a'.con" "NRootCC_4__NRootCC_4_ap_imag__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a'.con" "NRootCC_4__NRootCC_4_ap_imag__" as definition.
-inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b'.con" "NRootCC_4__NRootCC_4_ap_imag__".
+inline procedural "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b'.con" "NRootCC_4__NRootCC_4_ap_imag__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real'.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real'.con" as lemma.
(* UNEXPORTED
Hint Resolve nroot_minus_I_nexp: algebra.
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_imag.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_imag.con" as lemma.
(* UNEXPORTED
End NRootCC_4_ap_imag
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_4.con" as lemma.
(* UNEXPORTED
End NRootCC_4
Section NRootCC_5
*)
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a2.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a2.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a3.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a3.con" as lemma.
(* UNEXPORTED
Hint Resolve nrCC_5a3: algebra.
alias id "c_" = "cic:/CoRN/complex/NRootCC/NRootCC_5/c_.var".
-inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a4.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a4.con" as lemma.
-inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_5.con".
+inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_5.con" as lemma.
(* UNEXPORTED
End NRootCC_5
(*#* Final definition *)
-inline procedural "cic:/CoRN/complex/NRootCC/CnrootCC.con".
+inline procedural "cic:/CoRN/complex/NRootCC/CnrootCC.con" as definition.
(* Remark blz 65 1 *)
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation.con" as definition.
include "model/setoids/Zsetoid.ma".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation_Z_0.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_nullary_operation_Z_0.con" as lemma.
(* Remark blz 65 2 *)
include "devel/loeb/per/csetfun.ma".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/n_ary_operation.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/n_ary_operation.con" as definition.
include "model/setoids/Nsetoid.ma".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus1.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus1.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus1_strext.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus1_strext.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus2.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus2.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus2_strext.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_plus2_strext.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus3.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/plus3.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/on.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/on.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con" "__".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con" "__" as definition.
(* blz 65 Example 1 *)
include "model/semigroups/Zsemigroup.ma".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Zplus_is_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Zplus_is_CSemiGroup.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Zmult_is_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Zmult_is_CSemiGroup.con" as lemma.
(* blz 66 Example % 3 *)
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/FS_is_CSemiGroup.con" as lemma.
(* blz 66 Example % 4 *)
alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2b4/A.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/empty_word.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/empty_word.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_irreflexive.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_symmetric.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_cotransitive.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_cotransitive.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_tight.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ap_fm_tight.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_is_CSetoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_is_CSetoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_as_csetoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_csetoid_as_csetoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app_strext.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app_strext.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app_as_csb_fun.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/app_as_csb_fun.con" as definition.
include "algebra/CSemiGroups.ma".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm_reflexive.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/eq_fm_reflexive.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_is_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_is_CSemiGroup.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_as_CSemiGroup.con" as definition.
(* UNEXPORTED
End p66E2b4
(* Definition 5 *)
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit.con" as definition.
(* blz 67 Remark 1 *)
include "model/monoids/Zmonoid.ma".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Z_0.con" as lemma.
(* blz 67 Remark 2 *)
alias id "X" = "cic:/CoRN/devel/loeb/IDA/Ch6/p67R2/X.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con" as lemma.
(* UNEXPORTED
End p67R2
(* blz 67 Remark 3 *)
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Astar_empty_word.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_Astar_empty_word.con" as lemma.
(* Lemma 6 *)
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/unique_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/unique_unit.con" as lemma.
(* blz 67 Example 1 *)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1.ind".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_irreflexive.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_symmetric.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_cotransitive.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_cotransitive.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq_dec.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_eq_dec.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_e1.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_e1.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_M1_eq_e1_u.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_M1_eq_e1_u.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_tight.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_ap_tight.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSetoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSetoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSetoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSetoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult_strext.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_CS_mult_strext.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult_as_bin_fun.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_mult_as_bin_fun.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CSemiGroup.con" as lemma.
include "algebra/CMonoids.ma".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CSemiGroup.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_as_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult_strext.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_CS_mult_strext.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult_as_bin_fun.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_mult_as_bin_fun.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CSemiGroup.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CSemiGroup.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit_M2.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_lft_unit_M2.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit_M2.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1_is_rht_unit_M2.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M2_as_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/two_element_CMonoids.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/two_element_CMonoids.con" as lemma.
(* UNEXPORTED
End p68E1b1
alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M2.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_strext.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_strext.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_as_csb_fun.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod_as_csb_fun.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CSemiGroup.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CSemiGroup.con" as definition.
(* UNEXPORTED
End D9S
alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M2.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_lft_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CMonoid.con" as definition.
(* UNEXPORTED
End D9M
Section p69E1
*)
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/PM1M2.con" "p69E1__".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/PM1M2.con" "p69E1__" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/uu.con" "p69E1__".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/uu.con" "p69E1__" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/e1u.con" "p69E1__".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/e1u.con" "p69E1__" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ex_69.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ex_69.con" as lemma.
(* UNEXPORTED
End p69E1
alias id "op_pres_C" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/op_pres_C.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_K.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_K.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K_is_Monoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K_is_Monoid.con" as definition.
(* UNEXPORTED
End Th11
alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th12/A.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_lft_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_is_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_as_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_as_CMonoid.con" as definition.
(* UNEXPORTED
End Th12
include "devel/loeb/per/lst2fun.ma".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p70text/A.con" "p70text__".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p70text/A.con" "p70text__" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ZerolessOne.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/ZerolessOne.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'_strext.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word'_strext.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_as_CSetoid_fun.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_as_CSetoid_fun.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_bijective.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/to_word_bijective.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/pres_plus_to_word.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/pres_plus_to_word.con" as lemma.
(* UNEXPORTED
End p70text
alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M2.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphism.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphism.con" as definition.
(* UNEXPORTED
End Th13
alias id "c" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/c.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid_CSetoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid_CSetoid.con" as definition.
alias id "is_generated_by" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/is_generated_by.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/f.con" "p71E1__".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/f.con" "p71E1__" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/surjective_f.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/surjective_f.con" as lemma.
(* UNEXPORTED
End p71E1
Section p71E1'
*)
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_injective_f.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_injective_f.con" as lemma.
(* UNEXPORTED
End p71E1'
alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/A.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/L.con" "p71E2__".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/L.con" "p71E2__" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_strext.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_strext.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_as_CSetoid_fun.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_as_CSetoid_fun.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_is_morphism.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/L_is_morphism.con" as lemma.
(* UNEXPORTED
End p71E2
alias id "S2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S2.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con" as definition.
(* UNEXPORTED
End p71R1
alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R2/M.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con" as definition.
(* UNEXPORTED
End p71R2
alias id "isof" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/isof.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_inv.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_inv.con" as lemma.
(* UNEXPORTED
End Th14
Section p71E2b1
*)
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_isomorphic_M1_M2.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/not_isomorphic_M1_M2.con" as lemma.
(* UNEXPORTED
End p71E2b1
alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M2.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/f.con" "p71E2b2__".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/f.con" "p71E2b2__" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext'.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext'.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun'.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/f_as_CSetoid_fun'.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic_PM1M2_PM2M1.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic_PM1M2_PM2M1.con" as lemma.
(* UNEXPORTED
End p71E2b2
alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/M.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum.con" as definition.
alias id "D" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/D.var".
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member.con" as definition.
(* UNEXPORTED
Implicit Arguments member [A].
*)
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_unit.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member_app.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member_app.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum_app.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum_app.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_Dbrack.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_Dbrack.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_as_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_as_CMonoid.con" as definition.
(* UNEXPORTED
End Th15
include "algebra/CSetoidFun.ma".
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/ap_fun.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/ap_fun.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/eq_fun.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/eq_fun.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/irrefl_apfun.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/irrefl_apfun.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/cotrans_apfun.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/cotrans_apfun.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/ta_apfun.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/ta_apfun.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/sym_apfun.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/sym_apfun.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CSetoid.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CSetoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSetoid.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSetoid.con" as definition.
(* UNEXPORTED
Print associative.
*)
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/comp.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/comp.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/comp_as_bin_op.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/comp_as_bin_op.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/assoc_comp.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/assoc_comp.con" as lemma.
include "algebra/CSemiGroups.ma".
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CSemiGroup.con" as definition.
include "algebra/CMonoids.ma".
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_id.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_id.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/id_is_rht_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/id_is_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/id_is_lft_unit.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/id_is_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/FS_as_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CMonoid.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CMonoid.con" as definition.
include "algebra/CGroups.ma".
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/Inv_is_bij.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/Inv_is_bij.con" as lemma.
(* Lemma Inv_is_bij :
forall (A B : CSetoid) (f : CSetoid_fun A B) (H : bijective f),
intuition.
Qed.*)
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_Inv.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_Inv.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/Inv_as_un_op.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/Inv_as_un_op.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_is_CGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_is_CGroup.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CGroup.con".
+inline procedural "cic:/CoRN/devel/loeb/per/csetfun/PS_as_CGroup.con" as definition.
(* In het algemeen niet Abels! *)
include "CoRN.ma".
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/F'.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/F'.con" as definition.
inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/F.ind".
cic:/matita/CoRN-Procedural/devel/loeb/per/lst2fun/F_crr.con
*)
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/to_nat.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/to_nat.con" as definition.
(* UNEXPORTED
Implicit Arguments to_nat [n].
include "algebra/CSetoids.ma".
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Feq.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Feq.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_irreflexive.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_symmetric.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_cotransitive.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_cotransitive.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_tight.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/Fap_tight.con" as lemma.
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/less.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/less.con" as definition.
-inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/CSetoid_of_less.con".
+inline procedural "cic:/CoRN/devel/loeb/per/lst2fun/CSetoid_of_less.con" as definition.
Hint Resolve AbsIR_sqrt_sqr: algebra.
*)
-inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_re.con".
+inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_re.con" as lemma.
-inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_im.con".
+inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_im.con" as lemma.
-inline procedural "cic:/CoRN/fta/CC_Props/seq_re.con".
+inline procedural "cic:/CoRN/fta/CC_Props/seq_re.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/seq_im.con".
+inline procedural "cic:/CoRN/fta/CC_Props/seq_im.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy_prop.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy_prop.con" as definition.
inline procedural "cic:/CoRN/fta/CC_Props/CC_CauchySeq.ind".
cic:/matita/CoRN-Procedural/fta/CC_Props/CC_seq.con
*)
-inline procedural "cic:/CoRN/fta/CC_Props/re_is_Cauchy.con".
+inline procedural "cic:/CoRN/fta/CC_Props/re_is_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/fta/CC_Props/im_is_Cauchy.con".
+inline procedural "cic:/CoRN/fta/CC_Props/im_is_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2re.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2re.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2im.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2im.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/LimCC.con".
+inline procedural "cic:/CoRN/fta/CC_Props/LimCC.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_sqr.con".
+inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_sqr.con" as lemma.
-inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_AbsCC.con".
+inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_AbsCC.con" as lemma.
-inline procedural "cic:/CoRN/fta/CC_Props/LimCC_is_lim.con".
+inline procedural "cic:/CoRN/fta/CC_Props/LimCC_is_lim.con" as lemma.
-inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_uniq.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_uniq.con" as lemma.
-inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con" as lemma.
(*#* ** Continuity for [CC]
*)
(* (CSetoid_un_op CC). *)
-inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/CCcontinAt.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CCcontinAt.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/CCcontin.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CCcontin.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim_SeqLimit.con".
+inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim_SeqLimit.con" as lemma.
-inline procedural "cic:/CoRN/fta/CC_Props/f_seq.con".
+inline procedural "cic:/CoRN/fta/CC_Props/f_seq.con" as definition.
-inline procedural "cic:/CoRN/fta/CC_Props/poly_pres_lim.con".
+inline procedural "cic:/CoRN/fta/CC_Props/poly_pres_lim.con" as lemma.
(* UNEXPORTED
End Continuity_for_CC
*)
-inline procedural "cic:/CoRN/fta/CC_Props/seq_yields_zero.con".
+inline procedural "cic:/CoRN/fta/CC_Props/seq_yields_zero.con" as lemma.
Section Mult_CC_Continuous
*)
-inline procedural "cic:/CoRN/fta/CPoly_Contin1/mult_absCC.con".
+inline procedural "cic:/CoRN/fta/CPoly_Contin1/mult_absCC.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Contin1/estimate_absCC.con".
+inline procedural "cic:/CoRN/fta/CPoly_Contin1/estimate_absCC.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Contin1/mult_CC_contin.con".
+inline procedural "cic:/CoRN/fta/CPoly_Contin1/mult_CC_contin.con" as lemma.
(* UNEXPORTED
End Mult_CC_Continuous
alias id "g" = "cic:/CoRN/fta/CPoly_Contin1/CPoly_CC_Continuous/g.var".
-inline procedural "cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con".
+inline procedural "cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Contin1/contin_polyCC.con".
+inline procedural "cic:/CoRN/fta/CPoly_Contin1/contin_polyCC.con" as lemma.
(* UNEXPORTED
End CPoly_CC_Continuous
(* begin hide *)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Monomials/RX.con" "Monomials__".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Monomials/RX.con" "Monomials__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/monom.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/monom.con" as definition.
-inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff'.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_coeff'.con" as lemma.
(* UNEXPORTED
Hint Resolve monom_coeff monom_coeff': algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_degree.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_degree.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_S.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_S.con" as lemma.
(* UNEXPORTED
Hint Resolve monom_S: algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_wd_lft.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_wd_lft.con" as lemma.
(* UNEXPORTED
Hint Resolve monom_wd_lft: algebra_c.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult'.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult'.con" as lemma.
(* UNEXPORTED
Hint Resolve monom_mult': algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_mult.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_sum.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/monom_sum.con" as lemma.
(* UNEXPORTED
End Monomials
(* begin hide *)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/RX.con" "Poly_Reverse__".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/RX.con" "Poly_Reverse__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev.con" as definition.
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff'.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_coeff'.con" as lemma.
(* UNEXPORTED
Hint Resolve Rev_coeff Rev_coeff': algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_wd.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_wd.con" as lemma.
(* UNEXPORTED
Hint Resolve Rev_wd: algebra_c.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_rev.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_rev.con" as lemma.
(* UNEXPORTED
Hint Resolve Rev_rev: algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree_le.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree_le.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_degree.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_monom.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_monom.con" as lemma.
(* UNEXPORTED
Hint Resolve Rev_monom: algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_zero.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_zero.con" as lemma.
(* UNEXPORTED
Hint Resolve Rev_zero: algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_plus.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_plus.con" as lemma.
(* UNEXPORTED
Hint Resolve Rev_plus: algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_minus.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_minus.con" as lemma.
(* UNEXPORTED
Hint Resolve Rev_minus: algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum0.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum0.con" as lemma.
(* UNEXPORTED
Hint Resolve Rev_sum0: algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_sum.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_mult.con".
+inline procedural "cic:/CoRN/fta/CPoly_Rev/Rev_mult.con" as lemma.
(* UNEXPORTED
End Poly_Reverse
Section Poly_Shifted
*)
-inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift.con".
+inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift.con" as definition.
-inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_apply.con".
+inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_apply.con" as lemma.
(* UNEXPORTED
Hint Resolve Shift_apply: algebra.
*)
-inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_wdr.con".
+inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_wdr.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_shift.con".
+inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_shift.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_mult.con".
+inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_mult.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_degree_le.con".
+inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_degree_le.con" as lemma.
-inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_monic.con".
+inline procedural "cic:/CoRN/fta/CPoly_Shift/Shift_monic.con" as lemma.
(* UNEXPORTED
End Poly_Shifted
alias id "f_degree" = "cic:/CoRN/fta/FTA/FTA_reg'/f_degree.var".
-inline procedural "cic:/CoRN/fta/FTA/FTA_reg'.con".
+inline procedural "cic:/CoRN/fta/FTA/FTA_reg'.con" as lemma.
(* UNEXPORTED
End FTA_reg'
alias id "f_c" = "cic:/CoRN/fta/FTA/FTA_1/f_c.var".
-inline procedural "cic:/CoRN/fta/FTA/FTA_1a.con".
+inline procedural "cic:/CoRN/fta/FTA/FTA_1a.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTA/FTA_1/g.con" "FTA_1__".
+inline procedural "cic:/CoRN/fta/FTA/FTA_1/g.con" "FTA_1__" as definition.
-inline procedural "cic:/CoRN/fta/FTA/FTA_1b.con".
+inline procedural "cic:/CoRN/fta/FTA/FTA_1b.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTA/FTA_1.con".
+inline procedural "cic:/CoRN/fta/FTA/FTA_1.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTA/FTA_1'.con".
+inline procedural "cic:/CoRN/fta/FTA/FTA_1'.con" as lemma.
(* UNEXPORTED
End FTA_1
Section Fund_Thm_Alg
*)
-inline procedural "cic:/CoRN/fta/FTA/FTA'.con".
+inline procedural "cic:/CoRN/fta/FTA/FTA'.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTA/FTA.con".
+inline procedural "cic:/CoRN/fta/FTA/FTA.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTA/FTA_a_la_Henk.con".
+inline procedural "cic:/CoRN/fta/FTA/FTA_a_la_Henk.con" as lemma.
(* UNEXPORTED
End Fund_Thm_Alg
cic:/matita/CoRN-Procedural/fta/FTAreg/Kntup.con
*)
-inline procedural "cic:/CoRN/fta/FTAreg/Knes_fun.con".
+inline procedural "cic:/CoRN/fta/FTAreg/Knes_fun.con" as definition.
-inline procedural "cic:/CoRN/fta/FTAreg/Knes_fun_it.con".
+inline procedural "cic:/CoRN/fta/FTAreg/Knes_fun_it.con" as definition.
-inline procedural "cic:/CoRN/fta/FTAreg/sK.con".
+inline procedural "cic:/CoRN/fta/FTAreg/sK.con" as definition.
-inline procedural "cic:/CoRN/fta/FTAreg/sK_c.con".
+inline procedural "cic:/CoRN/fta/FTAreg/sK_c.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/sK_c0.con".
+inline procedural "cic:/CoRN/fta/FTAreg/sK_c0.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/sK_prop1.con".
+inline procedural "cic:/CoRN/fta/FTAreg/sK_prop1.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/sK_it.con".
+inline procedural "cic:/CoRN/fta/FTAreg/sK_it.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/sK_prop2.con".
+inline procedural "cic:/CoRN/fta/FTAreg/sK_prop2.con" as lemma.
(* UNEXPORTED
End Kneser_Sequence
(*#* **Main results
*)
-inline procedural "cic:/CoRN/fta/FTAreg/seq_exists.con".
+inline procedural "cic:/CoRN/fta/FTAreg/seq_exists.con" as lemma.
(* UNEXPORTED
End Seq_Exists_Main
(* begin hide *)
-inline procedural "cic:/CoRN/fta/FTAreg/N_Exists/q_.con" "N_Exists__".
+inline procedural "cic:/CoRN/fta/FTAreg/N_Exists/q_.con" "N_Exists__" as definition.
(* end hide *)
alias id "zlte" = "cic:/CoRN/fta/FTAreg/N_Exists/zlte.var".
-inline procedural "cic:/CoRN/fta/FTAreg/N_exists.con".
+inline procedural "cic:/CoRN/fta/FTAreg/N_exists.con" as lemma.
(* UNEXPORTED
End N_Exists
(* begin hide *)
-inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q_.con" "Seq_is_CC_CAuchy__".
+inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q_.con" "Seq_is_CC_CAuchy__" as definition.
-inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq.con" "Seq_is_CC_CAuchy__".
+inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq.con" "Seq_is_CC_CAuchy__" as definition.
-inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtc.con" "Seq_is_CC_CAuchy__".
+inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtc.con" "Seq_is_CC_CAuchy__" as definition.
-inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtqlt1.con" "Seq_is_CC_CAuchy__".
+inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtqlt1.con" "Seq_is_CC_CAuchy__" as definition.
-inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq_.con" "Seq_is_CC_CAuchy__".
+inline procedural "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq_.con" "Seq_is_CC_CAuchy__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/fta/FTAreg/zlt_nrtq.con".
+inline procedural "cic:/CoRN/fta/FTAreg/zlt_nrtq.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/zlt_nrtc.con".
+inline procedural "cic:/CoRN/fta/FTAreg/zlt_nrtc.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/nrt_pow.con".
+inline procedural "cic:/CoRN/fta/FTAreg/nrt_pow.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/abs_pow_ltRe.con".
+inline procedural "cic:/CoRN/fta/FTAreg/abs_pow_ltRe.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/abs_pow_ltIm.con".
+inline procedural "cic:/CoRN/fta/FTAreg/abs_pow_ltIm.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/SublemmaRe.con".
+inline procedural "cic:/CoRN/fta/FTAreg/SublemmaRe.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/SublemmaIm.con".
+inline procedural "cic:/CoRN/fta/FTAreg/SublemmaIm.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/seq_is_CC_Cauchy.con".
+inline procedural "cic:/CoRN/fta/FTAreg/seq_is_CC_Cauchy.con" as lemma.
(* UNEXPORTED
End Seq_is_CC_CAuchy
*)
-inline procedural "cic:/CoRN/fta/FTAreg/FTA_monic.con".
+inline procedural "cic:/CoRN/fta/FTAreg/FTA_monic.con" as lemma.
-inline procedural "cic:/CoRN/fta/FTAreg/FTA_reg.con".
+inline procedural "cic:/CoRN/fta/FTAreg/FTA_reg.con" as lemma.
alias id "eps_le_a_0" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_le_a_0.var".
-inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_fuzz.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_fuzz.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/lem_1a.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/lem_1a.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/lem_1b.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/lem_1b.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/lem_1c.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/lem_1c.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/lem_1.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/lem_1.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m.con" as definition.
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_pos.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_pos.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_S.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_S.con" as lemma.
(* UNEXPORTED
Hint Resolve p3m_S: algebra.
*)
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_P.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_P.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_aux.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_aux.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_pow.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_pow.con" as lemma.
(* UNEXPORTED
Hint Resolve p3m_aux: algebra.
*)
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_0.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_0.con" as lemma.
(* UNEXPORTED
Hint Resolve p3m_0: algebra.
*)
-inline procedural "cic:/CoRN/fta/KeyLemma/third_pos.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/third_pos.con" as lemma.
(* UNEXPORTED
Hint Resolve third_pos: algebra.
*)
-inline procedural "cic:/CoRN/fta/KeyLemma/third_less_one.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/third_less_one.con" as lemma.
(* UNEXPORTED
Hint Resolve third_less_one: algebra.
*)
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_mon.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_mon.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_mon'.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_mon'.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_small.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_small.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/p3m_smaller.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/p3m_smaller.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/chfun.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/chfun.con" as definition.
-inline procedural "cic:/CoRN/fta/KeyLemma/chfun_1.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/chfun_1.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/chfun_2.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/chfun_2.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/chfun_3.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/chfun_3.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/chfun_4.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/chfun_4.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps.con" as definition.
-inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_pos.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_pos.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_Halfeps.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_Halfeps.con" as lemma.
(* UNEXPORTED
Hint Resolve Halfeps_Halfeps: algebra.
*)
-inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_eps.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_eps.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_trans.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Halfeps_trans.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/Key_1a.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Key_1a.con" as lemma.
(* UNEXPORTED
Hint Resolve Key_1a: algebra.
*)
-inline procedural "cic:/CoRN/fta/KeyLemma/Key_1b.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Key_1b.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/Key_1.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Key_1.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/Key_2.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Key_2.con" as lemma.
-inline procedural "cic:/CoRN/fta/KeyLemma/Key.con".
+inline procedural "cic:/CoRN/fta/KeyLemma/Key.con" as lemma.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0.con" "Kneser_Lemma__".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0.con" "Kneser_Lemma__" as definition.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n.con" "Kneser_Lemma__".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n.con" "Kneser_Lemma__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/two_n.con" "Kneser_Lemma__".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/two_n.con" "Kneser_Lemma__" as definition.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Small.con" "Kneser_Lemma__".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Small.con" "Kneser_Lemma__" as definition.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smaller.con" "Kneser_Lemma__".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smaller.con" "Kneser_Lemma__" as definition.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smallest.con" "Kneser_Lemma__".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smallest.con" "Kneser_Lemma__" as definition.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/q.con" "Kneser_Lemma__".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/q.con" "Kneser_Lemma__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/fta/KneserLemma/b_0'_exists.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/b_0'_exists.con" as lemma.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/eta_0.con" "Kneser_Lemma__".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/eta_0.con" "Kneser_Lemma__" as definition.
-inline procedural "cic:/CoRN/fta/KneserLemma/eta_0_pos.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/eta_0_pos.con" as lemma.
-inline procedural "cic:/CoRN/fta/KneserLemma/eta_exists.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/eta_exists.con" as lemma.
-inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists_1.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists_1.con" as lemma.
(* less_cotransitive_unfolded on
{Zero [<] y[/]x[//]H3[-]Half[*]eps} +
{y[/]x[//]H3[-]Half[*]eps [<] Half[*]eps}. *)
-inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/a.con" "Kneser_Lemma__".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/a.con" "Kneser_Lemma__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/fta/KneserLemma/z_exists.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/z_exists.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1'.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1'.con" as lemma.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1''.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1''.con" as lemma.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1.con" as lemma.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2a.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2a.con" as lemma.
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2b.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2b.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2c.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2c.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_3.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_3.con" as lemma.
(* UNEXPORTED
End Kneser_Lemma
*)
-inline procedural "cic:/CoRN/fta/KneserLemma/Kneser.con".
+inline procedural "cic:/CoRN/fta/KneserLemma/Kneser.con" as lemma.
alias id "eps_le_a_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_le_a_0.var".
-inline procedural "cic:/CoRN/fta/MainLemma/a_0_pos.con".
+inline procedural "cic:/CoRN/fta/MainLemma/a_0_pos.con" as lemma.
(*#*
%\begin{convention}% We define the following local abbreviations:
(* begin hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/two_n.con" "Main_Lemma__".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/two_n.con" "Main_Lemma__" as definition.
-inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Small.con" "Main_Lemma__".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Small.con" "Main_Lemma__" as definition.
-inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Smaller.con" "Main_Lemma__".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Smaller.con" "Main_Lemma__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main_1a'.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_1a'.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main_1b'.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_1b'.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main_1a.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_1a.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main_1b.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_1b.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main_1.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_1.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main_2'.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_2'.con" as lemma.
-inline procedural "cic:/CoRN/fta/MainLemma/Main_2.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_2.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main_3a.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_3a.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main_3.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main_3.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/fta/MainLemma/Main.con".
+inline procedural "cic:/CoRN/fta/MainLemma/Main.con" as lemma.
(* end hide *)
alias id "F" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/F.var".
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con" as lemma.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun.con" as definition.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_1.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_2a.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_2a.con" as lemma.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_2.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_3a.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_3a.con" as lemma.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_3b.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_3b.con" as lemma.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4a.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4a.con" as lemma.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4b.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4b.con" as lemma.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4c.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4c.con" as lemma.
-inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4d.con".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_4d.con" as lemma.
(* begin hide *)
inline procedural "cic:/CoRN/ftc/COrdLemmas/Sumx_Sum_Sum
(* end show *)
- (* begin hide *).con".
+ (* begin hide *).con" as lemma.
(* end hide *)
inline procedural "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum
(* end show *)
- (* begin hide *).con".
+ (* begin hide *).con" as lemma.
(* UNEXPORTED
End Lemmas
Section More_Lemmas
*)
-inline procedural "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/f'.con" "More_Lemmas__".
+inline procedural "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/f'.con" "More_Lemmas__" as definition.
(* end hide *)
inline procedural "cic:/CoRN/ftc/COrdLemmas/str_Sumx_Sum_Sum'
(* end show *)
- (* begin hide *).con".
+ (* begin hide *).con" as lemma.
(* end hide *)
(sometimes called Heine continuity).
*)
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_comm_Lim.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_comm_Lim.con" as lemma.
(*#*
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 procedural "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/Continuous_imp_pos.con" as lemma.
(*#*
Similar results for increasing functions:
*)
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues.con" as lemma.
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues'.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_inc_glues'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues.con" as lemma.
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues'.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/strict_dec_glues'.con" as lemma.
(*#* More on glueing intervals. *)
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clor_nonneg.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clor_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_olcr_nonneg.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_olcr_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clcr_nonneg.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/olor_pos_clcr_nonneg.con" as lemma.
(*#*
Any function that has the null function as its derivative must be constant.
*)
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/FConst_prop.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/FConst_prop.con" as lemma.
(*#* As a corollary, two functions with the same derivative must differ
by a constant.
*)
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/Feq_crit_with_const.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/Feq_crit_with_const.con" as lemma.
(*#* 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 procedural "cic:/CoRN/ftc/CalculusTheorems/Feq_criterium.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/Feq_criterium.con" as lemma.
(*#*
Finally, a well known result: any function with a (strictly) positive
formalization and from the mathematical point of view.
*)
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_leEq.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less'.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/Derivative_imp_resp_less'.con" as lemma.
(*#* From these results we can finally prove that exponentiation to a
real power preserves the less or equal than relation!
Transparent nring.
*)
-inline procedural "cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con".
+inline procedural "cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con" as lemma.
(* UNEXPORTED
End Various_Theorems
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/I.con" "Maps_into_Compacts__Part_Funct__".
+inline procedural "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/I.con" "Maps_into_Compacts__Part_Funct__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/maps_into_compacts.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_into_compacts.con" as definition.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/maps_lemma'.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_lemma'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/maps_lemma.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_less.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_less.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_inc.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_inc.con" as lemma.
(* UNEXPORTED
End Part_Funct
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/included_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/included_comp.con" as lemma.
(* UNEXPORTED
End Mapping
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Composition/Interval_Continuity/I.con" "Interval_Continuity__".
+inline procedural "cic:/CoRN/ftc/Composition/Interval_Continuity/I.con" "Interval_Continuity__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/Continuous_I_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Continuous_I_comp.con" as lemma.
(* UNEXPORTED
End Interval_Continuity
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hab.con" "Derivative__".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hab.con" "Derivative__" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hcd.con" "Derivative__".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hcd.con" "Derivative__" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/Derivative/I.con" "Derivative__".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative/I.con" "Derivative__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/included_comp'.con".
+inline procedural "cic:/CoRN/ftc/Composition/included_comp'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/maps'.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/Derivative_I_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative_I_comp.con" as lemma.
(*#*
The next lemma will be useful when we move on to differentiability.
*)
-inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con".
+inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con" as lemma.
(* UNEXPORTED
End Derivative
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hab.con" "Differentiability__".
+inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hab.con" "Differentiability__" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hcd.con" "Differentiability__".
+inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hcd.con" "Differentiability__" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/Differentiability/I.con" "Differentiability__".
+inline procedural "cic:/CoRN/ftc/Composition/Differentiability/I.con" "Differentiability__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp.con" as lemma.
(* UNEXPORTED
End Differentiability
alias id "pJ" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/pJ.var".
-inline procedural "cic:/CoRN/ftc/Composition/maps_compacts_into.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_compacts_into.con" as definition.
(*#*
Now everything comes naturally:
*)
-inline procedural "cic:/CoRN/ftc/Composition/comp_inc_lemma.con".
+inline procedural "cic:/CoRN/ftc/Composition/comp_inc_lemma.con" as lemma.
alias id "F" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/F.var".
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/Continuous_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Continuous_comp.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/Derivative_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative_comp.con" as lemma.
(* UNEXPORTED
End Generalized_Intervals
Finally, some criteria to prove that a function with a specific domain maps compacts into compacts:
*)
-inline procedural "cic:/CoRN/ftc/Composition/positive_fun.con".
+inline procedural "cic:/CoRN/ftc/Composition/positive_fun.con" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/negative_fun.con".
+inline procedural "cic:/CoRN/ftc/Composition/negative_fun.con" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/positive_imp_maps_compacts_into.con".
+inline procedural "cic:/CoRN/ftc/Composition/positive_imp_maps_compacts_into.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/negative_imp_maps_compacts_into.con".
+inline procedural "cic:/CoRN/ftc/Composition/negative_imp_maps_compacts_into.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/Continuous_imp_maps_compacts_into.con".
+inline procedural "cic:/CoRN/ftc/Composition/Continuous_imp_maps_compacts_into.con" as lemma.
(*#*
As a corollary, we get the generalization of differentiability property.
*)
-inline procedural "cic:/CoRN/ftc/Composition/Diffble_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Diffble_comp.con" as lemma.
(* UNEXPORTED
End Corollaries
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/I.con" "Definitions_and_Basic_Results__".
+inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/I.con" "Definitions_and_Basic_Results__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/P.con" "Definitions_and_Basic_Results__".
+inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/P.con" "Definitions_and_Basic_Results__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I.con" as definition.
(*#*
For convenience, we distinguish the two properties of continuous functions.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/contin_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/Continuity/contin_imp_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/contin_prop.con".
+inline procedural "cic:/CoRN/ftc/Continuity/contin_prop.con" as lemma.
(*#*
Assume [F] to be continuous in [I]. Then it has a least upper bound and a greater lower bound on [I].
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hinc'.con" "Definitions_and_Basic_Results__".
+inline procedural "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hinc'.con" "Definitions_and_Basic_Results__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_tb_image.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_tb_image.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_lub.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_lub.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_glb.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_glb.con" as lemma.
(*#*
We now make this glb and lub into operators.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/lub_funct.con".
+inline procedural "cic:/CoRN/ftc/Continuity/lub_funct.con" as definition.
-inline procedural "cic:/CoRN/ftc/Continuity/glb_funct.con".
+inline procedural "cic:/CoRN/ftc/Continuity/glb_funct.con" as definition.
(*#*
These operators have the expected properties.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/lub_is_lub.con".
+inline procedural "cic:/CoRN/ftc/Continuity/lub_is_lub.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/glb_is_glb.con".
+inline procedural "cic:/CoRN/ftc/Continuity/glb_is_glb.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/glb_prop.con".
+inline procedural "cic:/CoRN/ftc/Continuity/glb_prop.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/lub_prop.con".
+inline procedural "cic:/CoRN/ftc/Continuity/lub_prop.con" as lemma.
(*#*
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 procedural "cic:/CoRN/ftc/Continuity/Norm_Funct.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Norm_Funct.con" as definition.
(*#*
The norm effectively bounds the absolute value of a function.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/norm_bnd_AbsIR.con".
+inline procedural "cic:/CoRN/ftc/Continuity/norm_bnd_AbsIR.con" as lemma.
(*#*
The following is another way of characterizing the norm:
*)
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_abs_lub.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_imp_abs_lub.con" as lemma.
(*#*
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 procedural "cic:/CoRN/ftc/Continuity/positive_norm.con".
+inline procedural "cic:/CoRN/ftc/Continuity/positive_norm.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/norm_fun_lub.con".
+inline procedural "cic:/CoRN/ftc/Continuity/norm_fun_lub.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/leEq_Norm_Funct.con".
+inline procedural "cic:/CoRN/ftc/Continuity/leEq_Norm_Funct.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/less_Norm_Funct.con".
+inline procedural "cic:/CoRN/ftc/Continuity/less_Norm_Funct.con" as lemma.
(* UNEXPORTED
End Definitions_and_Basic_Results
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/I.con" "Local_Results__".
+inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/I.con" "Local_Results__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/P.con" "Local_Results__".
+inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/P.con" "Local_Results__" as definition.
-inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/Q.con" "Local_Results__".
+inline procedural "cic:/CoRN/ftc/Continuity/Local_Results/Q.con" "Local_Results__" as definition.
(* end hide *)
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 procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change.con".
+inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change_pos.con".
+inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change_pos.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change_neg.con".
+inline procedural "cic:/CoRN/ftc/Continuity/cont_no_sign_change_neg.con" as lemma.
(*#*
Being continuous is an extensional property.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_wd.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_wd.con" as lemma.
(*#*
A continuous function remains continuous if you restrict its domain.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/included_imp_contin.con".
+inline procedural "cic:/CoRN/ftc/Continuity/included_imp_contin.con" as lemma.
(*#*
Constant functions and identity are continuous.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_const.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_id.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_id.con" as lemma.
(*#*
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.
alias id "contG" = "cic:/CoRN/ftc/Continuity/Local_Results/contG.var".
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_inv.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_mult.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_mult.con" as lemma.
(* UNEXPORTED
Opaque AbsIR Max.
Transparent AbsIR Max.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_max.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_max.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_recip.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_recip.con" as lemma.
(* UNEXPORTED
End Local_Results
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/I.con" "Corolaries__".
+inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/I.con" "Corolaries__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/P.con" "Corolaries__".
+inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/P.con" "Corolaries__" as definition.
-inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/Q.con" "Corolaries__".
+inline procedural "cic:/CoRN/ftc/Continuity/Corolaries/Q.con" "Corolaries__" as definition.
(* end hide *)
product and constant functions.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_minus.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_scal.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_nth.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_nth.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_min.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_min.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con" as lemma.
alias id "Hg'" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg'.var".
alias id "Hg''" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg''.var".
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_div.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_div.con" as lemma.
(* UNEXPORTED
End Corolaries
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Other/Sums/I.con" "Other__Sums__".
+inline procedural "cic:/CoRN/ftc/Continuity/Other/Sums/I.con" "Other__Sums__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sum0.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sum0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sumx.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sumx.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sum.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_Sum.con" as lemma.
(* UNEXPORTED
End Sums
For practical purposes, these characterization results are useful:
*)
-inline procedural "cic:/CoRN/ftc/Continuity/lub_charact.con".
+inline procedural "cic:/CoRN/ftc/Continuity/lub_charact.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Continuity/glb_charact.con".
+inline procedural "cic:/CoRN/ftc/Continuity/glb_charact.con" as lemma.
(*#*
The following result is also extremely useful, as it allows us to set a lower bound on the glb of a function.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/leEq_glb.con".
+inline procedural "cic:/CoRN/ftc/Continuity/leEq_glb.con" as lemma.
(*#*
The norm is also an extensional property.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/Norm_Funct_wd.con".
+inline procedural "cic:/CoRN/ftc/Continuity/Norm_Funct_wd.con" as lemma.
(*#*
The value of the norm is covariant with the length of the interval.
*)
-inline procedural "cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con".
+inline procedural "cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con" as lemma.
(* UNEXPORTED
End Other
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Derivative/Definitions/Hab.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/Derivative/Definitions/Hab.con" "Definitions__" as definition.
-inline procedural "cic:/CoRN/ftc/Derivative/Definitions/I.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/Derivative/Definitions/I.con" "Definitions__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Derivative/Definitions/P.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/Derivative/Definitions/P.con" "Definitions__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I.con".
+inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I.con" as definition.
(* UNEXPORTED
End Definitions
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab.con" "Basic_Properties__".
+inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab.con" "Basic_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/I.con" "Basic_Properties__".
+inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/I.con" "Basic_Properties__" as definition.
(* end hide *)
Like we did for equality, we begin by stating a lemma that makes proofs of derivation easier in practice.
*)
-inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_char.con".
+inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_char.con" as lemma.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/P.con" "Basic_Properties__".
+inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/P.con" "Basic_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Q.con" "Basic_Properties__".
+inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Q.con" "Basic_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/R.con" "Basic_Properties__".
+inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/R.con" "Basic_Properties__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_wdl.con".
+inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_wdl.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_wdr.con".
+inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_wdr.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Derivative_I_unique_lemma.con" "Basic_Properties__".
+inline procedural "cic:/CoRN/ftc/Derivative/Basic_Properties/Derivative_I_unique_lemma.con" "Basic_Properties__" as definition.
(* end hide *)
Derivative is unique.
*)
-inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_unique.con".
+inline procedural "cic:/CoRN/ftc/Derivative/Derivative_I_unique.con" as lemma.
(*#*
Finally, the set where we are considering the relation is included in the domain of both functions.
*)
-inline procedural "cic:/CoRN/ftc/Derivative/derivative_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/Derivative/derivative_imp_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con".
+inline procedural "cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con" as lemma.
(*#*
Any function that is or has a derivative is continuous.
alias id "Hab''" = "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab''.var".
-inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con".
+inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin_I.con".
+inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin_I.con" as lemma.
(* UNEXPORTED
End Basic_Properties
If [G] is the derivative of [F] in a given interval, then [G] is also the derivative of [F] in any smaller interval.
*)
-inline procedural "cic:/CoRN/ftc/Derivative/included_imp_deriv.con".
+inline procedural "cic:/CoRN/ftc/Derivative/included_imp_deriv.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/I.con" "Lemmas__".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/I.con" "Lemmas__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/P.con" "Lemmas__".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Lemmas/P.con" "Lemmas__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con" as lemma.
(* UNEXPORTED
End Lemmas
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab.con" "Local_Results__".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab.con" "Local_Results__" as definition.
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Local_Results/I.con" "Local_Results__".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Local_Results/I.con" "Local_Results__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_const.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con" as lemma.
alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var".
alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var".
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_inv.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_mult.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_mult.con" as lemma.
(*#*
As was the case for continuity, the rule for the reciprocal function has a side condition.
(* end show *)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con" as lemma.
(* UNEXPORTED
End Local_Results
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab.con" "Corolaries__".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab.con" "Corolaries__" as definition.
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Corolaries/I.con" "Corolaries__".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Corolaries/I.con" "Corolaries__" as definition.
(* end hide *)
From this lemmas the rules for the other algebraic operations follow directly.
*)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_minus.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_scal.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con" as lemma.
alias id "Gbnd" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var".
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con" as lemma.
(* UNEXPORTED
End Corolaries
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/I.con" "Derivative_Sums__".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/I.con" "Derivative_Sums__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum0.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sumx.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sumx.con" as lemma.
-inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum.con".
+inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum.con" as lemma.
(* UNEXPORTED
End Derivative_Sums
problems.
*)
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I.con" as definition.
(* UNEXPORTED
End Definitions
A function differentiable in [[a,b]] is differentiable in every proper compact subinterval of [[a,b]].
*)
-inline procedural "cic:/CoRN/ftc/Differentiability/included_imp_diffble.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/included_imp_diffble.con" as lemma.
(*#*
A function differentiable in an interval is everywhere defined in that interval.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab.con" "Local_Properties__".
+inline procedural "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab.con" "Local_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/Differentiability/Local_Properties/I.con" "Local_Properties__".
+inline procedural "cic:/CoRN/ftc/Differentiability/Local_Properties/I.con" "Local_Properties__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Differentiability/diffble_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/diffble_imp_inc.con" as lemma.
(*#*
If a function has a derivative in an interval then it is differentiable in that interval.
*)
-inline procedural "cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con" as lemma.
(* UNEXPORTED
End Local_Properties
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Differentiability/Operations/Hab.con" "Operations__".
+inline procedural "cic:/CoRN/ftc/Differentiability/Operations/Hab.con" "Operations__" as definition.
-inline procedural "cic:/CoRN/ftc/Differentiability/Operations/I.con" "Operations__".
+inline procedural "cic:/CoRN/ftc/Differentiability/Operations/I.con" "Operations__" as definition.
(* end hide *)
Section Constants
*)
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_const.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_id.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_id.con" as lemma.
(* UNEXPORTED
End Constants
alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/diffF.var".
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con" as lemma.
(* UNEXPORTED
End Well_Definedness
alias id "diffG" = "cic:/CoRN/ftc/Differentiability/Operations/diffG.var".
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_inv.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con" as lemma.
(* UNEXPORTED
End Operations
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Differentiability/Corollaries/Hab.con" "Corollaries__".
+inline procedural "cic:/CoRN/ftc/Differentiability/Corollaries/Hab.con" "Corollaries__" as definition.
-inline procedural "cic:/CoRN/ftc/Differentiability/Corollaries/I.con" "Corollaries__".
+inline procedural "cic:/CoRN/ftc/Differentiability/Corollaries/I.con" "Corollaries__" as definition.
(* end hide *)
alias id "diffG" = "cic:/CoRN/ftc/Differentiability/Corollaries/diffG.var".
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con" as lemma.
alias id "Gbnd" = "cic:/CoRN/ftc/Differentiability/Corollaries/Gbnd.var".
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con" as lemma.
(* UNEXPORTED
End Corollaries
alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Other_Properties/Hab'.var".
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sumx.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sumx.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con" as lemma.
(* UNEXPORTED
End Other_Properties
%\end{convention}%
*)
-inline procedural "cic:/CoRN/ftc/Differentiability/diffble_imp_contin_I.con".
+inline procedural "cic:/CoRN/ftc/Differentiability/diffble_imp_contin_I.con" as lemma.
(* UNEXPORTED
Hint Immediate included_imp_contin deriv_imp_contin_I deriv_imp_contin'_I
alias id "Ha" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/Ha.var".
-inline procedural "cic:/CoRN/ftc/FTC/prim_lemma.con".
+inline procedural "cic:/CoRN/ftc/FTC/prim_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FTC/Fprim_strext.con".
+inline procedural "cic:/CoRN/ftc/FTC/Fprim_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FTC/Fprim.con".
+inline procedural "cic:/CoRN/ftc/FTC/Fprim.con" as definition.
(* UNEXPORTED
End Indefinite_Integral
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FTC/FTC/G.con" "FTC__".
+inline procedural "cic:/CoRN/ftc/FTC/FTC/G.con" "FTC__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/FTC/Continuous_prim.con".
+inline procedural "cic:/CoRN/ftc/FTC/Continuous_prim.con" as lemma.
(*#*
The derivative of [G] is simply [F].
alias id "pJ" = "cic:/CoRN/ftc/FTC/FTC/pJ.var".
-inline procedural "cic:/CoRN/ftc/FTC/FTC1.con".
+inline procedural "cic:/CoRN/ftc/FTC/FTC1.con" as theorem.
(*#*
Any other function [G0] with derivative [F] must differ from [G] by a constant.
alias id "derG0" = "cic:/CoRN/ftc/FTC/FTC/derG0.var".
-inline procedural "cic:/CoRN/ftc/FTC/FTC2.con".
+inline procedural "cic:/CoRN/ftc/FTC/FTC2.con" as theorem.
(*#*
The following is another statement of the Fundamental Theorem of Calculus, also known as Barrow's rule.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FTC/FTC/G0_inc.con" "FTC__".
+inline procedural "cic:/CoRN/ftc/FTC/FTC/G0_inc.con" "FTC__" as definition.
(* end hide *)
Opaque G.
*)
-inline procedural "cic:/CoRN/ftc/FTC/Barrow.con".
+inline procedural "cic:/CoRN/ftc/FTC/Barrow.con" as theorem.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/g.con" "Limit_of_Integral_Seq__Compact__".
+inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/g.con" "Limit_of_Integral_Seq__Compact__" as definition.
-inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/G.con" "Limit_of_Integral_Seq__Compact__".
+inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/G.con" "Limit_of_Integral_Seq__Compact__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con".
+inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con" as lemma.
(* UNEXPORTED
End Compact
And now we can generalize it step by step.
*)
-inline procedural "cic:/CoRN/ftc/FTC/limit_of_integral.con".
+inline procedural "cic:/CoRN/ftc/FTC/limit_of_integral.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FTC/limit_of_Integral.con".
+inline procedural "cic:/CoRN/ftc/FTC/limit_of_Integral.con" as lemma.
(* UNEXPORTED
Section General
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/g.con" "Limit_of_Integral_Seq__General__".
+inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/g.con" "Limit_of_Integral_Seq__General__" as definition.
-inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/G.con" "Limit_of_Integral_Seq__General__".
+inline procedural "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/G.con" "Limit_of_Integral_Seq__General__" as definition.
(* end hide *)
alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contG.var".
-inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con".
+inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con" as lemma.
(* UNEXPORTED
End General
alias id "derf" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/derf.var".
-inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con".
+inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con" as lemma.
(* UNEXPORTED
End Limit_of_Derivative_Seq
alias id "derF" = "cic:/CoRN/ftc/FTC/Derivative_Series/derF.var".
-inline procedural "cic:/CoRN/ftc/FTC/Derivative_FSeries.con".
+inline procedural "cic:/CoRN/ftc/FTC/Derivative_FSeries.con" as lemma.
(* UNEXPORTED
End Derivative_Series
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/I.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/I.con" "Definitions__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/incf.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/incf.con" "Definitions__" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/incF.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Definitions/incF.con" "Definitions__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'.con" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1.con" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'.con" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2.con" as definition.
(*#*
These definitions are all shown to be equivalent.
*)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq2.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_seq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_norm.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_norm.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_norm_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_norm_seq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq1.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_seq1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq1.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_seq1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_seq.con" as lemma.
(*#*
A Cauchy sequence of functions is pointwise a Cauchy sequence.
*)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con" as lemma.
(* UNEXPORTED
End Definitions
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/More_Definitions/I.con" "More_Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/More_Definitions/I.con" "More_Definitions__" as definition.
(* end hide *)
partial functions, for reasons which were already explained.
*)
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq.con" as definition.
(*#*
It is useful to extract the limit as a partial function:
(* end show *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con" as definition.
(* UNEXPORTED
End More_Definitions
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/I.con" "Irrelevance_of_Proofs__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/I.con" "Irrelevance_of_Proofs__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq'_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq2_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_norm_fun_seq_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_wd.con" as lemma.
(* UNEXPORTED
End Irrelevance_of_Proofs
Section More_Proof_Irrelevance
*)
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq_wd.con" as lemma.
(* UNEXPORTED
End More_Proof_Irrelevance
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/More_Properties/I.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/More_Properties/I.con" "More_Properties__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con" as lemma.
alias id "F" = "cic:/CoRN/ftc/FunctSequence/More_Properties/F.var".
(* end show *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdl'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_fun_seq'_wdr'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_cont_Lim.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_cont_Lim.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/conv_Cauchy_fun_seq.con" as lemma.
(*#*
More interesting is the fact that a convergent sequence of functions converges pointwise as a sequence of real numbers.
*)
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_conv_imp_seq_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_conv_imp_seq_conv.con" as lemma.
(*#*
And a sequence of real numbers converges iff the corresponding sequence of constant functions converges to the corresponding constant function.
*)
-inline procedural "cic:/CoRN/ftc/FunctSequence/seq_conv_imp_fun_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/seq_conv_imp_fun_conv.con" as lemma.
(* UNEXPORTED
End More_Properties
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/I.con" "Algebraic_Properties__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/I.con" "Algebraic_Properties__" as definition.
(* end hide *)
First, the limit function is unique.
*)
-inline procedural "cic:/CoRN/ftc/FunctSequence/FLim_unique.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/FLim_unique.con" as lemma.
(*#* Constant sequences (not sequences of constant functions!) always converge.
*)
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_const.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_const.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_const.con" as lemma.
(*#*
We now prove that if two sequences converge than their sum (difference, product) also converge to the sum (difference, product) of their limits.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incf.con" "Algebraic_Properties__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incf.con" "Algebraic_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incg.con" "Algebraic_Properties__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incg.con" "Algebraic_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incF.con" "Algebraic_Properties__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incF.con" "Algebraic_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incG.con" "Algebraic_Properties__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incG.con" "Algebraic_Properties__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult'.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult'.con" as lemma.
(* UNEXPORTED
End Algebraic_Properties
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/I.con" "More_Algebraic_Properties__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/I.con" "More_Algebraic_Properties__" as definition.
(* end hide *)
(* end hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_plus.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_minus.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_mult.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_mult.con" as lemma.
(* UNEXPORTED
End More_Algebraic_Properties
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/I.con" "Still_More_Algebraic_Properties__".
+inline procedural "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/I.con" "Still_More_Algebraic_Properties__" as definition.
(* end hide *)
As a corollary, we get the analogous property for the sequence of algebraic inverse functions.
*)
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_inv.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_inv.con".
+inline procedural "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_inv.con" as lemma.
(* UNEXPORTED
End Still_More_Algebraic_Properties
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__" as definition.
(* end hide *)
alias id "f" = "cic:/CoRN/ftc/FunctSeries/Definitions/f.var".
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_cont.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent.con" as definition.
(*#*
For what comes up next we need to know that the convergence of a
real number series.
*)
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv_imp_conv.con" as lemma.
(*#* We then define the sum of the series as being the pointwise sum of
the corresponding series.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/contf.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/contf.con" "Definitions__" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/incf.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Definitions/incf.con" "Definitions__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con" as definition.
(* UNEXPORTED
End Definitions
(*#* A series can also be absolutely convergent. *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con" as definition.
(* UNEXPORTED
End More_Definitions
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/Operations/I.con" "Operations__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Operations/I.con" "Operations__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_const_series.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_const_series_sum.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_zero_fun_series.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_zero.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_convergent_wd.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_wd'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_min.con" as lemma.
(*#*
%\begin{convention}% Let [c:IR].
alias id "contH" = "cic:/CoRN/ftc/FunctSeries/Operations/contH.var".
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con" as lemma.
(* UNEXPORTED
End Operations
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__" as definition.
(* end hide *)
alias id "convF" = "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var".
-inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con" as lemma.
(* UNEXPORTED
End More_Operations
series.
*)
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_series_conv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_cont.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_char.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con" as lemma.
(* UNEXPORTED
End Other_Results
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Criteria__".
+inline procedural "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Criteria__" as definition.
(* end hide *)
Opaque fun_seq_part_sum.
*)
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_str_comparison.con" as lemma.
(* UNEXPORTED
Transparent FAbs.
*)
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_comparison.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_comparison.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/abs_imp_conv.con" as lemma.
(* UNEXPORTED
Opaque FAbs.
*)
-inline procedural "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con".
+inline procedural "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con" as lemma.
(* UNEXPORTED
End Convergence_Criteria
( [FSum]).
*)
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum0.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum0.con" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum.con" as definition.
(*#*
Although [FSum] is here defined directly, it has the same relationship
those results.
*)
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum0.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_one.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_one.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_first.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_first.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_last.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_last.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_last'.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_last'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_plus_FSum.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_plus_FSum.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/inv_FSum.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/inv_FSum.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_minus_FSum.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_minus_FSum.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_wd'.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_wd'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_resp_less.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_resp_leEq.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_comm_scal.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_comm_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_comm_scal'.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_comm_scal'.con" as lemma.
(*#*
Also important is the case when we have a finite family
to use the [FSumx] operator.
*)
-inline procedural "cic:/CoRN/ftc/FunctSums/FSumx.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSumx.con" as definition.
(*#*
This operator is well defined, as expected.
*)
-inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_wd.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_wd'.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_wd'.con" as lemma.
(*#*
As was already the case for [Sumx], in many cases we will need to
function $f_i$#f<sub>i</sub>#.
*)
-inline procedural "cic:/CoRN/ftc/FunctSums/ext_fun_seq.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/ext_fun_seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSums/ext_fun_seq'.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/ext_fun_seq'.con" as definition.
(* UNEXPORTED
Implicit Arguments ext_fun_seq [n].
Under these assumptions, we can characterize the domain and the value of the sum function from the domains and values of the summands:
*)
-inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_pred.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_pred.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_pred'.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_pred'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_char.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_char.con" as lemma.
(*#*
As we did for arbitrary groups, it is often useful to rewrite this sums as ordinary sums.
*)
-inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_to_FSum.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_to_FSum.con" as definition.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_lt.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_lt.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_le.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSumx_le.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSumx_to_FSum.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSumx_to_FSum.con" as lemma.
(*#*
Some useful lemmas follow.
*)
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_0.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_S.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum0_S.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_0.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_S.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_S.con" as lemma.
-inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum0'.con".
+inline procedural "cic:/CoRN/ftc/FunctSums/FSum_FSum0'.con" as lemma.
Section Lemmas
*)
-inline procedural "cic:/CoRN/ftc/Integral/Lemmas/Sumx_wd_weird.con" "Lemmas__".
+inline procedural "cic:/CoRN/ftc/Integral/Lemmas/Sumx_wd_weird.con" "Lemmas__" as definition.
-inline procedural "cic:/CoRN/ftc/Integral/Sumx_weird_lemma.con".
+inline procedural "cic:/CoRN/ftc/Integral/Sumx_weird_lemma.con" as lemma.
(* UNEXPORTED
End Lemmas
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Integral/Integral/I.con" "Integral__".
+inline procedural "cic:/CoRN/ftc/Integral/Integral/I.con" "Integral__" as definition.
alias id "F" = "cic:/CoRN/ftc/Integral/Integral/F.var".
alias id "contF" = "cic:/CoRN/ftc/Integral/Integral/contF.var".
-inline procedural "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__".
+inline procedural "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__" as definition.
(* end hide *)
Section Darboux_Sum
*)
-inline procedural "cic:/CoRN/ftc/Integral/integral_seq.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/Integral/Cauchy_Darboux_Seq.con".
+inline procedural "cic:/CoRN/ftc/Integral/Cauchy_Darboux_Seq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/integral.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral.con" as definition.
(* UNEXPORTED
End Darboux_Sum
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/d.con" "Integral__Integral_Thm__".
+inline procedural "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/d.con" "Integral__Integral_Thm__" as definition.
(* end hide *)
alias id "incF" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/incF.var".
-inline procedural "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con" as lemma.
(* UNEXPORTED
End Integral_Thm
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Integral/Basic_Properties/I.con" "Basic_Properties__".
+inline procedural "cic:/CoRN/ftc/Integral/Basic_Properties/I.con" "Basic_Properties__" as definition.
(* end hide *)
alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contG.var".
-inline procedural "cic:/CoRN/ftc/Integral/integral_strext.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/integral_strext'.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_strext'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/integral_wd.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/integral_wd'.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_wd'.con" as lemma.
(* UNEXPORTED
End Well_Definedness
The integral is a linear and monotonous function; in order to prove these facts we also need the important equalities $\int_a^bdx=b-a$#∫<sub>a</sub><sup>b</sup>dx=b-a# and $\int_a^af(x)dx=0$#∫<sub>a</sub><sup>a</sup>=0#.
*)
-inline procedural "cic:/CoRN/ftc/Integral/integral_one.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_one.con" as lemma.
alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/F.var".
alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contG.var".
-inline procedural "cic:/CoRN/ftc/Integral/integral_comm_scal.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_comm_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/integral_plus.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_plus.con" as lemma.
(* UNEXPORTED
Transparent Even_Partition.
*)
-inline procedural "cic:/CoRN/ftc/Integral/integral_empty.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_empty.con" as lemma.
(* UNEXPORTED
End Linearity_and_Monotonicity
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/h.con" "Basic_Properties__Linearity_and_Monotonicity'__".
+inline procedural "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/h.con" "Basic_Properties__Linearity_and_Monotonicity'__" as definition.
(* end hide *)
alias id "contH" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contH.var".
-inline procedural "cic:/CoRN/ftc/Integral/linear_integral.con".
+inline procedural "cic:/CoRN/ftc/Integral/linear_integral.con" as lemma.
(* UNEXPORTED
Opaque nring.
*)
-inline procedural "cic:/CoRN/ftc/Integral/monotonous_integral.con".
+inline procedural "cic:/CoRN/ftc/Integral/monotonous_integral.con" as lemma.
(* UNEXPORTED
Transparent nring.
As corollaries we can calculate integrals of group operations applied to functions.
*)
-inline procedural "cic:/CoRN/ftc/Integral/integral_const.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/integral_minus.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/integral_inv.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_inv.con" as lemma.
(*#*
We can also bound integrals by bounding the integrated functions.
*)
-inline procedural "cic:/CoRN/ftc/Integral/lb_integral.con".
+inline procedural "cic:/CoRN/ftc/Integral/lb_integral.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/ub_integral.con".
+inline procedural "cic:/CoRN/ftc/Integral/ub_integral.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/integral_leEq_norm.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_leEq_norm.con" as lemma.
(* UNEXPORTED
End Corollaries
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_aux.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_aux.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_fun.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_fun.con" as definition.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Integral/pjf_1.con".
+inline procedural "cic:/CoRN/ftc/Integral/pjf_1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/pjf_2.con".
+inline procedural "cic:/CoRN/ftc/Integral/pjf_2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/pjf_2'.con".
+inline procedural "cic:/CoRN/ftc/Integral/pjf_2'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/pjf_3.con".
+inline procedural "cic:/CoRN/ftc/Integral/pjf_3.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_prf1.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_prf1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_prf2.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_prf2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_start.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_start.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_finish.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_finish.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/partition_join.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join.con" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_aux'.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_aux'.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_pts.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_pts.con" as definition.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Integral/pjp_1.con".
+inline procedural "cic:/CoRN/ftc/Integral/pjp_1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/pjp_2.con".
+inline procedural "cic:/CoRN/ftc/Integral/pjp_2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/pjp_3.con".
+inline procedural "cic:/CoRN/ftc/Integral/pjp_3.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_Pts_in_partition.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_Pts_in_partition.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_Pts_wd.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_Pts_wd.con" as lemma.
(* UNEXPORTED
Opaque partition_join.
Transparent minus.
*)
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_Sum_lemma.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_Sum_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Integral/partition_join_mesh.con".
+inline procedural "cic:/CoRN/ftc/Integral/partition_join_mesh.con" as lemma.
(* UNEXPORTED
End Partition_Join
Opaque Even_Partition.
*)
-inline procedural "cic:/CoRN/ftc/Integral/integral_plus_integral.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_plus_integral.con" as lemma.
(* UNEXPORTED
End Integral_Sum
The following are simple consequences of this result and of previous ones.
*)
-inline procedural "cic:/CoRN/ftc/Integral/integral_less_norm.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_less_norm.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Integral/integral_gt_zero.con".
+inline procedural "cic:/CoRN/ftc/Integral/integral_gt_zero.con" as lemma.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/IntervalFunct/Operations/I.con" "Operations__".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/Operations/I.con" "Operations__" as definition.
(* end hide *)
alias id "c" = "cic:/CoRN/ftc/IntervalFunct/Operations/Const/c.var".
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst.con" as definition.
(* UNEXPORTED
End Const
*)
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IId_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IId_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IId.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IId.con" as definition.
(*#*
Next, we define addition, algebraic inverse, subtraction and product of functions.
*)
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IPlus_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IPlus_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IPlus.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IPlus.con" as definition.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IInv_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IInv_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IInv.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IInv.con" as definition.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IMinus_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IMinus_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IMinus.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IMinus.con" as definition.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IMult_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IMult_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IMult.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IMult.con" as definition.
(* UNEXPORTED
Section Nth_Power
alias id "n" = "cic:/CoRN/ftc/IntervalFunct/Operations/Nth_Power/n.var".
-inline procedural "cic:/CoRN/ftc/IntervalFunct/INth_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/INth_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/INth.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/INth.con" as definition.
(* UNEXPORTED
End Nth_Power
(* end show *)
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IRecip_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IRecip_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IRecip.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IRecip.con" as definition.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IDiv_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IDiv_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IDiv.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IDiv.con" as definition.
(* UNEXPORTED
End Recip_Div
Absolute value will also be needed at some point.
*)
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IAbs_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IAbs_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IAbs.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IAbs.con" as definition.
(* UNEXPORTED
End Operations
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I.con" "Composition__".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I.con" "Composition__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I'.con" "Composition__".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/Composition/I'.con" "Composition__" as definition.
(* end hide *)
alias id "Hfg" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hfg.var".
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp_strext.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp.con".
+inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp.con" as definition.
(* UNEXPORTED
End Composition
alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var".
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_IR.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_IR.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_IR.con" as definition.
(*#*
The equivalences between these definitions still hold.
*)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq'_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq'_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_seq2_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_seq2_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_seq_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_seq_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con" as lemma.
(* UNEXPORTED
End Definitions
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_IR.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con" as lemma.
(* UNEXPORTED
End More_Definitions
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wd_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wd_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_wd_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq2_wd_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con" as lemma.
(* UNEXPORTED
End Irrelevance_of_Proofs
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con" as lemma.
alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/F.var".
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl'_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdl'_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr'_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq'_wdr'_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_cont_Lim_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_cont_Lim_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con" as lemma.
(* UNEXPORTED
End More_Properties
alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var".
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_wd_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_wd_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_const_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con" as lemma.
alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/F.var".
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus'_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus'_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus'_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus'_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con" as lemma.
(* UNEXPORTED
End Algebraic_Properties
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_plus_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_plus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_inv_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_inv_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_inv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_minus_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_minus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con" as lemma.
(* UNEXPORTED
End More_Algebraic_Properties
Finally, we define a mapping between sequences of real numbers and sequences of (constant) functions and prove that convergence is preserved.
*)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/seq_to_funseq.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/seq_to_funseq.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/funseq_conv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/funseq_conv.con" as lemma.
(*#*
Another interesting fact: if a sequence of constant functions converges then it must converge to a constant function.
*)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con" as lemma.
(* UNEXPORTED
End Other
alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var".
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_conv_imp_conv_IR.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_inc_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_inc_IR.con" as lemma.
(*#* Assume [h(x)] is the pointwise series of [f(x)] *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/h.con" "Series_Definitions__".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/h.con" "Series_Definitions__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_strext_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_strext_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con" as lemma.
(* UNEXPORTED
End Series_Definitions
Absolute convergence still exists.
*)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con" as definition.
(* UNEXPORTED
End More_Series_Definitions
alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var".
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_Continuous.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/convergent_imp_Continuous.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con" as lemma.
(* UNEXPORTED
End Convergence_Results
alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Operations/J.var".
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_const_series_Sum_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_const_series_Sum_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_zero_fun_series_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con" as lemma.
alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Operations/f.var".
alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/Operations/g.var".
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_wd'.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_wd'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus_conv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus_conv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv_conv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv_conv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus_conv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus_conv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_minus.con" as lemma.
(*#*
%\begin{convention}% Let [c:IR] and [H:PartIR] be continuous in [J].
alias id "contH" = "cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var".
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con" as lemma.
(* UNEXPORTED
End Operations
alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var".
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_comparison_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_comparison_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/abs_imp_conv_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/abs_imp_conv_IR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con" as lemma.
(* UNEXPORTED
End Convergence_Criteria
alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var".
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_cont.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_cont.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum_char.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum_char.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_conv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_conv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con".
+inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con" as lemma.
(* UNEXPORTED
End Insert_Series
Trivial stuff.
*)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_imp_inc.con" as lemma.
(*#*
%\begin{convention}% Assume that [I] is compact and [F] is continuous in [I].
alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/contF.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_I_imp_tb_image.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_I_imp_tb_image.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con" as lemma.
(* UNEXPORTED
End Basic_Results
alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/G.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Continuous.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Continuous.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Continuous.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Continuous.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_const.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_id.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_id.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_plus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_inv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_minus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_mult.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_mult.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_nth.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_nth.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_scal.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_abs.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con" as lemma.
(* UNEXPORTED
End Other_Results
alias id "contG" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/contG.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con" as lemma.
(* UNEXPORTED
End Corollaries
alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Sums/I.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con" as lemma.
(*#*
%\begin{convention}% Assume [f] is a sequence of continuous functions.
alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Sums/contF.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con" as lemma.
(* UNEXPORTED
End Sums
alias id "H" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/H.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdr.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdr.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_unique.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_unique.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc'.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_inc'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con" as lemma.
(* UNEXPORTED
End Basic_Properties
alias id "derG" = "cic:/CoRN/ftc/MoreFunctions/More_Results/derG.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_const.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_id.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_id.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_plus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_inv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_minus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_mult.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_mult.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_scal.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_nth.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_nth.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con" as lemma.
(* UNEXPORTED
End More_Results
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con" as lemma.
(* UNEXPORTED
End More_Corollaries
alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/pI.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con" as lemma.
(* UNEXPORTED
End More_Sums
alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/pI.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Diffble.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con" as lemma.
alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/F.var".
%\end{convention}%
*)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_const.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_id.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_id.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_plus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_inv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_minus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_mult.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_mult.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_nth.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_nth.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con" as lemma.
(* UNEXPORTED
End Diffble_Basic_Properties
alias id "diffG" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffG.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum0.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sumx.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con" as lemma.
(* UNEXPORTED
End Diffble_Corollaries
alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/diffF.var".
-inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con" as definition.
inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_char
- (* begin hide *).con".
+ (* begin hide *).con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_strext.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con" as definition.
(* UNEXPORTED
End Definitions
All the usual results hold.
*)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_wd.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdr.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdr.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdl.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_wdl.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_unique.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_unique.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_Diffble.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_Diffble.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/le_imp_Diffble_n.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/le_imp_Diffble_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_le.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_le.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_n_imp_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble_n.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Diffble_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc'.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_inc'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative_n.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble_n.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Diffble_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative_n.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Derivative_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Included_imp_Diffble_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con" as lemma.
(* UNEXPORTED
End Basic_Results
Some new results hold, too:
*)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_Feq.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_Feq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_lemma.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_S.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_S.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_plus.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_plus.con" as lemma.
(*#*
Some useful characterization results.
*)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_O.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con" as lemma.
(* UNEXPORTED
End More_Results
(* end show *)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_Diffble_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Deriv.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Deriv.con" as definition.
(* UNEXPORTED
End Derivating_Diffble
%\ldots%#...# for which the expected property also holds.
*)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Deriv_lemma.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Deriv_lemma.con" as lemma.
(*#*
Some more interesting properties.
*)
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_1.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_chain.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_chain.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con".
+inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con" as lemma.
(* UNEXPORTED
End Corollaries
alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Lemmas/Hab.var".
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_rht.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_rht.con" as lemma.
(* UNEXPORTED
End Lemmas
alias id "HF" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/HF.var".
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc2.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_integral.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_integral.con" as lemma.
(* UNEXPORTED
End Definitions
alias id "contG" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contG.var".
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_wd.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_wd'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_wd'.con" as lemma.
(*#*
The integral is a linear operator.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_const.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_comm_scal.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_comm_scal.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_plus.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inv.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_minus.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/linear_Integral.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/linear_Integral.con" as lemma.
(*#*
If the endpoints are equal then the integral vanishes.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_empty.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_empty.con" as lemma.
(*#*
And the norm provides an upper bound for the absolute value of the integral.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con" as lemma.
(* UNEXPORTED
End Properties_of_Integral
Two other ways of stating the addition law for domains.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/integral_plus_Integral.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/integral_plus_Integral.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/integral_plus_integral'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/integral_plus_integral'.con" as lemma.
(*#*
And now we can prove the addition law for domains with our general operator.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ab.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ab.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ac.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ac.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_cb.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_cb.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_a.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_a.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_b.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_b.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_c.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_c.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_a.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_a.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_c.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_c.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_a.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_a.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_b.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_b.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_b.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_b.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_c.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_c.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_abc.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_abc.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ab.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ab.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ac.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ac.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_cb.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_cb.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_a.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_a.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_b.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_b.con" "More_Properties__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_c.con" "More_Properties__".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_c.con" "More_Properties__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_plus_Integral.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_plus_Integral.con" as lemma.
(*#*
Notice that, unlike in the classical case, an extra hypothesis (the
(*#* As a corollary, we get the following rule: *)
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_op.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_op.con" as lemma.
(*#* Finally, some miscellaneous results: *)
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_less_norm.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_less_norm.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/ub_Integral.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/ub_Integral.con" as lemma.
(* UNEXPORTED
End Corollaries
*)
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_ap_zero.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_eq_zero.con".
+inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_eq_zero.con" as lemma.
To each interval a predicate (set) is assigned by the following map:
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop.con" as definition.
(* begin hide *)
finite and compact in the obvious way.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/proper.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/proper.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/finite.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/finite.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_.con" as definition.
(*#* Finite intervals have a left end and a right end. *)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/left_end.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/left_end.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/right_end.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/right_end.con" as definition.
(*#*
Some trivia: compact intervals are finite; proper intervals are nonvoid; an interval is nonvoid iff it contains some point.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_finite.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_finite.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_nonvoid.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_nonvoid.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid_point.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid_point.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid_char.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/nonvoid_char.con" as lemma.
(*#*
For practical reasons it helps to define left end and right end of compact intervals.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Lend.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Lend.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Rend.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Rend.con" as definition.
(*#* In a compact interval, the left end is always less than or equal
to the right end.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Lend_leEq_Rend.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Lend_leEq_Rend.con" as lemma.
(*#*
Some nice characterizations of inclusion:
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_included.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_included.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/included_interval'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/included_interval'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/included_interval.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/included_interval.con" as lemma.
(*#*
A weirder inclusion result.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/included3_interval.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/included3_interval.con" as lemma.
(*#*
Finally, all intervals are characterized by well defined predicates.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_wd.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_wd.con" as lemma.
(* UNEXPORTED
End Intervals
alias id "Hx" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/Hx.var".
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single.con" as definition.
(*#*
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 procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_prop.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_prop.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_pt.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_pt.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_inc.con" as lemma.
(* UNEXPORTED
End Single_Compact_Interval
The special case of intervals is worth singling out, as one of the hypothesis becomes a theorem.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_iprop.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single_iprop.con" as definition.
(*#*
Now for more interesting and important results.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc1.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc2.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval_inc2.con" as lemma.
(*#*
If [x [=] y] then the construction yields the same interval whether we
definition rather than as an existential formula.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd1.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd2.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_wd2.con" as lemma.
(*#*
We can make an analogous construction for two points.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval2.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval2.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval2.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_compact_in_interval2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/proper_compact_in_interval2'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval2.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/included_compact_in_interval2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2x'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2y'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc1.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc2.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/iprop_compact_in_interval2_inc2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_lft.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_lft.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_lft.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_lft.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_rht.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_x_rht.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_rht.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_rht.con" as lemma.
(* UNEXPORTED
End Proper_Compact_with_One_or_Two_Points
Compact intervals are exactly compact intervals(!).
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/interval_compact_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/interval_compact_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_interval_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_interval_inc.con" as lemma.
(*#*
A generalization of the previous results: if $[a,b]\subseteq J$#[a,b]⊆J#
$[a,b]\subseteq[a',b']\subseteq J$#[a,b]⊆[a',b']⊆J#.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_proper_in_interval.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_proper_in_interval.con" as lemma.
(* UNEXPORTED
End Compact_Constructions
alias id "I" = "cic:/CoRN/ftc/MoreIntervals/Functions/I.var".
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative_n.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative_n.con" as definition.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble_n.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble_n.con" as definition.
(* UNEXPORTED
End Functions
In the case of compact intervals, this definitions collapse to the old ones.
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous_Int.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous_Int.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Continuous.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Continuous.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative_Int.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Derivative_Int.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Derivative.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Derivative.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble_Int.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Diffble_Int.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Diffble.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/Int_Diffble.con" as lemma.
(* UNEXPORTED
End Reflexivity_Properties
Interestingly, inclusion and equality in an interval are also characterizable in a similar way:
*)
-inline procedural "cic:/CoRN/ftc/MoreIntervals/included_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/included_imp_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/included_Feq''.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/included_Feq''.con" as lemma.
-inline procedural "cic:/CoRN/ftc/MoreIntervals/included_Feq'.con".
+inline procedural "cic:/CoRN/ftc/MoreIntervals/included_Feq'.con" as lemma.
(* UNEXPORTED
End Lemmas
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab.con" "Nth_Derivative__".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab.con" "Nth_Derivative__" as definition.
-inline procedural "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/I.con" "Nth_Derivative__".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/I.con" "Nth_Derivative__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n.con" as definition.
(*#*
Unlike first order differentiability, for our definition to be
[Derivative_I_n] relation.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n.con" as definition.
(* UNEXPORTED
End Nth_Derivative
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Trivia/Hab.con" "Trivia__".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Trivia/Hab.con" "Trivia__" as definition.
-inline procedural "cic:/CoRN/ftc/NthDerivative/Trivia/I.con" "Trivia__".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Trivia/I.con" "Trivia__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_wd.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdr.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdr.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdl.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_wdl.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_unique.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_unique.con" as lemma.
(* UNEXPORTED
End Trivia
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab.con" "Basic_Results__".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab.con" "Basic_Results__" as definition.
-inline procedural "cic:/CoRN/ftc/NthDerivative/Basic_Results/I.con" "Basic_Results__".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Basic_Results/I.con" "Basic_Results__" as definition.
(* end hide *)
We begin by showing that having a higher order derivative implies being differentiable.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_diffble.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_diffble.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_diffble.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_diffble.con" as lemma.
(*#*
If a function is [n] times differentiable then it is also [m] times differentiable for every [m] less or equal than [n].
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/le_imp_Diffble_I.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/le_imp_Diffble_I.con" as lemma.
(*#*
The next result consolidates our intuition that a function is [n]
derivatives.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_imp_le.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_imp_le.con" as lemma.
(*#*
As expected, an [n] times differentiable in [[a,b]] function must be
defined in that interval.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_inc.con" as lemma.
(*#*
Also, the notions of derivative and differentiability are related as expected.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_deriv_n.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Diffble_I_n_imp_deriv_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_Diffble_I_n.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_n_imp_Diffble_I_n.con" as lemma.
(*#*
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 procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc'.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc'.con" as lemma.
(* UNEXPORTED
Section aux
(* end show *)
-inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv'.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv'.con" as lemma.
(* UNEXPORTED
End aux
As usual, nth order derivability is preserved by shrinking the interval.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/included_imp_deriv_n.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/included_imp_deriv_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/included_imp_diffble_n.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/included_imp_diffble_n.con" as lemma.
(*#*
And finally we have an addition rule for the order of the derivative.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con" as lemma.
(* UNEXPORTED
End Basic_Results
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/NthDerivative/More_Results/Hab.con" "More_Results__".
+inline procedural "cic:/CoRN/ftc/NthDerivative/More_Results/Hab.con" "More_Results__" as definition.
-inline procedural "cic:/CoRN/ftc/NthDerivative/More_Results/I.con" "More_Results__".
+inline procedural "cic:/CoRN/ftc/NthDerivative/More_Results/I.con" "More_Results__" as definition.
(* end hide *)
as an existential quantification of the nth derivative relation.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I.con" as definition.
(*#*
This operator is well defined and works as expected.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_lemma.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_inc.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_inc.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_inc'.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_inc'.con" as lemma.
(*#*
Some basic properties of this operation.
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_Sn_deriv.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_Sn_deriv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_plus.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_plus.con" as lemma.
(* UNEXPORTED
End More_Results
Some not so basic properties of this operation (needed in rather specific situations).
*)
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd'.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd''.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_wd''.con" as lemma.
-inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_strext'.con".
+inline procedural "cic:/CoRN/ftc/NthDerivative/n_deriv_I_strext'.con" as lemma.
(* UNEXPORTED
End More_on_n_deriv
definition makes this possible.
*)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/subset.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/subset.con" as definition.
(*#*
The core of our work will revolve around the following fundamental
with proving the main properties of this equality relation.
*)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq.con" as definition.
(*#*
Notice that, because the quantification over the proofs is universal,
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Equality_Results/P.con" "Equality_Results__".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Equality_Results/P.con" "Equality_Results__" as definition.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Equality_Results/Q.con" "Equality_Results__".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Equality_Results/Q.con" "Equality_Results__" as definition.
(* end hide *)
this definition:
*)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/eq_imp_Feq.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/eq_imp_Feq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/included_IR.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/included_IR.con" as lemma.
(* UNEXPORTED
End Equality_Results
If two function coincide on a given subset then they coincide in any smaller subset.
*)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/included_Feq.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/included_Feq.con" as lemma.
(* UNEXPORTED
End Some_More
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/P.con" "Away_from_Zero__Definitions__".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/P.con" "Away_from_Zero__Definitions__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero.con" as definition.
(*#*
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].
(* end show *)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_ap_zero.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con" as lemma.
(* UNEXPORTED
End Definitions
alias id "Q" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Q.var".
-inline procedural "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd.con" as lemma.
(*#*
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 procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_everywhere.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_everywhere.con" as definition.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_in_P.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_in_P.con" as definition.
(*#*
An immediate consequence:
*)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con" as lemma.
(* UNEXPORTED
End Away_from_Zero
alias id "H" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/H.var".
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con" as lemma.
(* UNEXPORTED
End Feq_Equivalence
alias id "G'" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G'.var".
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_inv.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_minus.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_mult.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_mult.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_nth.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_nth.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_recip.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_recip.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_recip'.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_recip'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_div.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_div.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_div'.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_div'.con" as lemma.
(*#*
Notice that in the case of division we only need to require boundedness away from zero for one of the functions (as they are equal); thus the two last lemmas are stated in two different ways, as according to the context one or the other condition may be easier to prove.
The restriction of a function is well defined.
*)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_wd.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/FRestr_wd.con" as lemma.
(*#*
The image of a set is extensional.
*)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con" as lemma.
(* UNEXPORTED
End Operations
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Nth_Power/P.con" "Nth_Power__".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Nth_Power/P.con" "Nth_Power__" as definition.
(* end hide *)
alias id "Hf" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Hf.var".
-inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con" as lemma.
alias id "n" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/n.var".
alias id "H'" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H'.var".
-inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con" as lemma.
(* UNEXPORTED
End Nth_Power
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/I.con" "Strong_Nth_Power__".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/I.con" "Strong_Nth_Power__" as definition.
(* end hide *)
alias id "incF" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/incF.var".
-inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con".
+inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con" as lemma.
(* UNEXPORTED
End Strong_Nth_Power
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/PartInterval/Conversion/I.con" "Conversion__".
+inline procedural "cic:/CoRN/ftc/PartInterval/Conversion/I.con" "Conversion__" as definition.
(* end hide *)
alias id "Hf" = "cic:/CoRN/ftc/PartInterval/Conversion/Hf.var".
-inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR.con" as definition.
(* UNEXPORTED
End Conversion
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/PartInterval/AntiConversion/I.con" "AntiConversion__".
+inline procedural "cic:/CoRN/ftc/PartInterval/AntiConversion/I.con" "AntiConversion__" as definition.
(* end hide *)
alias id "f" = "cic:/CoRN/ftc/PartInterval/AntiConversion/f.var".
-inline procedural "cic:/CoRN/ftc/PartInterval/PartInt_strext.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/PartInt_strext.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartInterval/PartInt.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/PartInt.con" as definition.
(* UNEXPORTED
End AntiConversion
In one direction these operators are inverses.
*)
-inline procedural "cic:/CoRN/ftc/PartInterval/int_part_int.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/int_part_int.con" as lemma.
(* UNEXPORTED
End Inverses
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/PartInterval/Equivalences/I.con" "Equivalences__".
+inline procedural "cic:/CoRN/ftc/PartInterval/Equivalences/I.con" "Equivalences__" as definition.
(* end hide *)
alias id "Gg" = "cic:/CoRN/ftc/PartInterval/Equivalences/Gg.var".
-inline procedural "cic:/CoRN/ftc/PartInterval/part_int_const.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/part_int_const.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartInterval/part_int_id.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/part_int_id.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartInterval/part_int_plus.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/part_int_plus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartInterval/part_int_inv.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/part_int_inv.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartInterval/part_int_minus.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/part_int_minus.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartInterval/part_int_mult.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/part_int_mult.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartInterval/part_int_nth.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/part_int_nth.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/PartInterval/part_int_recip.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/part_int_recip.con" as lemma.
-inline procedural "cic:/CoRN/ftc/PartInterval/part_int_div.con".
+inline procedural "cic:/CoRN/ftc/PartInterval/part_int_div.con" as lemma.
(* UNEXPORTED
End Equivalences
[i < j] and that [ai] is in [[a,b]] for all [i].
*)
-inline procedural "cic:/CoRN/ftc/Partitions/Partition_mon.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Partition_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/Partition_in_compact.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Partition_in_compact.con" as lemma.
(*#*
Each partition of [[a,b]] implies a partition of the interval
define it.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/part_pred_lemma.con".
+inline procedural "cic:/CoRN/ftc/Partitions/part_pred_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/Partition_Dom.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Partition_Dom.con" as definition.
(*#*
The mesh of a partition is the greatest distance between two
helps us in this case.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/Part_Mesh_List.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Part_Mesh_List.con" as definition.
-inline procedural "cic:/CoRN/ftc/Partitions/Mesh.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Mesh.con" as definition.
-inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh.con".
+inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh.con" as definition.
(*#*
Even partitions (partitions where all the points are evenly spaced)
presented simply to make the definition of even partition lighter.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/even_part_1.con".
+inline procedural "cic:/CoRN/ftc/Partitions/even_part_1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/even_part_2.con".
+inline procedural "cic:/CoRN/ftc/Partitions/even_part_2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition.con" as definition.
(* UNEXPORTED
Section Refinements
[P] and prove the main property of refinements.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/Refinement.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Refinement.con" as definition.
-inline procedural "cic:/CoRN/ftc/Partitions/Refinement_prop.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Refinement_prop.con" as lemma.
(*#*
We will also need to consider arbitrary sums %of the form
some condition. We define the condition and the sum for a fixed [P]:
*)
-inline procedural "cic:/CoRN/ftc/Partitions/Points_in_Partition.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Points_in_Partition.con" as definition.
-inline procedural "cic:/CoRN/ftc/Partitions/Pts_part_lemma.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Pts_part_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/Partition_Sum.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Partition_Sum.con" as definition.
(* UNEXPORTED
End Refinements
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Partitions/Definitions/I.con" "Definitions__".
+inline procedural "cic:/CoRN/ftc/Partitions/Definitions/I.con" "Definitions__" as definition.
(* end hide *)
alias id "Q" = "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/Q.var".
-inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points.con" as definition.
-inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points_1.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points_1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points_2.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points_2.con" as lemma.
(* UNEXPORTED
End Getting_Points
alias id "contF" = "cic:/CoRN/ftc/Partitions/Definitions/contF.var".
-inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con" as definition.
(* UNEXPORTED
End Definitions
If a partition has more than one point then its mesh list is nonempty.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/length_Part_Mesh_List.con".
+inline procedural "cic:/CoRN/ftc/Partitions/length_Part_Mesh_List.con" as lemma.
(*#*
Any element of the auxiliary list defined to calculate the mesh of a partition has a very specific form.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/Part_Mesh_List_lemma.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Part_Mesh_List_lemma.con" as lemma.
(*#*
Mesh and antimesh are always nonnegative.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/Mesh_nonneg.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Mesh_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh_nonneg.con".
+inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh_nonneg.con" as lemma.
(*#*
Most important, [AntiMesh] and [Mesh] provide lower and upper bounds
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Partitions/Lemmas/I.con" "Lemmas__".
+inline procedural "cic:/CoRN/ftc/Partitions/Lemmas/I.con" "Lemmas__" as definition.
(* end hide *)
alias id "P" = "cic:/CoRN/ftc/Partitions/Lemmas/P.var".
-inline procedural "cic:/CoRN/ftc/Partitions/Mesh_lemma.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Mesh_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh_lemma.con".
+inline procedural "cic:/CoRN/ftc/Partitions/AntiMesh_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/Mesh_leEq.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Mesh_leEq.con" as lemma.
(* UNEXPORTED
End Lemmas
(*#* More technical stuff. Two equal partitions have the same mesh.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/Mesh_wd.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Mesh_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/Mesh_wd'.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Mesh_wd'.con" as lemma.
(*#*
The mesh of an even partition is easily calculated.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/even_partition_Mesh.con".
+inline procedural "cic:/CoRN/ftc/Partitions/even_partition_Mesh.con" as lemma.
(*#* ** Miscellaneous
%\begin{convention}% Throughout this section, let [a,b:IR] and [I] be [[a,b]].
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/I.con" "Even_Partitions__".
+inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/I.con" "Even_Partitions__" as definition.
(* end hide *)
An interesting property: in a partition, if [ai [<] aj] then [i < j].
*)
-inline procedural "cic:/CoRN/ftc/Partitions/Partition_Points_mon.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Partition_Points_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/refinement_resp_mult.con".
+inline procedural "cic:/CoRN/ftc/Partitions/refinement_resp_mult.con" as lemma.
(*#*
%\begin{convention}% Assume [m,n] are positive natural numbers and
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/P.con" "Even_Partitions__".
+inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/P.con" "Even_Partitions__" as definition.
-inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/Q.con" "Even_Partitions__".
+inline procedural "cic:/CoRN/ftc/Partitions/Even_Partitions/Q.con" "Even_Partitions__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Partitions/even_partition_refinement.con".
+inline procedural "cic:/CoRN/ftc/Partitions/even_partition_refinement.con" as lemma.
(* UNEXPORTED
End Even_Partitions
alias id "Hab" = "cic:/CoRN/ftc/Partitions/More_Definitions/Hab.var".
-inline procedural "cic:/CoRN/ftc/Partitions/_Separated.con".
+inline procedural "cic:/CoRN/ftc/Partitions/_Separated.con" as definition.
(*#*
Two partitions are said to be (mutually) separated if they are both
alias id "Q" = "cic:/CoRN/ftc/Partitions/More_Definitions/Q.var".
-inline procedural "cic:/CoRN/ftc/Partitions/Separated.con".
+inline procedural "cic:/CoRN/ftc/Partitions/Separated.con" as definition.
(* UNEXPORTED
End More_Definitions
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Partitions/Sep_Partitions/I.con" "Sep_Partitions__".
+inline procedural "cic:/CoRN/ftc/Partitions/Sep_Partitions/I.con" "Sep_Partitions__" as definition.
(* end hide *)
The antimesh of a separated partition is always positive.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/pos_AntiMesh.con".
+inline procedural "cic:/CoRN/ftc/Partitions/pos_AntiMesh.con" as lemma.
(*#*
A partition can have only one point iff the endpoints of the interval
endpoints of the interval are the same then it must have one point.
*)
-inline procedural "cic:/CoRN/ftc/Partitions/partition_length_zero.con".
+inline procedural "cic:/CoRN/ftc/Partitions/partition_length_zero.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/_Separated_imp_length_zero.con".
+inline procedural "cic:/CoRN/ftc/Partitions/_Separated_imp_length_zero.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Partitions/partition_less_imp_gt_zero.con".
+inline procedural "cic:/CoRN/ftc/Partitions/partition_less_imp_gt_zero.con" as lemma.
(* UNEXPORTED
End Sep_Partitions
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/I.con" "Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/I.con" "Refinement_Lemma__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF'.con" "Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF'.con" "Refinement_Lemma__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/d.con" "Refinement_Lemma__First_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/d.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/sub.con" "Refinement_Lemma__First_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/sub.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_0.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_n.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_mon.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_mon'.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_mon'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_hyp.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_hyp.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_S.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_S.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H.con" "Refinement_Lemma__First_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H'.con" "Refinement_Lemma__First_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H'.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H0.con" "Refinement_Lemma__First_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H0.con" "Refinement_Lemma__First_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_SS.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_sub_SS.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_h.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_h.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_g.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_g.con" as definition.
(* NOTATION
Notation g := RL_g.
Notation h := RL_h.
*)
-inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc1.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc1.con" as lemma.
(* NOTATION
Notation just1 := (incF _ (Pts_part_lemma _ _ _ _ _ _ HfP _ _)).
Notation just2 := (incF _ (Pts_part_lemma _ _ _ _ _ _ HfQ _ _)).
*)
-inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc2.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc3.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc3.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc4.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc4.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc5.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc5.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc6.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc6.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc7.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc7.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc8.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/ref_calc8.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con" as lemma.
(* UNEXPORTED
End First_Refinement_Lemma
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d.con" "Refinement_Lemma__Second_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d.con" "Refinement_Lemma__Second_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d'.con" "Refinement_Lemma__Second_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d'.con" "Refinement_Lemma__Second_Refinement_Lemma__" as definition.
(* end hide *)
alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR'.var".
-inline procedural "cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con" as lemma.
(* UNEXPORTED
End Second_Refinement_Lemma
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/alpha.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/alpha.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_alpha.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_alpha.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi1.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi1.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi1.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta1.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta1.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_delta1.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_delta1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_sep.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_sep.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_Mesh.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_Mesh.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_fP'_in_P'.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_fP'_in_P'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_P_sum.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_P'_P_sum.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi2.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi2.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi2.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta2.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta2.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_delta2.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_delta2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_sep.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_sep.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_Mesh.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_Mesh.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR'.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_fR'_in_R'.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_fR'_in_R'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_R_sum.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_R'_R_sum.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi3.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi3.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi3.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_csi3.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Q.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Q.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_Mesh.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_Mesh.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_sep.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_sep.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fQ.con" "Refinement_Lemma__Third_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fQ.con" "Refinement_Lemma__Third_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_fQ_in_Q.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_fQ_in_Q.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_P'_sum.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_Q_P'_sum.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con" as lemma.
(* UNEXPORTED
End Third_Refinement_Lemma
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Fa.con" "Refinement_Lemma__Fourth_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Fa.con" "Refinement_Lemma__Fourth_Refinement_Lemma__" as definition.
(* NOTATION
Notation just := (fun z => incF _ (Pts_part_lemma _ _ _ _ _ _ z _ _)).
*)
-inline procedural "cic:/CoRN/ftc/RefLemma/RL_sum_lemma_aux.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/RL_sum_lemma_aux.con" as lemma.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d.con" "Refinement_Lemma__Fourth_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d.con" "Refinement_Lemma__Fourth_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d'.con" "Refinement_Lemma__Fourth_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d'.con" "Refinement_Lemma__Fourth_Refinement_Lemma__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con" as lemma.
(* UNEXPORTED
End Fourth_Refinement_Lemma
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d.con" "Refinement_Lemma__Main_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d.con" "Refinement_Lemma__Main_Refinement_Lemma__" as definition.
-inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d'.con" "Refinement_Lemma__Main_Refinement_Lemma__".
+inline procedural "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d'.con" "Refinement_Lemma__Main_Refinement_Lemma__" as definition.
(* end hide *)
alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR'.var".
-inline procedural "cic:/CoRN/ftc/RefLemma/refinement_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefLemma/refinement_lemma.con" as lemma.
(* UNEXPORTED
End Main_Refinement_Lemma
alias id "Hab" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/Hab.var".
-inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/I.con" "Refining_Separated__".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/I.con" "Refining_Separated__" as definition.
alias id "F" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/F.var".
alias id "HPR" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/HPR.var".
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP'.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HR.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HR'.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HR'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_mn0.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_mn0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_nm0.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_nm0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_H'.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_H'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/f'.con" "Refining_Separated__".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/f'.con" "Refining_Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/g'.con" "Refining_Separated__".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/g'.con" "Refining_Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_nlnf.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_nlnf.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_g'_nlnf.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_g'_nlnf.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_mon.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_g'_mon.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_g'_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_ap_g'.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_f'_ap_g'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/h.con" "Refining_Separated__".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Refining_Separated/h.con" "Refining_Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_nlnf.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_nlnf.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_mon.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_mon'.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_mon'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_f'.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_f'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_g'.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_g'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_PropAll.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_PropAll.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_PropEx.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_PropEx.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_fun.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_fun.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma1.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma3.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma3.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma4.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma4.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma2.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lemma2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma0.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_inj.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_h_inj.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemmai.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemmai.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemman.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemman.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma1.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma2.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxP_lemma2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lft.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_lft.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma0.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmai.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmai.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmam.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemmam.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma1.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma2.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_auxR_lemma2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_rht.con".
+inline procedural "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_rht.con" as lemma.
(* UNEXPORTED
End Refining_Separated
alias id "Hab" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab.var".
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/I.con" "Separating__Separated__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/I.con" "Separating__Separated__" as definition.
alias id "F" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/F.var".
alias id "HR" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HR.var".
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_n.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_m.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_m.con" as lemma.
alias id "alpha" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/alpha.var".
alias id "Halpha" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Halpha.var".
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/e.con" "Separating__Separated__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/e.con" "Separating__Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_He.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_He.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF'.con" "Separating__Separated__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF'.con" "Separating__Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/d.con" "Separating__Separated__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/d.con" "Separating__Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd'.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd'.con" as lemma.
alias id "csi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/csi.var".
alias id "Hcsi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hcsi.var".
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/M.con" "Separating__Separated__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/M.con" "Separating__Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaP.con" "Separating__Separated__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaP.con" "Separating__Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaR.con" "Separating__Separated__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaR.con" "Separating__Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/delta.con" "Separating__Separated__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/delta.con" "Separating__Separated__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaP.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaP.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaR.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaR.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_csi.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_csi.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_d.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_d.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_pos.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/RS_delta_pos.con" as lemma.
(* UNEXPORTED
Section Defining_ai'
alias id "Hi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi.var".
-inline procedural "cic:/CoRN/ftc/RefSeparated/separation_conseq.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/separation_conseq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred1.con" "Separating__Separated__Defining_ai'__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred1.con" "Separating__Separated__Defining_ai'__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred2.con" "Separating__Separated__Defining_ai'__".
+inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred2.con" "Separating__Separated__Defining_ai'__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_aux_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_aux_lemma.con" as lemma.
alias id "Hi0" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi0.var".
alias id "Hin" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hin.var".
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_leEq.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_leEq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_less.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_less.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_ap.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_ap.con" as lemma.
(* UNEXPORTED
End Defining_ai'
*)
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_delta.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_delta.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_delta.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_delta.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_mon_i.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_mon_i.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_mon.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_wd.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_wd.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_part.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_part.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con" as lemma.
alias id "g" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/g.var".
alias id "gP" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/gP.var".
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_aux.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_aux.con" as lemma.
(* NOTATION
Notation just1 := (incF _ (Pts_part_lemma _ _ _ _ _ _ gP _ _)).
(incF _ (Pts_part_lemma _ _ _ _ _ _ sep__sep_points_lemma _ _)).
*)
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_Sum.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_Sum.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_Mesh.con".
+inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_Mesh.con" as lemma.
(* UNEXPORTED
End Separating__Separated
alias id "Hab" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab.var".
-inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/I.con" "Separating_Partition__".
+inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/I.con" "Separating_Partition__" as definition.
alias id "F" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/F.var".
alias id "Hcsi" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hcsi.var".
-inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/M.con" "Separating_Partition__".
+inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/M.con" "Separating_Partition__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_pos_n.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_pos_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/SPap_n.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/SPap_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/delta.con" "Separating_Partition__".
+inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/delta.con" "Separating_Partition__" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_pos.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_pos.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con" as lemma.
alias id "Hab''" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab''.var".
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_bnd.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_bnd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_1.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_2.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_3.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_mon_3.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_app_n.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_app_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma2.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma3.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_h_lemma3.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta2_delta4.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta2_delta4.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m1.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m1.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m.con" as definition.
(* NOTATION
Notation m := RS'_m.
*)
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_length.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_length.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m_m1.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_m_m1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_pos_m.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_pos_m.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_0.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_0.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_m.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_m.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i'.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_i'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd'.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_bnd'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_wd.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_wd.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon_pts.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_fun_mon_pts.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con" as lemma.
alias id "g" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/g.var".
alias id "gP'" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP'.var".
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts.con" as definition.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts_lemma.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts_in_Partition.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts_in_Partition.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_Hsep_S.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_Hsep_S.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_Hsep.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_Hsep.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_h.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_h.con" as definition.
(* NOTATION
Notation h := RS'_h.
(incF _ (Pts_part_lemma _ _ _ _ _ _ sep__part_pts_in_Partition _ _)).
*)
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_suRS'_m1.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_suRS'_m1.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum2.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum3.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum3.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum4.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum4.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_aux.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_aux.con" as lemma.
-inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum.con".
+inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_Sum.con" as lemma.
(* UNEXPORTED
End Separating_Partition
alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Rolle/Hab'.var".
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hab.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hab.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/I.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/I.con" "Rolle__" as definition.
alias id "F" = "cic:/CoRN/ftc/Rolle/Rolle/F.var".
alias id "He" = "cic:/CoRN/ftc/Rolle/Rolle/He.var".
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/contF'.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/contF'.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/derivF.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/derivF.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma2.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma2.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/df.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/df.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hdf.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hdf.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hf.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hf.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma3.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma3.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/df'.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/df'.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hdf'.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hdf'.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hf'.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hf'.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/d.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/d.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hd.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hd.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/incF.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/incF.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/n.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/n.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/fcp.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/fcp.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma1.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma1.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/incF'.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/incF'.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/fcp'.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/fcp'.con" "Rolle__" as definition.
(* NOTATION
Notation cp := (compact_part a b Hab' d Hd).
*)
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma4.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma4.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma5.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma5.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma6.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma6.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma7.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma7.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/j.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/j.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hj.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hj.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hj'.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hj'.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/k.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/k.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hk.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hk.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hk'.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hk'.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma8.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma8.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma9.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma9.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma10.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma10.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma11.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma11.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma12.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma12.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma13.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma13.con" "Rolle__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma15.con" "Rolle__".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma15.con" "Rolle__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle.con".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle.con" as theorem.
(* UNEXPORTED
End Rolle
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab.con" "Law_of_the_Mean__".
+inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab.con" "Law_of_the_Mean__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/I.con" "Law_of_the_Mean__".
+inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/I.con" "Law_of_the_Mean__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con".
+inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con" as lemma.
(* UNEXPORTED
End Law_of_the_Mean
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Rolle/Corollaries/Hab.con" "Corollaries__".
+inline procedural "cic:/CoRN/ftc/Rolle/Corollaries/Hab.con" "Corollaries__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Rolle/Rolle'.con".
+inline procedural "cic:/CoRN/ftc/Rolle/Rolle'.con" as theorem.
-inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con".
+inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con" as lemma.
(* UNEXPORTED
End Corollaries
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Rolle/Generalizations/incF.con" "Generalizations__".
+inline procedural "cic:/CoRN/ftc/Rolle/Generalizations/incF.con" "Generalizations__" as definition.
-inline procedural "cic:/CoRN/ftc/Rolle/Generalizations/incF'.con" "Generalizations__".
+inline procedural "cic:/CoRN/ftc/Rolle/Generalizations/incF'.con" "Generalizations__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean.con".
+inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean.con" as theorem.
(*#*
We further generalize the mean law by writing as an explicit bound.
*)
-inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con".
+inline procedural "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con" as theorem.
(* UNEXPORTED
End Generalizations
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I.con" "IVT'__".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I.con" "IVT'__" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I'.con" "IVT'__".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/I'.con" "IVT'__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/incF.con" "IVT'__".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/incF.con" "IVT'__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Ha.con" "IVT'__".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Ha.con" "IVT'__" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Hb.con" "IVT'__".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/Hb.con" "IVT'__" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/HFab'.con" "IVT'__".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/HFab'.con" "IVT'__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con" as lemma.
(* end hide *)
inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_aux_seq_type.ind".
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_iter.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_iter.con" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_I.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_I.con" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_I.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_I.con" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xa.con" "IVT'__".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xa.con" "IVT'__" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xb.con" "IVT'__".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'/xb.con" "IVT'__" as definition.
-inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_I.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_I.con" as lemma.
(* UNEXPORTED
End IVT'
theorem to more widely applicable forms.
*)
-inline procedural "cic:/CoRN/ftc/StrongIVT/Weak_IVT.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/Weak_IVT.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_inc.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_inc.con" as lemma.
(* UNEXPORTED
Transparent Min.
*)
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_dec.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT_dec.con" as lemma.
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_inc.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_inc.con" as lemma.
(* UNEXPORTED
Transparent Min.
*)
-inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_dec.con".
+inline procedural "cic:/CoRN/ftc/StrongIVT/IVT'_dec.con" as lemma.
(* begin show *)
-inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/deriv_Sn.con" "More_Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/deriv_Sn.con" "More_Taylor_Defs__" as definition.
(* end show *)
(* begin show *)
-inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/fi.con" "More_Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/fi.con" "More_Taylor_Defs__" as definition.
-inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/funct_i.con" "More_Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/funct_i.con" "More_Taylor_Defs__" as definition.
(* end show *)
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq'.con".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq'.con" as definition.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Taylor/TaylorB.con".
+inline procedural "cic:/CoRN/ftc/Taylor/TaylorB.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Rem.con".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Rem.con" as definition.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Sumx_lemma.con".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Sumx_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor_lemma_ap.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor'.con".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor'.con" as theorem.
(* UNEXPORTED
End More_Taylor_Defs
(* begin show *)
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/funct_i.con" "Taylor_Theorem__".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/funct_i.con" "Taylor_Theorem__" as definition.
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq.con".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/deriv_Sn.con" "Taylor_Theorem__".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor_Theorem/deriv_Sn.con" "Taylor_Theorem__" as definition.
(* end show *)
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor_aux.con".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor_aux.con" as lemma.
(* UNEXPORTED
Transparent N_Deriv.
*)
-inline procedural "cic:/CoRN/ftc/Taylor/Taylor.con".
+inline procedural "cic:/CoRN/ftc/Taylor/Taylor.con" as theorem.
(* UNEXPORTED
End Taylor_Theorem
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab'.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab'.con" "Taylor_Defs__" as definition.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab.con" "Taylor_Defs__" as definition.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/I.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/I.con" "Taylor_Defs__" as definition.
(* end hide *)
(* begin show *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/fi.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/fi.con" "Taylor_Defs__" as definition.
(* end show *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con" as lemma.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_a.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_a.con" "Taylor_Defs__" as definition.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_b.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_b.con" "Taylor_Defs__" as definition.
(* NOTATION
Notation A := (Build_subcsetoid_crr IR _ _ TL_compact_a).
(* begin show *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i.con" "Taylor_Defs__" as definition.
(* end show *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i'.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i'.con" "Taylor_Defs__" as definition.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_a_i.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_a_i.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_b_i.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_b_i.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_x_i.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_x_i.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con" as lemma.
(* end hide *)
Taylor sum of order [n].
*)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con" as definition.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Taylor_seq'_aux.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Taylor_seq'_aux.con" "Taylor_Defs__" as definition.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con" as lemma.
(* end hide *)
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 procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con" as definition.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g.con" "Taylor_Defs__" as definition.
(* UNEXPORTED
Opaque Taylor_seq'_aux Taylor_rem.
Opaque funct_i.
*)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con" as lemma.
(* UNEXPORTED
Transparent funct_i funct_i'.
Opaque funct_i'.
*)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con" as lemma.
(* UNEXPORTED
Transparent funct_i' FSumx.
*)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_aux.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_aux.con" "Taylor_Defs__" as definition.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con" as lemma.
(* UNEXPORTED
Ltac Lazy_Included :=
| apply csf_wd_unfolded ]; Algebra.
*)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con" as lemma.
(* UNEXPORTED
Opaque funct_aux.
Transparent funct_aux.
*)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con" as lemma.
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g'.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g'.con" "Taylor_Defs__" as definition.
(* UNEXPORTED
Opaque Taylor_rem funct_aux.
*)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con" as lemma.
(* UNEXPORTED
Transparent Taylor_rem funct_aux.
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con" as lemma.
(* end hide *)
(* begin show *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/deriv_Sn'.con" "Taylor_Defs__".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/deriv_Sn'.con" "Taylor_Defs__" as definition.
(* end show *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/TLH.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/TLH.con" as lemma.
(* end hide *)
Transparent Taylor_rem funct_aux.
*)
-inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con".
+inline procedural "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con" as lemma.
(* UNEXPORTED
End Taylor_Defs
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma1/I.con" "Lemma1__".
+inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma1/I.con" "Lemma1__" as definition.
(* end hide *)
enough to [z].
*)
-inline procedural "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con" as lemma.
(* UNEXPORTED
End Lemma1
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma2/I.con" "Lemma2__".
+inline procedural "cic:/CoRN/ftc/WeakIVT/Lemma2/I.con" "Lemma2__" as definition.
(* end hide *)
If [f(b) [<] f(a)], a similar result holds:
*)
-inline procedural "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con" as lemma.
(* UNEXPORTED
End Lemma2
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/I.con" "IVT__".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/I.con" "IVT__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/incF.con" "IVT__".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/incF.con" "IVT__" as definition.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/Ha.con" "IVT__".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/Ha.con" "IVT__" as definition.
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/Hb.con" "IVT__".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/Hb.con" "IVT__" as definition.
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/HFab'.con" "IVT__".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/HFab'.con" "IVT__" as definition.
(* end hide *)
and [x' [<=] z [<=] y'].
*)
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_seq_lemma.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_seq_lemma.con" as lemma.
(* end hide *)
inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_aux_seq_type.ind".
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_iter.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_iter.con" as definition.
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_seq.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_seq.con" as definition.
(*#*
We now define the sequences built from this iteration, starting with [a] and [b].
*)
-inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq.con" as definition.
-inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_I.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_I.con" as definition.
-inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_I.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_I.con" as definition.
-inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_less_b_seq.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_less_b_seq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_leEq_z.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_leEq_z.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/z_leEq_b_seq.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/z_leEq_b_seq.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_mon.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_mon.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_mon.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist_n.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist_n.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_dist.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_Cauchy.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_Cauchy.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/b_seq_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/xa.con" "IVT__".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/xa.con" "IVT__" as definition.
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/xb.con" "IVT__".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT/xb.con" "IVT__" as definition.
-inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_lim.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_lim.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/xa_in_interval.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/xa_in_interval.con" as lemma.
-inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_I.con".
+inline procedural "cic:/CoRN/ftc/WeakIVT/IVT_I.con" as lemma.
(* UNEXPORTED
End IVT
(*#* **Metric Space basics
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_CMetricSpace_apdiag_imp_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_CMetricSpace_apdiag_imp_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_zero_imp_eq.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con" as lemma.
(* UNEXPORTED
End MS_basics
The product of two metric spaces is again a metric space.
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpaces_apdiag_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpaces_apdiag_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Prod0CMetricSpace.con" as definition.
(*#*
A subspace of a metric space is again a metric space.
Implicit Arguments SubPsMetricSpace [X].
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace_apdiag_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace_apdiag_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/SubMetricSpace.con" as definition.
(* UNEXPORTED
Implicit Arguments SubMetricSpace [X].
Not all pseudo metric spaces are a metric space:
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/zf_nis_CMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/zf_nis_CMetricSpace.con" as lemma.
(*#*
But a pseudo metric space induces a metric space:
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_eq.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_eq.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_irreflexive.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_symmetric.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_cotransitive.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_cotransitive.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_tight.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_ap_tight.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSet_is_CSetoid.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSet_is_CSetoid.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSetoid.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_CSetoid.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d_strext.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/metric_d_strext.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_com.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_com.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_nneg.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_nneg.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_pos_imp_ap.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_pos_imp_ap.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_tri_ineq.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_tri_ineq.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCSetoid_is_CPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCSetoid_is_CPsMetricSpace.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCPsMetricSpace.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_apdiag_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Metric_d_apdiag_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/QuotientCMetricSpace.con" as definition.
(*#*
Some pseudo metric spaces already are a metric space:
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/dIR_apdiag_grzero.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/dIR_apdiag_grzero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/IR_as_CMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/IR_as_CMetricSpace.con" as definition.
(*#*
In that case the induced metric space is equivalent to the original one:
*)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb_strext.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/emb_strext.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Emb.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Emb.con" as definition.
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con" as lemma.
(* UNEXPORTED
End Zeroff
(* begin hide *)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/nz.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/nz.con" as lemma.
(* end hide *)
(* begin hide *)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_wd.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/d_wd.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con".
+inline procedural "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con" as lemma.
(* UNEXPORTED
End Limitt
the proofs a bit easier.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/MSmember.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/MSmember.con" as definition.
(* UNEXPORTED
Implicit Arguments MSmember [X].
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/to_IR.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/to_IR.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/from_IR.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/from_IR.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/list_IR.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/list_IR.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/is_P.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/is_P.con" as lemma.
(*#*
If a real number is element of a list in the above defined sense,
that uses the setoid equality.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/member1.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/member1.con" as lemma.
(*#*
The image under a certain mapping of an element of a list $l$ #<I>l</I># is member
of the list of images of elements of $l$ #<I>l</I>#.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/map_member.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/map_member.con" as lemma.
(* UNEXPORTED
End lists
(*#* **Pseudo Metric Space theory
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/Re_co_do.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/Re_co_do.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/Re_co_do_strext.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/Re_co_do_strext.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/re_co_do.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/re_co_do.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/re_co_do_well_def.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/re_co_do_well_def.con" as lemma.
(* UNEXPORTED
Implicit Arguments MSmember [X].
#<I>l</I># is member of the list of images of elements of $l$ #<I>l</I>#.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/map_member'.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/map_member'.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/bounded.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/bounded.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded.con" as definition.
(*#*
Total boundedness is preserved under uniformly continuous mappings.
Implicit Arguments SubPsMetricSpace [X].
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/unicon_resp_totallybounded.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/unicon_resp_totallybounded.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotallybounded_totallybounded.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotallybounded_totallybounded.con" as lemma.
(*#*
Every image under an uniformly continuous function of an totally bounded
pseudo metric space has an infimum and a supremum.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/infimum_exists.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/infimum_exists.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/supremum_exists.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/supremum_exists.con" as lemma.
(*#*
A subspace $P$#<I>P</I># of a pseudo metric space $X$#<I>X</I># is said to be located if for all
Implicit Arguments dsub'_as_cs_fun [X].
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/located.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/located.con" as definition.
(* UNEXPORTED
Implicit Arguments located [X].
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/located'.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/located'.con" as definition.
(* UNEXPORTED
Implicit Arguments located' [X].
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/located_imp_located'.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/located_imp_located'.con" as lemma.
(*#*
Every totally bounded pseudo metric space is located.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/MStotally_bounded_imp_located.con" as lemma.
(*#*
For all $x$#<I>x</I># in a pseudo metric space $X$#<I>X</I>#, for all located subspaces $P$#<I>P</I># of $X$#<I>X</I>#,
one to use the latter as an argument of [map].
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/Floc.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/Floc.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPMSTheory/Flocfun.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/Flocfun.con" as definition.
(*#*
A located subset $P$#<I>P</I># of a totally bounded pseudo metric space $X$
bounded.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/locatedsub_totallybounded_imp_totallyboundedsub.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/locatedsub_totallybounded_imp_totallyboundedsub.con" as lemma.
(*#*
Here are some definitions that could come in handy:
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/MSCauchy_seq.con" as definition.
(* UNEXPORTED
Implicit Arguments MSseqLimit' [X].
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/MSComplete.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/MSComplete.con" as definition.
(*#*
A compact pseudo metric space is a pseudo metric space which is complete and
totally bounded.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/MSCompact.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/MSCompact.con" as definition.
(*#*
A subset $P$#<I>P</I># is %\emph{open}%#<I>open</I># if for all $x$#<I>x</I># in $P$#<I>P</I># there exists an open sphere
with centre $x$#<I>x</I># that is contained in $P$#<I>P</I>#.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/open.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/open.con" as definition.
(* UNEXPORTED
Implicit Arguments open [X].
subspace $P$#<I>P</I># of $X$#<I>X</I>#.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/infima.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/infima.con" as definition.
(* UNEXPORTED
Implicit Arguments infima [X].
all points that are in some sense close to $P$#<I>P</I>#.
*)
-inline procedural "cic:/CoRN/metrics/CPMSTheory/well_contained.con".
+inline procedural "cic:/CoRN/metrics/CPMSTheory/well_contained.con" as definition.
(* UNEXPORTED
End loc_and_bound
Unset Strict Implicit.
*)
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/com.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/com.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/nneg.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/nneg.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/tri_ineq.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/tri_ineq.con" as definition.
(* UNEXPORTED
Set Strict Implicit.
Unset Implicit Arguments.
*)
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con" as definition.
(* UNEXPORTED
End Relations
alias id "A" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_axioms/A.var".
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_com.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_com.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_nneg.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_nneg.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_pos_imp_ap.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_pos_imp_ap.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con" as lemma.
(* UNEXPORTED
End PsMS_axioms
alias id "Y" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_basics/Y.var".
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con" as lemma.
(*#*
Instead of taking [pos_imp_ap] as axiom,
we could as well have taken [diag_zero].
*)
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero_imp_pos_imp_ap.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/diag_zero_imp_pos_imp_ap.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap_imp_diag_zero.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/pos_imp_ap_imp_diag_zero.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con" as lemma.
(* UNEXPORTED
End PsMS_basics
a pseudo metric space.
*)
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_strext.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_strext.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/Zero_fun.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/Zero_fun.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_com.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_com.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_nneg.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_nneg.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_pos_imp_ap.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_pos_imp_ap.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_tri_ineq.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zero_fun_tri_ineq.con" as lemma.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zf_is_CPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zf_is_CPsMetricSpace.con" as definition.
-inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con" as definition.
(* UNEXPORTED
End Zerof
We will look at some notions of continuous functions.
*)
-inline procedural "cic:/CoRN/metrics/ContFunctions/continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/continuous.con" as definition.
-inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'.con" as definition.
-inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous.con" as definition.
-inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'.con" as definition.
-inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous''.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous''.con" as definition.
-inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz.con" as definition.
-inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz'.con" as definition.
(* UNEXPORTED
End Continuous_functions
(* begin hide *)
-inline procedural "cic:/CoRN/metrics/ContFunctions/nexp_power.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/nexp_power.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/metrics/ContFunctions/continuous_imp_continuous'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/continuous_imp_continuous'.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'_imp_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'_imp_continuous.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_uni_continuous'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_uni_continuous'.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous''.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous'_imp_uni_continuous''.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_lipschitz'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_lipschitz'.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz'_imp_lipschitz.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz'_imp_lipschitz.con" as lemma.
(*#*
Every uniformly continuous function is continuous and
every Lipschitz function is uniformly continuous.
*)
-inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/uni_continuous_imp_continuous.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con" as lemma.
(* UNEXPORTED
End Lemmas
Hence it is uniformly continuous and continuous.
*)
-inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_lipschitz.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_lipschitz.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_uni_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_uni_continuous.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/id_is_continuous.con" as lemma.
(* UNEXPORTED
End Identity
alias id "X" = "cic:/CoRN/metrics/ContFunctions/Constant/X.var".
-inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_uni_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_uni_continuous.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con" as lemma.
(* UNEXPORTED
End Constant
alias id "g" = "cic:/CoRN/metrics/ContFunctions/Composition/g.var".
-inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_uni_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_uni_continuous.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con" as lemma.
(* UNEXPORTED
End Composition
(*#* **Limit
*)
-inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit.con" as definition.
(* UNEXPORTED
Implicit Arguments MSseqLimit [X].
*)
-inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit'.con" as definition.
(* UNEXPORTED
Implicit Arguments MSseqLimit' [X].
*)
-inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit_imp_MSseqLimit'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit_imp_MSseqLimit'.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit'_imp_MSseqLimit.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/MSseqLimit'_imp_MSseqLimit.con" as lemma.
-inline procedural "cic:/CoRN/metrics/ContFunctions/seqcontinuous'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/seqcontinuous'.con" as definition.
(* UNEXPORTED
Implicit Arguments seqcontinuous' [A B].
*)
-inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con".
+inline procedural "cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con" as lemma.
(* UNEXPORTED
End Limit
bijective, structure-preserving function between them.
*)
-inline procedural "cic:/CoRN/metrics/Equiv/equivalent_psmetric.con".
+inline procedural "cic:/CoRN/metrics/Equiv/equivalent_psmetric.con" as definition.
-inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry.con".
+inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry.con" as definition.
(* UNEXPORTED
Implicit Arguments isopsmetry [X Y].
*)
-inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry_imp_bij.con".
+inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry_imp_bij.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry_imp_lipschitz.con".
+inline procedural "cic:/CoRN/metrics/Equiv/isopsmetry_imp_lipschitz.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Equiv/id_is_isopsmetry.con".
+inline procedural "cic:/CoRN/metrics/Equiv/id_is_isopsmetry.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Equiv/comp_resp_isopsmetry.con".
+inline procedural "cic:/CoRN/metrics/Equiv/comp_resp_isopsmetry.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Equiv/inv_isopsmetry.con".
+inline procedural "cic:/CoRN/metrics/Equiv/inv_isopsmetry.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Equiv/MSequivalent.con".
+inline procedural "cic:/CoRN/metrics/Equiv/MSequivalent.con" as definition.
(*#*
Not all pseudo metric spaces are equivalent:
*)
-inline procedural "cic:/CoRN/metrics/Equiv/MSequivalent_discr.con".
+inline procedural "cic:/CoRN/metrics/Equiv/MSequivalent_discr.con" as lemma.
(* UNEXPORTED
End equivalent
The real numbers with the usual distance form a pseudo metric space.
*)
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR.con" as definition.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_dIR.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/bin_fun_strext_dIR.con" as lemma.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_as_CSetoid_fun.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_as_CSetoid_fun.con" as definition.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_nneg.con" as lemma.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_com.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_com.con" as lemma.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_pos_imp_ap.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_tri_ineq.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_tri_ineq.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/dIR_tri_ineq.con" as lemma.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_dIR_is_CPsMetricSpace.con" as definition.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con" as definition.
alias id "X" = "cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var".
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con" as lemma.
(*#*
A pseudo metric is Lipschitz. Hence it is uniformly continuous and continuous.
*)
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_lipschitz.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_lipschitz.con" as lemma.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_uni_continuous.con" as lemma.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con" as lemma.
(* UNEXPORTED
End Reals
Lipschitz/uniformly continuous/continuous.
*)
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_lipschitz.con" as lemma.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_uni_continuous.con" as lemma.
-inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con".
+inline procedural "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con" as lemma.
(* UNEXPORTED
End Addition
$\RR^{2}$ #IR<SUP>2</SUP># out of the metric of $\RR$ #IR#.
*)
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0.con" as definition.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0_strext.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dprod0_strext.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/d_prod0.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/d_prod0.con" as definition.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/prod0cpsmetricspace_is_CPsMetricSpace.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con" as definition.
(* UNEXPORTED
End prodpsmetrics
the pseudo metric on $X$ #X# restricted to $Y$ #Y#.
*)
-inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun.con" as definition.
(* UNEXPORTED
Implicit Arguments restr_bin_fun [X].
*)
-inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun'.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun'.con" as definition.
(* UNEXPORTED
Implicit Arguments restr_bin_fun' [X].
*)
-inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun_strext.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/restr_bin_fun_strext.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/Build_SubCSetoid_bin_fun.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/Build_SubCSetoid_bin_fun.con" as definition.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub.con" as definition.
(* UNEXPORTED
Implicit Arguments dsub [X].
*)
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_com.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_com.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_nneg.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_nneg.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_pos_imp_ap.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_pos_imp_ap.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_tri_ineq.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub_tri_ineq.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/is_SubPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/is_SubPsMetricSpace.con" as definition.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/SubPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/SubPsMetricSpace.con" as definition.
(* UNEXPORTED
Implicit Arguments SubPsMetricSpace [X].
*)
-inline procedural "cic:/CoRN/metrics/Prod_Sub/from_SubPsMetricSpace.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/from_SubPsMetricSpace.con" as definition.
(*#*
The function [dsub'] is used in the definition of %''located''% #"located"#.
pseudo metric space and a certain subspace.
*)
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'.con" as definition.
(* UNEXPORTED
Implicit Arguments dsub' [X].
*)
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_strext.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_strext.con" as lemma.
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_as_cs_fun.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_as_cs_fun.con" as definition.
(* UNEXPORTED
Implicit Arguments dsub'_as_cs_fun [X].
*)
-inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con".
+inline procedural "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con" as lemma.
(* UNEXPORTED
End subpsmetrics
The positive rational numbers form with the operation $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2# an abelian group.
*)
-inline procedural "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_is_CAbGroup.con".
+inline procedural "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_is_CAbGroup.con" as lemma.
-inline procedural "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_as_CAbGroup.con".
+inline procedural "cic:/CoRN/model/abgroups/QSposabgroup/Qpos_multdiv2_as_CAbGroup.con" as definition.
CAbGroup.
*)
-inline procedural "cic:/CoRN/model/abgroups/Qabgroup/Q_is_CAbGroup.con".
+inline procedural "cic:/CoRN/model/abgroups/Qabgroup/Q_is_CAbGroup.con" as lemma.
-inline procedural "cic:/CoRN/model/abgroups/Qabgroup/Q_as_CAbGroup.con".
+inline procedural "cic:/CoRN/model/abgroups/Qabgroup/Q_as_CAbGroup.con" as definition.
The positive rationals form with the multiplication a CAbgroup.
*)
-inline procedural "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_is_CAbGroup.con".
+inline procedural "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_is_CAbGroup.con" as definition.
-inline procedural "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_as_CAbGroup.con".
+inline procedural "cic:/CoRN/model/abgroups/Qposabgroup/Qpos_mult_as_CAbGroup.con" as definition.
(*#* **Example of an abelian group: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
*)
-inline procedural "cic:/CoRN/model/abgroups/Zabgroup/Z_is_CAbGroup.con".
+inline procedural "cic:/CoRN/model/abgroups/Zabgroup/Z_is_CAbGroup.con" as lemma.
-inline procedural "cic:/CoRN/model/abgroups/Zabgroup/Z_as_CAbGroup.con".
+inline procedural "cic:/CoRN/model/abgroups/Zabgroup/Z_as_CAbGroup.con" as definition.
(*#* The term [Z_as_CAbGroup] is of type [CAbGroup]. Hence we have proven that [Z] is a constructive Abelian group. *)
So, [Q] not only forms a ring, but even a field.
*)
-inline procedural "cic:/CoRN/model/fields/Qfield/Q_is_CField.con".
+inline procedural "cic:/CoRN/model/fields/Qfield/Q_is_CField.con" as lemma.
-inline procedural "cic:/CoRN/model/fields/Qfield/Q_as_CField.con".
+inline procedural "cic:/CoRN/model/fields/Qfield/Q_as_CField.con" as definition.
#(x,y) ↦ xy/2# a CGroup.
*)
-inline procedural "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_is_CGroup.con".
+inline procedural "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_is_CGroup.con" as lemma.
-inline procedural "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_as_CGroup.con".
+inline procedural "cic:/CoRN/model/groups/QSposgroup/Qpos_multdiv2_as_CGroup.con" as definition.
The rational numbers with addition form a group. The inverse function is taking the opposite.
*)
-inline procedural "cic:/CoRN/model/groups/Qgroup/Q_is_CGroup.con".
+inline procedural "cic:/CoRN/model/groups/Qgroup/Q_is_CGroup.con" as lemma.
-inline procedural "cic:/CoRN/model/groups/Qgroup/Q_as_CGroup.con".
+inline procedural "cic:/CoRN/model/groups/Qgroup/Q_as_CGroup.con" as definition.
The positive rational numbers form a multiplicative group.
*)
-inline procedural "cic:/CoRN/model/groups/Qposgroup/Qpos_is_CGroup.con".
+inline procedural "cic:/CoRN/model/groups/Qposgroup/Qpos_is_CGroup.con" as lemma.
-inline procedural "cic:/CoRN/model/groups/Qposgroup/Qpos_as_CGroup.con".
+inline procedural "cic:/CoRN/model/groups/Qposgroup/Qpos_as_CGroup.con" as definition.
(*#* **Example of a group: $\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
*)
-inline procedural "cic:/CoRN/model/groups/Zgroup/Z_is_CGroup.con".
+inline procedural "cic:/CoRN/model/groups/Zgroup/Z_is_CGroup.con" as lemma.
-inline procedural "cic:/CoRN/model/groups/Zgroup/Z_as_CGroup.con".
+inline procedural "cic:/CoRN/model/groups/Zgroup/Z_as_CGroup.con" as definition.
(*#* The term [Z_as_CGroup] is of type [CGroup]. Hence we have proven that [Z] is a constructive group. *)
Zero is an unit for the addition.
*)
-inline procedural "cic:/CoRN/model/monoids/Nmonoid/O_as_rht_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Nmonoid/O_as_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Nmonoid/O_as_lft_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Nmonoid/O_as_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Nmonoid/nat_is_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Nmonoid/nat_is_CMonoid.con" as definition.
(*#*
Whence we can define #<i>#%\emph{%the monoid of natural numbers%}%#</i>#:
*)
-inline procedural "cic:/CoRN/model/monoids/Nmonoid/nat_as_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Nmonoid/nat_as_CMonoid.con" as definition.
positive natural numbers.
*)
-inline procedural "cic:/CoRN/model/monoids/Nposmonoid/rhtunitNpos.con".
+inline procedural "cic:/CoRN/model/monoids/Nposmonoid/rhtunitNpos.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Nposmonoid/lftunitNpos.con".
+inline procedural "cic:/CoRN/model/monoids/Nposmonoid/lftunitNpos.con" as lemma.
(*#* So, the positive natural numbers with multiplication form a CMonoid.
*)
-inline procedural "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_is_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_as_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Nposmonoid/Nposmult_as_CMonoid.con" as definition.
↦ xy/2# on the positive rationals. So we have another monoid structure on the positive rational numbers.
*)
-inline procedural "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_rht_unit.con".
+inline procedural "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_lft_unit.con".
+inline procedural "cic:/CoRN/model/monoids/QSposmonoid/QTWOpos_is_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_is_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_as_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/QSposmonoid/Qpos_multdiv2_as_CMonoid.con" as definition.
The rational numbers form with addition a CMonoid. [QZERO] is the unit.
*)
-inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_rht_unit3.con".
+inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_rht_unit3.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_lft_unit3.con".
+inline procedural "cic:/CoRN/model/monoids/Qmonoid/ZEROQ_as_lft_unit3.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_is_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_as_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_as_CMonoid.con" as definition.
(*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
Also with multiplication Q forms a CMonoid. Here, the unit is [QONE].
*)
-inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_rht_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_lft_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Qmonoid/ONEQ_as_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_is_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_as_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Qmonoid/Q_mul_as_CMonoid.con" as definition.
One is the unit for multiplication on positive integers. Therefore the positive rational numbers together with the multiplication are a CMonoid.
*)
-inline procedural "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_rht_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_lft_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Qposmonoid/QONEpos_is_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_is_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_as_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Qposmonoid/Qpos_mult_as_CMonoid.con" as definition.
unit of monoid:
*)
-inline procedural "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_rht_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_lft_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Zmonoid/ZERO_as_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_is_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_as_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_as_CMonoid.con" as definition.
(*#* The term [Z_as_CMonoid] is of type [CMonoid]. Hence we have proven that [Z] is a constructive monoid.
the representation we have for integers.
*)
-inline procedural "cic:/CoRN/model/monoids/Zmonoid/ONE_as_rht_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Zmonoid/ONE_as_rht_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Zmonoid/ONE_as_lft_unit.con".
+inline procedural "cic:/CoRN/model/monoids/Zmonoid/ONE_as_lft_unit.con" as lemma.
-inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_mul_is_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_mul_is_CMonoid.con" as definition.
-inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_mul_as_CMonoid.con".
+inline procedural "cic:/CoRN/model/monoids/Zmonoid/Z_mul_as_CMonoid.con" as definition.
(*#* The term [Z_mul_as_CMonoid] is another term of type [CMonoid]. *)
There is no inverse function for the natural numbers with addition.
*)
-inline procedural "cic:/CoRN/model/non_examples/N_no_group/no_inverse_nat_plus.con".
+inline procedural "cic:/CoRN/model/non_examples/N_no_group/no_inverse_nat_plus.con" as lemma.
(*#* Hence they do not form a CGroup.
*)
-inline procedural "cic:/CoRN/model/non_examples/N_no_group/no_group_nat_plus.con".
+inline procedural "cic:/CoRN/model/non_examples/N_no_group/no_group_nat_plus.con" as lemma.
There is no inverse for multiplication on the positive natural numbers.
*)
-inline procedural "cic:/CoRN/model/non_examples/Npos_no_group/no_inverse_Nposmult.con".
+inline procedural "cic:/CoRN/model/non_examples/Npos_no_group/no_inverse_Nposmult.con" as lemma.
(*#* Hence the natural numbers with multiplication do not form a group.
*)
-inline procedural "cic:/CoRN/model/non_examples/Npos_no_group/no_group_Nposmult.con".
+inline procedural "cic:/CoRN/model/non_examples/Npos_no_group/no_group_Nposmult.con" as lemma.
There is no right unit for the addition on the positive natural numbers.
*)
-inline procedural "cic:/CoRN/model/non_examples/Npos_no_monoid/no_rht_unit_Npos.con".
+inline procedural "cic:/CoRN/model/non_examples/Npos_no_monoid/no_rht_unit_Npos.con" as lemma.
(*#* Therefore the set of positive natural numbers doesn't form a group with
addition.
*)
-inline procedural "cic:/CoRN/model/non_examples/Npos_no_monoid/no_monoid_Npos.con".
+inline procedural "cic:/CoRN/model/non_examples/Npos_no_monoid/no_monoid_Npos.con" as lemma.
[Q] is an archemaedian ordered field.
*)
-inline procedural "cic:/CoRN/model/ordfields/Qordfield/Qlt_is_strict_order.con".
+inline procedural "cic:/CoRN/model/ordfields/Qordfield/Qlt_is_strict_order.con" as definition.
-inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_is_COrdField.con".
+inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_is_COrdField.con" as definition.
-inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_as_COrdField.con".
+inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_as_COrdField.con" as definition.
-inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_is_archemaedian.con".
+inline procedural "cic:/CoRN/model/ordfields/Qordfield/Q_is_archemaedian.con" as theorem.
of the real numbers as Cauchy sequences of rationals.
*)
-inline procedural "cic:/CoRN/model/reals/Cauchy_IR/Cauchy_IR.con".
+inline procedural "cic:/CoRN/model/reals/Cauchy_IR/Cauchy_IR.con" as definition.
(*#* The term [Cauchy_IR] is of type [CReals]. *)
multiplication and it satisfies the distributive law, it is a ring.
*)
-inline procedural "cic:/CoRN/model/rings/Qring/Q_mult_plus_is_dist.con".
+inline procedural "cic:/CoRN/model/rings/Qring/Q_mult_plus_is_dist.con" as lemma.
-inline procedural "cic:/CoRN/model/rings/Qring/Q_is_CRing.con".
+inline procedural "cic:/CoRN/model/rings/Qring/Q_is_CRing.con" as definition.
-inline procedural "cic:/CoRN/model/rings/Qring/Q_as_CRing.con".
+inline procedural "cic:/CoRN/model/rings/Qring/Q_as_CRing.con" as definition.
(*#* The following lemmas are used in the proof that [Q] is Archimeadian.
*)
-inline procedural "cic:/CoRN/model/rings/Qring/injz_Nring.con".
+inline procedural "cic:/CoRN/model/rings/Qring/injz_Nring.con" as lemma.
-inline procedural "cic:/CoRN/model/rings/Qring/injZ_eq.con".
+inline procedural "cic:/CoRN/model/rings/Qring/injZ_eq.con" as lemma.
-inline procedural "cic:/CoRN/model/rings/Qring/nring_Q.con".
+inline procedural "cic:/CoRN/model/rings/Qring/nring_Q.con" as lemma.
The multiplication and the addition are distributive.
*)
-inline procedural "cic:/CoRN/model/rings/Zring/Z_mult_plus_is_dist.con".
+inline procedural "cic:/CoRN/model/rings/Zring/Z_mult_plus_is_dist.con" as lemma.
-inline procedural "cic:/CoRN/model/rings/Zring/Z_is_CRing.con".
+inline procedural "cic:/CoRN/model/rings/Zring/Z_is_CRing.con" as definition.
-inline procedural "cic:/CoRN/model/rings/Zring/Z_as_CRing.con".
+inline procedural "cic:/CoRN/model/rings/Zring/Z_as_CRing.con" as definition.
(*#* The term [Z_as_CRing] is of type [CRing]. Hence we have proven that [Z] is a constructive ring. *)
of the semigroup of the natural numbers with addition.
*)
-inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Npos_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Npos_as_CSemiGroup.con" as definition.
(*#* ***$\langle$#⟨#[Npos],[[*]]$\rangle$#⟩#
Also together with multiplication, the positive numbers form a semigroup.
*)
-inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_is_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_is_CSemiGroup.con" as lemma.
-inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/Npossemigroup/Nposmult_as_CSemiGroup.con" as definition.
(*#* Because addition is associative, the natural numbers form a CSemiGroup.
*)
-inline procedural "cic:/CoRN/model/semigroups/Nsemigroup/nat_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/Nsemigroup/nat_as_CSemiGroup.con" as definition.
$(x,y) \mapsto xy/2$#(x,y) ↦ xy/2# a CSemiGroup.
*)
-inline procedural "cic:/CoRN/model/semigroups/QSpossemigroup/Qpos_multdiv2_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/QSpossemigroup/Qpos_multdiv2_as_CSemiGroup.con" as definition.
The positive rationals form with the multiplication a CSemiGroup.
*)
-inline procedural "cic:/CoRN/model/semigroups/Qpossemigroup/Qpos_mult_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/Qpossemigroup/Qpos_mult_as_CSemiGroup.con" as definition.
***$\langle$#⟨#[Q],[[+]]$\rangle$#⟩#
*)
-inline procedural "cic:/CoRN/model/semigroups/Qsemigroup/Q_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/Qsemigroup/Q_as_CSemiGroup.con" as definition.
(*#* ***$\langle$#⟨#[Q],[[*]]$\rangle$#⟩#
*)
-inline procedural "cic:/CoRN/model/semigroups/Qsemigroup/Q_mul_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/Qsemigroup/Q_mul_as_CSemiGroup.con" as definition.
***$\langle$#⟨#[Z],[[+]]$\rangle$#⟩#
*)
-inline procedural "cic:/CoRN/model/semigroups/Zsemigroup/Z_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/Zsemigroup/Z_as_CSemiGroup.con" as definition.
(*#* The term [Z_as_CSemiGroup] is of type [CSemiGroup]. Hence we have proven that [Z] is a constructive semi-group. *)
(*#* ***$\langle$#⟨#[Z],[[*]]$\rangle$#⟩#
*)
-inline procedural "cic:/CoRN/model/semigroups/Zsemigroup/Z_mul_as_CSemiGroup.con".
+inline procedural "cic:/CoRN/model/semigroups/Zsemigroup/Z_mul_as_CSemiGroup.con" as definition.
natural numbers.
*)
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/NposP.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/NposP.con" as definition.
(*#* One and two are elements of it.
*)
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/ONEpos.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/ONEpos.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/TWOpos.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/TWOpos.con" as definition.
(*#* ***Addition and multiplication
Because addition and multiplication preserve positivity, we can define
them on this subsetoid.
*)
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con" as definition.
(*#* The addition has no right unit on this set.
*)
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con" as lemma.
(*#* And the multiplication doesn't have an inverse, because there can't be an
inverse for 2.
*)
-inline procedural "cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con".
+inline procedural "cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con" as lemma.
We will show that the natural numbers form a CSetoid.
*)
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_irreflexive.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_symmetric.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_cotransitive.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_cotransitive.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_tight.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_tight.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_is_apartness.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/ap_nat_is_apartness.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/nat_as_CSetoid.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/nat_as_CSetoid.con" as definition.
(*#* ***Addition
*)
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_wd.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_wd.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_strext.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_strext.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_bin_fun.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_bin_fun.con" as definition.
(*#* It is associative and commutative.
*)
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_assoc.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_assoc.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_commut.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/plus_is_commut.con" as lemma.
(*#* ***Multiplication
*)
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_strext.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_strext.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_as_bin_fun.con".
+inline procedural "cic:/CoRN/model/setoids/Nsetoid/mult_as_bin_fun.con" as definition.
rational numbers.
*)
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QposP.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QposP.con" as definition.
(*#* One, two and four are elements of it.
*)
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con" as definition.
(*#* ***Multiplication
As we have seen, multiplication preserves positivity, so we can restrict it
nice properties.
*)
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con" as lemma.
(*#* ***Inverse
We restrict the domain of the inverse to the set of positive rationals.
*)
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con" as definition.
(*#* The restricted inverse preserves positivity.
*)
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con" as lemma.
(*#* Now, we can also restrict the co-domain.
*)
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con" as definition.
(*#* This restricted inverse map appears a setoid function.
*)
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con" as definition.
(*#* ***Special multiplication and inverse
We define [multdiv2]: $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#.
*)
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con" as lemma.
(*#* And its inverse [multdiv4]: $x \mapsto 4/x$ #x ↦ 4/x#.
*)
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/mult4.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/mult4.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Qpossetoid/divmult4.con".
+inline procedural "cic:/CoRN/model/setoids/Qpossetoid/divmult4.con" as definition.
***Setoid
*)
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_irreflexive1.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_irreflexive1.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_symmetric1.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_symmetric1.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_cotransitive1.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_cotransitive1.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_tight1.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_tight1.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_is_apartness.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_is_apartness.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Q_as_CSetoid.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Q_as_CSetoid.con" as definition.
(*#* ***Addition
*)
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_wd.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_wd.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_strext1.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_strext1.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_bin_fun.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_bin_fun.con" as definition.
(*#* It is associative and commutative.
*)
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_assoc.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_assoc.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_commut1.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_commut1.con" as lemma.
(*#* ***Opposite
*)
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_wd.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_wd.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_strext.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_strext.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_is_fun.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_is_fun.con" as definition.
(*#* ***Multiplication
*)
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_wd.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_wd.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_strext1.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_strext1.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_bin_fun.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_bin_fun.con" as definition.
(*#* It is associative and commutative.
*)
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_assoc.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_assoc.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_commut.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_commut.con" as lemma.
(*#* ***Less-than
*)
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_strext.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_strext.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_is_CSetoid_relation.con".
+inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_is_CSetoid_relation.con" as definition.
*** [Z]
*)
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_irreflexive.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_irreflexive.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_cotransitive.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_cotransitive.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_is_apartness.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/ap_Z_is_apartness.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.con" as definition.
(*#* 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 procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_wd.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_wd.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.con" as definition.
(*#* What's more: the addition is also associative and commutative.
*)
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_assoc.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_assoc.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.con" as lemma.
(*#* ***Opposite
Taking the opposite of an integer is a setoid function.
*)
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_wd.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_wd.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.con" as definition.
(*#* ***Multiplication
Finally the multiplication is a setoid function and is associative and commutative.
*)
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_wd.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_wd.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_bin_fun.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_bin_fun.con" as definition.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con" as lemma.
-inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con".
+inline procedural "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con" as lemma.
as multiplication preserve the feature of being positive.
*)
-inline procedural "cic:/CoRN/model/structures/Npossec/plus_resp_Npos0.con".
+inline procedural "cic:/CoRN/model/structures/Npossec/plus_resp_Npos0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Npossec/Npos_is_suc.con".
+inline procedural "cic:/CoRN/model/structures/Npossec/Npos_is_suc.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Npossec/mult_resp_Npos0.con".
+inline procedural "cic:/CoRN/model/structures/Npossec/mult_resp_Npos0.con" as lemma.
A variant of [0_S] from the standard library
*)
-inline procedural "cic:/CoRN/model/structures/Nsec/S_O.con".
+inline procedural "cic:/CoRN/model/structures/Nsec/S_O.con" as lemma.
(*#* ***Apartness
*)
-inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat.con".
+inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat.con" as definition.
(* NOTATION
Infix "{#N}" := ap_nat (no associativity, at level 90).
*)
-inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con".
+inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con".
+inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con".
+inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con".
+inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con" as lemma.
(*#* ***Addition
*)
-inline procedural "cic:/CoRN/model/structures/Nsec/plus_strext0.con".
+inline procedural "cic:/CoRN/model/structures/Nsec/plus_strext0.con" as lemma.
(*#* There is no inverse for addition, because every candidate will fail for 2
*)
-inline procedural "cic:/CoRN/model/structures/Nsec/no_inverse0.con".
+inline procedural "cic:/CoRN/model/structures/Nsec/no_inverse0.con" as lemma.
(*#* ***Multiplication
*)
-inline procedural "cic:/CoRN/model/structures/Nsec/mult_strext0.con".
+inline procedural "cic:/CoRN/model/structures/Nsec/mult_strext0.con" as lemma.
One, two and four are all bigger than zero.
*)
-inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QONE.con".
+inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QONE.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QTWO.con".
+inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QTWO.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con".
+inline procedural "cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con" as lemma.
(*#* A positive rational is not zero.
*)
-inline procedural "cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con".
+inline procedural "cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con" as definition.
(*#* ***Multiplication
The product of two positive rationals is again positive.
*)
-inline procedural "cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con".
+inline procedural "cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con" as lemma.
(*#* ***Inverse
The inverse of a positive rational is again positive.
*)
-inline procedural "cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con".
+inline procedural "cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con" as lemma.
(*#* ***Special multiplication
Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y)
\mapsto 4/x$ #x ↦ 4/x#.
*)
-inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con".
+inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con".
+inline procedural "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con".
+inline procedural "cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con" as lemma.
inline procedural "cic:/CoRN/model/structures/Qsec/Q.ind".
-inline procedural "cic:/CoRN/model/structures/Qsec/Qeq.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qeq.con" as definition.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qap.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qap.con" as definition.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qlt.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qlt.con" as definition.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qplus.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qplus.con" as definition.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qmult.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qmult.con" as definition.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qopp.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qopp.con" as definition.
-inline procedural "cic:/CoRN/model/structures/Qsec/QZERO.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/QZERO.con" as definition.
-inline procedural "cic:/CoRN/model/structures/Qsec/QONE.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/QONE.con" as definition.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qinv.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qinv.con" as definition.
(* UNEXPORTED
End Q
(*#* ***Constants
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/QTWO.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/QTWO.con" as definition.
-inline procedural "cic:/CoRN/model/structures/Qsec/QFOUR.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/QFOUR.con" as definition.
(*#* ***Equality
Here we prove that [QONE] is #<i>#%\emph{%not equal%}%#</i># to [QZERO]:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/ONEQ_neq_ZEROQ.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/ONEQ_neq_ZEROQ.con" as theorem.
-inline procedural "cic:/CoRN/model/structures/Qsec/refl_Qeq.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/refl_Qeq.con" as theorem.
-inline procedural "cic:/CoRN/model/structures/Qsec/sym_Qeq.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/sym_Qeq.con" as theorem.
-inline procedural "cic:/CoRN/model/structures/Qsec/trans_Qeq.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/trans_Qeq.con" as theorem.
(*#*
The equality is decidable:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/dec_Qeq.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/dec_Qeq.con" as theorem.
(*#* ***Apartness
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Q_non_zero.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Q_non_zero.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_irreflexive0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_irreflexive0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_symmetric0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_symmetric0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_cotransitive0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_cotransitive0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_tight0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/ap_Q_tight0.con" as lemma.
(*#* ***Addition
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_simpl.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_simpl.con" as theorem.
(*#*
Addition is associative:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_assoc.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_assoc.con" as theorem.
(*#*
[QZERO] as the neutral element for addition:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/QZERO_right.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/QZERO_right.con" as theorem.
(*#*
Commutativity of addition:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_sym.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_sym.con" as theorem.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_strext0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_strext0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/ZEROQ_as_rht_unit0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/ZEROQ_as_rht_unit0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/ZEROQ_as_lft_unit0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/ZEROQ_as_lft_unit0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_is_commut0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_is_commut0.con" as lemma.
(*#* ***Opposite
[{-Q}] is a well defined unary operation:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qopp_simpl.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qopp_simpl.con" as lemma.
(*#*
The group equation for [{-Q}]
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_inverse_r.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_inverse_r.con" as theorem.
(*#* ***Multiplication
Next we shall prove the properties of multiplication. First we prove
that [{*Q}] is well-defined
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_simpl.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_simpl.con" as theorem.
(*#*
and it is associative:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_assoc.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_assoc.con" as theorem.
(*#*
[QONE] is the neutral element for multiplication:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_n_1.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_n_1.con" as theorem.
(*#*
The commutativity for [{*Q}]:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_sym.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_sym.con" as theorem.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_plus_distr_r.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_plus_distr_r.con" as theorem.
(*#*
And a property of multiplication which says if [x [~=] Zero] and [xy [=] Zero] then [y [=] Zero]:
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_eq.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_eq.con" as theorem.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_strext0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_strext0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/nonZero.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/nonZero.con" as lemma.
(*#* ***Inverse
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qinv_strext.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qinv_strext.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qinv_is_inv.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qinv_is_inv.con" as lemma.
(*#* ***Less-than
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_wd_right.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_wd_right.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_wd_left.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_wd_left.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_eq_gt_dec.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_eq_gt_dec.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_transitive_unfolded.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_transitive_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_strext_unfolded.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_strext_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_irreflexive_unfolded.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_irreflexive_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_antisymmetric_unfolded.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_is_antisymmetric_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_resp_Qlt.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qplus_resp_Qlt.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_resp_pos_Qlt.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qmult_resp_pos_Qlt.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_gives_apartness.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Qlt_gives_apartness.con" as lemma.
(*#* ***Miscellaneous
We consider the injection [inject_Z] from [Z] to [Q] as a coercion.
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/inject_Z.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/inject_Z.con" as definition.
(* COERCION
cic:/matita/CoRN-Procedural/model/structures/Qsec/inject_Z.con
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/injz_plus.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/injz_plus.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Qsec/injZ_One.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/injZ_One.con" as lemma.
(*#* We can always find a natural number that is bigger than a given rational
number.
*)
-inline procedural "cic:/CoRN/model/structures/Qsec/Q_is_archemaedian0.con".
+inline procedural "cic:/CoRN/model/structures/Qsec/Q_is_archemaedian0.con" as theorem.
We define the apartness as the negation of the Leibniz equality:
*)
-inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z.con" as definition.
(* NOTATION
Infix "{#Z}" := ap_Z (no associativity, at level 90).
(*#* Some properties of apartness:
*)
-inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con" as lemma.
(*#* ***Addition
Some properties of the addition. [Zplus] is also defined in the standard
library.
*)
-inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con" as lemma.
(*#* ***Multiplication
The multiplication is extensional:
*)
-inline procedural "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con" as lemma.
(*#* ***Miscellaneous
*)
-inline procedural "cic:/CoRN/model/structures/Zsec/Zpos.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/Zpos.con" as definition.
(* begin hide *)
(* end hide *)
-inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_pos.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_pos.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_neg.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_neg.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con" as lemma.
-inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con".
+inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con" as lemma.
alias id "SS" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var".
-inline procedural "cic:/CoRN/reals/Bridges_LUB/member.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/member.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/Pmember.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/Pmember.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/l_u_b.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/l_u_b.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/supremum.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/supremum.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/Psupremum.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/Psupremum.con" as definition.
(* the following definitions are not used in *)
(* this file but later we will need them *)
-inline procedural "cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/g_l_b.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/g_l_b.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/infimum.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/infimum.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con" as definition.
(* UNEXPORTED
End lub_definitions
alias id "located" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var".
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink23d.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink23d.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink13d.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink13d.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink24d.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink24d.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/Real_Interval.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/Real_Interval.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con" as lemma.
(* NOTATION
Notation "( p , q )" := (pairT p q).
*)
-inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/V_increase.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/V_increase.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/W_decrease.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/W_decrease.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con" as lemma.
(* These lemma are *very* similar to those in *)
(* Cauchy_rationals_approach_reals.v *)
-inline procedural "cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_W.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_W.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/U_V_upper.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/U_V_upper.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/U_W_lower.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/U_W_lower.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con" as lemma.
(* Two properties of exponentiation in COrdFields *)
-inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con" as lemma.
(* A consequence of Archimedean property - *)
(* the every basis of definition of e=lim(1+1/n)^n *)
-inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_V.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_V.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_W.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_W.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con".
+inline procedural "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con" as theorem.
(* UNEXPORTED
End upper_bound_sequence
(* This lemma comes from lemmas.v of Martijn Oostdijk *)
-inline procedural "cic:/CoRN/reals/Bridges_iso/le_witness_informative.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/le_witness_informative.con" as lemma.
(* UNEXPORTED
Section bridges_axioms_imply_ours
alias id "is_Archimedes" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/is_Archimedes.var".
-inline procedural "cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con" as lemma.
(* UNEXPORTED
Section proofs_in_TCS
*)
-inline procedural "cic:/CoRN/reals/Bridges_iso/leEq_geEq.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/leEq_geEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/glbp.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/glbp.con" as theorem.
(* UNEXPORTED
Section supremum
alias id "P" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P.var".
-inline procedural "cic:/CoRN/reals/Bridges_iso/inequality1.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/inequality1.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/inequality2.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/inequality2.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/inequality3.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/inequality3.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/inequality4.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/inequality4.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Hum.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Hum.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bound_tk1.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bound_tk1.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bound_tk2.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bound_tk2.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/trick.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/trick.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/trick'.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/trick'.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/up_bound_for_n_element.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/up_bound_for_n_element.con" as theorem.
-inline procedural "cic:/CoRN/reals/Bridges_iso/low_bound_for_n_element.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/low_bound_for_n_element.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/saghf.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/saghf.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Psaghf.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Psaghf.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/kaf.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/kaf.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pkaf.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pkaf.con" as lemma.
alias id "is_finite_P" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/is_finite_P.var".
-inline procedural "cic:/CoRN/reals/Bridges_iso/card.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/card.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pcard1.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pcard1.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/seq.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/seq.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pseq1.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pseq1.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pseq1_unfolded.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pseq1_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/indeks.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/indeks.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pindeks.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pindeks.con" as lemma.
alias id "is_onto_seq_P" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/is_onto_seq_P.var".
-inline procedural "cic:/CoRN/reals/Bridges_iso/P_is_inhabited.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/P_is_inhabited.con" as lemma.
(*
Lemma bounded_quantifier:(N:nat;phi,psi:nat->Prop)
Qed.
*)
-inline procedural "cic:/CoRN/reals/Bridges_iso/bounded_quantifier_informative.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bounded_quantifier_informative.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma1a.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma1a.con" as lemma.
alias id "P_is_strongly_extensional" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P_is_strongly_extensional.var".
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma1b.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma1b.con" as lemma.
(* UNEXPORTED
End supremum
Section Every_Cauchy_Sequence_is_bounded
*)
-inline procedural "cic:/CoRN/reals/Bridges_iso/seq2set.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/seq2set.con" as definition.
alias id "g" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g.var".
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/P.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/P.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/fin_is_fin.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/fin_is_fin.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/card_fin.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/card_fin.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/finite_seq.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/finite_seq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma2a.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma2a.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/sup.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/sup.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Psup.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Psup.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_proj1.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_proj1.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded1.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded1.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma2b.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_lemma2b.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/inf.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/inf.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_proj1.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_proj1.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded1.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded1.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2.con" as lemma.
(* I tried very much not to mention this lemma! *)
-inline procedural "cic:/CoRN/reals/Bridges_iso/sup_leEq.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/sup_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/inf_geEq.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/inf_geEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/tail_is_Cauchy.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/tail_is_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/tail_seq.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/tail_seq.con" as definition.
(* UNEXPORTED
End Every_Cauchy_Sequence_is_bounded
alias id "g" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g.var".
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/sup_tail.con" "bridges_axioms_imply_ours__proofs_in_TCS__".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/sup_tail.con" "bridges_axioms_imply_ours__proofs_in_TCS__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_leEq.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_is_Cauchy.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_is_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_as_Cauchy.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_as_Cauchy.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/L.con" "bridges_axioms_imply_ours__proofs_in_TCS__".
+inline procedural "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/L.con" "bridges_axioms_imply_ours__proofs_in_TCS__" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_decrease.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/sup_tail_decrease.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/L_less_sup_n.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/L_less_sup_n.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2_informative.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Psup_unfolded2_informative.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2_informative.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Pinf_unfolded2_informative.con" as lemma.
-inline procedural "cic:/CoRN/reals/Bridges_iso/convergent_subseq.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/convergent_subseq.con" as lemma.
(* very elegant proof almost as short as text version! *)
-inline procedural "cic:/CoRN/reals/Bridges_iso/lubp_gives_Cauchy.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/lubp_gives_Cauchy.con" as theorem.
(* UNEXPORTED
End proofs_in_TCS
*)
-inline procedural "cic:/CoRN/reals/Bridges_iso/Bridges_R_is_CReals.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Bridges_R_is_CReals.con" as definition.
-inline procedural "cic:/CoRN/reals/Bridges_iso/Bridges_R_as_CReals.con".
+inline procedural "cic:/CoRN/reals/Bridges_iso/Bridges_R_as_CReals.con" as definition.
(* UNEXPORTED
End bridges_axioms_imply_ours
Section basics
*)
-inline procedural "cic:/CoRN/reals/CMetricFields/MAbs_one.con".
+inline procedural "cic:/CoRN/reals/CMetricFields/MAbs_one.con" as lemma.
-inline procedural "cic:/CoRN/reals/CMetricFields/Hulp.con".
+inline procedural "cic:/CoRN/reals/CMetricFields/Hulp.con" as lemma.
-inline procedural "cic:/CoRN/reals/CMetricFields/MAbs_one_recip_one.con".
+inline procedural "cic:/CoRN/reals/CMetricFields/MAbs_one_recip_one.con" as lemma.
(* end hide *)
%\end{convention}%
*)
-inline procedural "cic:/CoRN/reals/CMetricFields/MCauchy_prop.con".
+inline procedural "cic:/CoRN/reals/CMetricFields/MCauchy_prop.con" as definition.
inline procedural "cic:/CoRN/reals/CMetricFields/MCauchySeq.ind".
cic:/matita/CoRN-Procedural/reals/CMetricFields/MCS_seq.con
*)
-inline procedural "cic:/CoRN/reals/CMetricFields/MseqLimit.con".
+inline procedural "cic:/CoRN/reals/CMetricFields/MseqLimit.con" as definition.
-inline procedural "cic:/CoRN/reals/CMetricFields/is_MCauchyCompl.con".
+inline procedural "cic:/CoRN/reals/CMetricFields/is_MCauchyCompl.con" as definition.
(* UNEXPORTED
End CMetric_Field_Cauchy
include "reals/RealFuncts.ma".
-inline procedural "cic:/CoRN/reals/CPoly_Contin/plus_op_contin.con".
+inline procedural "cic:/CoRN/reals/CPoly_Contin/plus_op_contin.con" as lemma.
-inline procedural "cic:/CoRN/reals/CPoly_Contin/mult_op_contin.con".
+inline procedural "cic:/CoRN/reals/CPoly_Contin/mult_op_contin.con" as lemma.
-inline procedural "cic:/CoRN/reals/CPoly_Contin/linear_op_contin.con".
+inline procedural "cic:/CoRN/reals/CPoly_Contin/linear_op_contin.con" as lemma.
-inline procedural "cic:/CoRN/reals/CPoly_Contin/cpoly_op_contin.con".
+inline procedural "cic:/CoRN/reals/CPoly_Contin/cpoly_op_contin.con" as lemma.
(* End_SpecReals *)
-inline procedural "cic:/CoRN/reals/CReals/Lim.con".
+inline procedural "cic:/CoRN/reals/CReals/Lim.con" as definition.
(* UNEXPORTED
Implicit Arguments Lim [IR].
The sequence defined by $x_n=\frac2{n+1}$#x(n)=2/(n+1)#.
*)
-inline procedural "cic:/CoRN/reals/CReals1/twice_inv_seq_Lim.con".
+inline procedural "cic:/CoRN/reals/CReals1/twice_inv_seq_Lim.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/twice_inv_seq.con".
+inline procedural "cic:/CoRN/reals/CReals1/twice_inv_seq.con" as definition.
(*#*
Next, we prove that the sequence of absolute values of a Cauchy
sequence is also Cauchy.
*)
-inline procedural "cic:/CoRN/reals/CReals1/Cauchy_Lim_abs.con".
+inline procedural "cic:/CoRN/reals/CReals1/Cauchy_Lim_abs.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/Cauchy_abs.con".
+inline procedural "cic:/CoRN/reals/CReals1/Cauchy_abs.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/Lim_abs.con".
+inline procedural "cic:/CoRN/reals/CReals1/Lim_abs.con" as lemma.
(* UNEXPORTED
End More_Cauchy_Props
alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Subsequences/mon_seq2.var".
-inline procedural "cic:/CoRN/reals/CReals1/unbnd_f.con".
+inline procedural "cic:/CoRN/reals/CReals1/unbnd_f.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/reals/CReals1/Subsequences/mon_F'.con" "Subsequences__".
+inline procedural "cic:/CoRN/reals/CReals1/Subsequences/mon_F'.con" "Subsequences__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/CReals1/conv_subseq_imp_conv_seq.con".
+inline procedural "cic:/CoRN/reals/CReals1/conv_subseq_imp_conv_seq.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/Cprop2_seq_imp_Cprop2_subseq.con".
+inline procedural "cic:/CoRN/reals/CReals1/Cprop2_seq_imp_Cprop2_subseq.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/conv_seq_imp_conv_subseq.con".
+inline procedural "cic:/CoRN/reals/CReals1/conv_seq_imp_conv_subseq.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con".
+inline procedural "cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con" as lemma.
(* UNEXPORTED
End Subsequences
alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/mon_seq2.var".
-inline procedural "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con".
+inline procedural "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con".
+inline procedural "cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con" as lemma.
(* UNEXPORTED
End Cauchy_Subsequences
Finally, we prove that [x[^]n] grows to infinity if [x [>] One].
*)
-inline procedural "cic:/CoRN/reals/CReals1/power_big'.con".
+inline procedural "cic:/CoRN/reals/CReals1/power_big'.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/power_big.con".
+inline procedural "cic:/CoRN/reals/CReals1/power_big.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/qi_yields_zero.con".
+inline procedural "cic:/CoRN/reals/CReals1/qi_yields_zero.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/qi_lim_zero.con".
+inline procedural "cic:/CoRN/reals/CReals1/qi_lim_zero.con" as lemma.
(* UNEXPORTED
End Properties_of_Exponentiation
(*#* *** [IR] has characteristic zero *)
-inline procedural "cic:/CoRN/reals/CReals1/char0_IR.con".
+inline procedural "cic:/CoRN/reals/CReals1/char0_IR.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/poly_apzero_IR.con".
+inline procedural "cic:/CoRN/reals/CReals1/poly_apzero_IR.con" as lemma.
-inline procedural "cic:/CoRN/reals/CReals1/poly_IR_extensional.con".
+inline procedural "cic:/CoRN/reals/CReals1/poly_IR_extensional.con" as lemma.
alias id "c" = "cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var".
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum0_c_exp.
*)
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum_c_exp.
(*#* The following formulation is often more useful if [c [<] 1]. *)
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum_c_exp'.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum_c_exp'.
Hint Resolve Sum0_c_exp Sum_c_exp Sum_c_exp': algebra.
*)
-inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_Sum0.con" as lemma.
-inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_sum.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/diff_is_sum.con" as lemma.
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_pres_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_less.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum_pres_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal.con" as lemma.
(* UNEXPORTED
Hint Resolve Sum0_comm_scal: algebra.
*)
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal.con" as lemma.
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_comm_scal'.con" as lemma.
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum_comm_scal'.con" as lemma.
-inline procedural "cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sumx_comm_scal'.con" as lemma.
-inline procedural "cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con".
+inline procedural "cic:/CoRN/reals/CSumsReals/Sum2_comm_scal'.con" as lemma.
(*#* ** [CReals] axioms *)
-inline procedural "cic:/CoRN/reals/CauchySeq/CReals_is_CReals.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/CReals_is_CReals.con" as lemma.
(*#* First properties which follow trivially from the axioms. *)
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_Cauchy.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Archimedes.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Archimedes.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Archimedes'.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Archimedes'.con" as lemma.
(*#* A stronger version, which often comes in useful. *)
-inline procedural "cic:/CoRN/reals/CauchySeq/str_Archimedes.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/str_Archimedes.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/CauchySeqR.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/CauchySeqR.con" as definition.
(* UNEXPORTED
End CReals_axioms
sometimes easier and program extraction much more efficient.
*)
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop1.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop1.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop2.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop2.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4.con" as definition.
(* UNEXPORTED
End Cauchy_Defs
The next lemma is equal to lemma [Lim_Cauchy]. *)
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_complete.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_complete.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/less_Lim_so_less_seq.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/less_Lim_so_less_seq.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_so_seq_less.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_so_seq_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_Lim_so_seq_less_seq.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_Lim_so_seq_less_seq.con" as lemma.
(*#* The next lemma follows from [less_Lim_so_less_seq] with [y := (y[+] (Lim seq)) [/]TwoNZ]. *)
-inline procedural "cic:/CoRN/reals/CauchySeq/less_Lim_so.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/less_Lim_so.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_so.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_less_so.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/leEq_seq_so_leEq_Lim.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/leEq_seq_so_leEq_Lim.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/str_leEq_seq_so_leEq_Lim.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/str_leEq_seq_so_leEq_Lim.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_leEq_Lim.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_leEq_Lim.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/seq_leEq_so_Lim_leEq.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/seq_leEq_so_Lim_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/str_seq_leEq_so_Lim_leEq.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/str_seq_leEq_so_Lim_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Limits_unique.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Limits_unique.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_wd.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_strext.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_strext.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap'.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap'.con" as lemma.
(* UNEXPORTED
End Inequalities
(*#* *** Equivalence of formulations of Cauchy *)
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop1_prop.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop1_prop.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop2_prop.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop2_prop.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3_prop2.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop3_prop2.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop2.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop2.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop3_prop.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq1.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq1.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop3.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop3.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop2.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop4_prop2.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop3.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop3.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop4_prop.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4_y.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq4_y.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq4.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq4.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2_y.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Build_CauchySeq2_y.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq2.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_CauchySeq2.con" as lemma.
(*#* Well definedness. *)
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop_wd.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_prop_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2_wd.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_prop2_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_wd'.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_wd'.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_unique.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_unique.con" as lemma.
(* UNEXPORTED
End Equiv_Cauchy
We begin by defining the constant sequence and proving that it is Cauchy with the expected limit.
*)
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_const.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_const.con" as definition.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_const.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_const.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_plus.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_plus.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_plus.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_plus.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_plus.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_plus.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_inv.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_inv.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_inv.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_inv.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_inv.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_inv.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_minus.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_minus.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_minus.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_minus.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_minus.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_minus.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_mult.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_Lim_mult.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_mult.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Cauchy_mult.con" as lemma.
-inline procedural "cic:/CoRN/reals/CauchySeq/Lim_mult.con".
+inline procedural "cic:/CoRN/reals/CauchySeq/Lim_mult.con" as lemma.
(* UNEXPORTED
End Cauchy_props
Notation "'R_COrdField''" := (R_COrdField F).
*)
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/inject_Q.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/inject_Q.con" as definition.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_eq.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_eq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_plus.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_plus.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_min.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_min.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_lt.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_lt.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_ap.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_ap.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_eq.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_eq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_less.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_le.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_le.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_leEq.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_AbsSmall.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_cancel_AbsSmall.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_One.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_One.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_nring'.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_nring'.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_nring.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_nring.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_mult.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_mult.con" as lemma.
(* UNEXPORTED
Opaque R_COrdField.
*)
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_div_three.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_div_three.con" as lemma.
(* UNEXPORTED
Transparent R_COrdField.
*)
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_n.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/ing_n.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R.con" as theorem.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/conv_modulus.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/conv_modulus.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_CReals/T.con" "R_CReals__".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_CReals/T.con" "R_CReals__" as definition.
(*#* We now assume our original field is archimedean and prove that the
resulting one is, too.
alias id "F_is_archemaedian" = "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F_is_archemaedian.var".
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con" as theorem.
(* begin hide *)
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_CReals/PT.con" "R_CReals__".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_CReals/PT.con" "R_CReals__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/modulus_property.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/modulus_property.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/modulus_property_2.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/modulus_property_2.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R_2.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/expand_Q_R_2.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/CS_seq_diagonal.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/CS_seq_diagonal.con" as lemma.
(*#* ** Cauchy Completeness
We can also define a limit operator.
*)
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/Q_dense_in_R.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/Q_dense_in_R.con" as lemma.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/LimR_CauchySeq.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/LimR_CauchySeq.con" as definition.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_complete.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_complete.con" as theorem.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_CReals.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_CReals.con" as definition.
-inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_as_CReals.con".
+inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_as_CReals.con" as definition.
(* UNEXPORTED
End R_CReals
alias id "b_a" = "cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var".
-inline procedural "cic:/CoRN/reals/IVT/a_mon'.con".
+inline procedural "cic:/CoRN/reals/IVT/a_mon'.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/b_mon'.con".
+inline procedural "cic:/CoRN/reals/IVT/b_mon'.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/a_b'.con".
+inline procedural "cic:/CoRN/reals/IVT/a_b'.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/intervals_cauchy.con".
+inline procedural "cic:/CoRN/reals/IVT/intervals_cauchy.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/reals/IVT/Nested_Intervals/a'.con" "Nested_Intervals__".
+inline procedural "cic:/CoRN/reals/IVT/Nested_Intervals/a'.con" "Nested_Intervals__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_limit.con".
+inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_limit.con" as lemma.
(*#* %\begin{convention}% Let [f] be a continuous real function.
%\end{convention}%
alias id "f_contin" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var".
-inline procedural "cic:/CoRN/reals/IVT/f_contin_pos.con".
+inline procedural "cic:/CoRN/reals/IVT/f_contin_pos.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/f_contin_neg.con".
+inline procedural "cic:/CoRN/reals/IVT/f_contin_neg.con" as lemma.
(*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *)
alias id "f_b" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var".
-inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con".
+inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con" as lemma.
(* UNEXPORTED
End Nested_Intervals
(* begin hide *)
-inline procedural "cic:/CoRN/reals/IVT/Bisection/Small.con" "Bisection__".
+inline procedural "cic:/CoRN/reals/IVT/Bisection/Small.con" "Bisection__" as definition.
-inline procedural "cic:/CoRN/reals/IVT/Bisection/lft.con" "Bisection__".
+inline procedural "cic:/CoRN/reals/IVT/Bisection/lft.con" "Bisection__" as definition.
-inline procedural "cic:/CoRN/reals/IVT/Bisection/rht.con" "Bisection__".
+inline procedural "cic:/CoRN/reals/IVT/Bisection/rht.con" "Bisection__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/IVT/a_lft.con".
+inline procedural "cic:/CoRN/reals/IVT/a_lft.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/rht_b.con".
+inline procedural "cic:/CoRN/reals/IVT/rht_b.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/lft_rht.con".
+inline procedural "cic:/CoRN/reals/IVT/lft_rht.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/smaller_lft.con".
+inline procedural "cic:/CoRN/reals/IVT/smaller_lft.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/smaller_rht.con".
+inline procedural "cic:/CoRN/reals/IVT/smaller_rht.con" as lemma.
(* UNEXPORTED
Hint Resolve smaller_lft smaller_rht: algebra.
*)
-inline procedural "cic:/CoRN/reals/IVT/Cbisect'.con".
+inline procedural "cic:/CoRN/reals/IVT/Cbisect'.con" as lemma.
(* UNEXPORTED
End Bisection
(* begin hide *)
-inline procedural "cic:/CoRN/reals/IVT/Bisect_Interval/Small.con" "Bisect_Interval__".
+inline procedural "cic:/CoRN/reals/IVT/Bisect_Interval/Small.con" "Bisect_Interval__" as definition.
(* end hide *)
inline procedural "cic:/CoRN/reals/IVT/bisect_interval.ind".
-inline procedural "cic:/CoRN/reals/IVT/Cbisect_exists.con".
+inline procedural "cic:/CoRN/reals/IVT/Cbisect_exists.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/bisect.con".
+inline procedural "cic:/CoRN/reals/IVT/bisect.con" as definition.
-inline procedural "cic:/CoRN/reals/IVT/bisect_prop.con".
+inline procedural "cic:/CoRN/reals/IVT/bisect_prop.con" as lemma.
(* UNEXPORTED
End Bisect_Interval
(* begin hide *)
-inline procedural "cic:/CoRN/reals/IVT/IVT_Op/Small.con" "IVT_Op__".
+inline procedural "cic:/CoRN/reals/IVT/IVT_Op/Small.con" "IVT_Op__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/IVT/interval_sequence.con".
+inline procedural "cic:/CoRN/reals/IVT/interval_sequence.con" as definition.
-inline procedural "cic:/CoRN/reals/IVT/IVT_Op/a_.con" "IVT_Op__".
+inline procedural "cic:/CoRN/reals/IVT/IVT_Op/a_.con" "IVT_Op__" as definition.
-inline procedural "cic:/CoRN/reals/IVT/IVT_Op/b_.con" "IVT_Op__".
+inline procedural "cic:/CoRN/reals/IVT/IVT_Op/b_.con" "IVT_Op__" as definition.
-inline procedural "cic:/CoRN/reals/IVT/intervals_smaller.con".
+inline procedural "cic:/CoRN/reals/IVT/intervals_smaller.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/intervals_small''.con".
+inline procedural "cic:/CoRN/reals/IVT/intervals_small''.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/intervals_small'.con".
+inline procedural "cic:/CoRN/reals/IVT/intervals_small'.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/intervals_small.con".
+inline procedural "cic:/CoRN/reals/IVT/intervals_small.con" as lemma.
-inline procedural "cic:/CoRN/reals/IVT/Civt_op.con".
+inline procedural "cic:/CoRN/reals/IVT/Civt_op.con" as lemma.
(* UNEXPORTED
End IVT_Op
(*#* ** IVT for polynomials *)
-inline procedural "cic:/CoRN/reals/IVT/Civt_poly.con".
+inline procedural "cic:/CoRN/reals/IVT/Civt_poly.con" as lemma.
(* UNEXPORTED
End IVT_Poly
require [a [<=] b], as we want to work only in nonempty intervals.
*)
-inline procedural "cic:/CoRN/reals/Intervals/compact.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact.con" as definition.
(*#*
%\begin{convention}% Let [a,b : IR] and [Hab : a [<=] b].
alias id "Hab" = "cic:/CoRN/reals/Intervals/Intervals/Hab.var".
-inline procedural "cic:/CoRN/reals/Intervals/compact_inc_lft.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_inc_lft.con" as lemma.
-inline procedural "cic:/CoRN/reals/Intervals/compact_inc_rht.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_inc_rht.con" as lemma.
-inline procedural "cic:/CoRN/reals/Intervals/compact_Min_lft.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_Min_lft.con" as lemma.
-inline procedural "cic:/CoRN/reals/Intervals/compact_Min_rht.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_Min_rht.con" as lemma.
(*#*
As we will be interested in taking functions with domain in a compact
interval, we want this predicate to be well defined.
*)
-inline procedural "cic:/CoRN/reals/Intervals/compact_wd.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_wd.con" as lemma.
(*#*
Also, it will sometimes be necessary to rewrite the endpoints of an interval.
*)
-inline procedural "cic:/CoRN/reals/Intervals/compact_wd'.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_wd'.con" as lemma.
(*#*
As we identify subsets with predicates, inclusion is simply implication.
returns the restriction $F|_P$# of F to P#.
*)
-inline procedural "cic:/CoRN/reals/Intervals/Frestr.con".
+inline procedural "cic:/CoRN/reals/Intervals/Frestr.con" as definition.
(* UNEXPORTED
End Intervals
Section More_Intervals
*)
-inline procedural "cic:/CoRN/reals/Intervals/included_refl'.con".
+inline procedural "cic:/CoRN/reals/Intervals/included_refl'.con" as lemma.
(*#* We prove some inclusions of compact intervals. *)
-inline procedural "cic:/CoRN/reals/Intervals/compact_map1.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_map1.con" as definition.
-inline procedural "cic:/CoRN/reals/Intervals/compact_map2.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_map2.con" as definition.
-inline procedural "cic:/CoRN/reals/Intervals/compact_map3.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_map3.con" as definition.
(* UNEXPORTED
End More_Intervals
Notice the use of lists for quantification.
*)
-inline procedural "cic:/CoRN/reals/Intervals/totally_bounded.con".
+inline procedural "cic:/CoRN/reals/Intervals/totally_bounded.con" as definition.
(*#*
This definition is classically, but not constructively, equivalent to
and that we defined compacts as we did.
*)
-inline procedural "cic:/CoRN/reals/Intervals/compact_is_totally_bounded.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_is_totally_bounded.con" as lemma.
(*#*
Suprema and infima will be needed throughout; we define them here both
for arbitrary subsets of [IR] and for images of functions.
*)
-inline procedural "cic:/CoRN/reals/Intervals/set_glb_IR.con".
+inline procedural "cic:/CoRN/reals/Intervals/set_glb_IR.con" as definition.
-inline procedural "cic:/CoRN/reals/Intervals/set_lub_IR.con".
+inline procedural "cic:/CoRN/reals/Intervals/set_lub_IR.con" as definition.
-inline procedural "cic:/CoRN/reals/Intervals/fun_image.con".
+inline procedural "cic:/CoRN/reals/Intervals/fun_image.con" as definition.
-inline procedural "cic:/CoRN/reals/Intervals/fun_glb_IR.con".
+inline procedural "cic:/CoRN/reals/Intervals/fun_glb_IR.con" as definition.
-inline procedural "cic:/CoRN/reals/Intervals/fun_lub_IR.con".
+inline procedural "cic:/CoRN/reals/Intervals/fun_lub_IR.con" as definition.
(* begin hide *)
-inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub.con" "Totally_Bounded__".
+inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub.con" "Totally_Bounded__" as definition.
-inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub_prop.con" "Totally_Bounded__".
+inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub_prop.con" "Totally_Bounded__" as definition.
(* end hide *)
The following are probably the most important results in this section.
*)
-inline procedural "cic:/CoRN/reals/Intervals/totally_bounded_has_lub.con".
+inline procedural "cic:/CoRN/reals/Intervals/totally_bounded_has_lub.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb.con" "Totally_Bounded__".
+inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb.con" "Totally_Bounded__" as definition.
-inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb_prop.con" "Totally_Bounded__".
+inline procedural "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb_prop.con" "Totally_Bounded__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con".
+inline procedural "cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con" as lemma.
(* UNEXPORTED
End Totally_Bounded
The following characterization of inclusion can be very useful:
*)
-inline procedural "cic:/CoRN/reals/Intervals/included_compact.con".
+inline procedural "cic:/CoRN/reals/Intervals/included_compact.con" as lemma.
(*#*
At several points in our future development of a theory we will need
(* begin hide *)
-inline procedural "cic:/CoRN/reals/Intervals/Compact/I.con" "Compact__".
+inline procedural "cic:/CoRN/reals/Intervals/Compact/I.con" "Compact__" as definition.
(* end hide *)
We start by finding a natural number [n] such that [(b[-]a) [/] n [<] e].
*)
-inline procedural "cic:/CoRN/reals/Intervals/compact_nat.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_nat.con" as definition.
(*#* Obviously such an [n] must be greater than zero.*)
-inline procedural "cic:/CoRN/reals/Intervals/pos_compact_nat.con".
+inline procedural "cic:/CoRN/reals/Intervals/pos_compact_nat.con" as lemma.
(*#*
We now define a sequence on [n] points in [[a,b]] by
prove that all of its points are really in that interval.
*)
-inline procedural "cic:/CoRN/reals/Intervals/compact_part.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_part.con" as definition.
-inline procedural "cic:/CoRN/reals/Intervals/compact_part_hyp.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_part_hyp.con" as lemma.
(*#*
This sequence is strictly increasing and each two consecutive points
are apart by less than [e].*)
-inline procedural "cic:/CoRN/reals/Intervals/compact_less.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/Intervals/compact_leEq.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_leEq.con" as lemma.
(*#* When we proceed to integration, this lemma will also be useful: *)
-inline procedural "cic:/CoRN/reals/Intervals/compact_partition_lemma.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_partition_lemma.con" as lemma.
(*#* The next lemma provides an upper bound for the distance between two points in an interval: *)
-inline procedural "cic:/CoRN/reals/Intervals/compact_elements.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_elements.con" as lemma.
(* UNEXPORTED
Opaque Min Max.
(*#* The following is a variation on the previous lemma: *)
-inline procedural "cic:/CoRN/reals/Intervals/compact_elements'.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_elements'.con" as lemma.
(*#* 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 procedural "cic:/CoRN/reals/Intervals/compact_bnd_AbsIR.con".
+inline procedural "cic:/CoRN/reals/Intervals/compact_bnd_AbsIR.con" as lemma.
(*#* 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 procedural "cic:/CoRN/reals/Intervals/included2_compact.con".
+inline procedural "cic:/CoRN/reals/Intervals/included2_compact.con" as lemma.
-inline procedural "cic:/CoRN/reals/Intervals/included3_compact.con".
+inline procedural "cic:/CoRN/reals/Intervals/included3_compact.con" as lemma.
(* UNEXPORTED
End Compact
alias id "y" = "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/y.var".
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq.con" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq_char.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq_char.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Cauchy_Max_seq.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Cauchy_Max_seq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_CauchySeq.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_CauchySeq.con" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX.con" as definition.
(*#*
Constructively, the elementary properties of the maximum function are:
(So [Max] is [MAX] coupled with some proofs.)
*)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/lft_leEq_MAX.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/lft_leEq_MAX.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/rht_leEq_MAX.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/rht_leEq_MAX.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con" as lemma.
(* UNEXPORTED
End Max_function
*)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX_strext.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX_strext.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX_wd.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/MAX_wd.con" as lemma.
(* UNEXPORTED
Section properties_of_Max
(*#* *** Maximum *)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max.con" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_wd_unfolded.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_wd_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/lft_leEq_Max.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/lft_leEq_Max.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/rht_leEq_Max.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/rht_leEq_Max.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/less_Max_imp.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/less_Max_imp.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_leEq.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_less.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_max.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_max.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_id.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_id.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_comm.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_comm.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Max_is_rht.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Max_is_rht.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_is_rht_imp_leEq.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_is_rht_imp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_minus_eps_leEq.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_minus_eps_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/max_one_ap_zero.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/max_one_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/pos_max_one.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/pos_max_one.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con" as lemma.
(* UNEXPORTED
End properties_of_Max
[Min(x,y) [=] [--]Max( [--]x,[--]y)].
*)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN.con" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN_wd.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN_strext.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/MIN_strext.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min.con" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_wd_unfolded.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_wd_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_strext_unfolded.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_strext_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_lft.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_lft.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_rht.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_rht.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_imp.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_imp.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_Min.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_Min.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/less_Min.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/less_Min.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_min.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_min.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_id.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_id.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_comm.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_comm.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Min_is_lft.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Min_is_lft.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_is_lft_imp_leEq.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_is_lft_imp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con" as lemma.
alias id "a" = "cic:/CoRN/reals/Max_AbsIR/Minimum/a.var".
alias id "b" = "cic:/CoRN/reals/Max_AbsIR/Minimum/b.var".
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max'.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max'.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min3_leEq_Max3.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min3_leEq_Max3.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_Max.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_Max.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/ap_imp_Min_less_Max.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/ap_imp_Min_less_Max.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con" as lemma.
(* UNEXPORTED
End Minimum
(*#* *** Absolute value *)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR.con" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR_strext.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR_strext.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR_wd.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/ABSIR_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR.con" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wd.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdl.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdl.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdr.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdr.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIRz_isz.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIRz_isz.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_nonneg.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_pos.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_pos.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_cancel_ap_zero.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_cancel_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_resp_ap_zero.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_resp_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_AbsIR.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_AbsIR.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/inv_leEq_AbsIR.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/inv_leEq_AbsIR.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_e.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_e.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_imp_AbsIR.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_imp_AbsIR.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_AbsSmall.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_AbsSmall.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_imp_AbsSmall.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_imp_AbsSmall.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_transitive.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsSmall_transitive.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/zero_less_AbsIR_plus_one.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/zero_less_AbsIR_plus_one.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_inv.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_inv.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_minus.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_minus.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_x.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_x.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_inv_x.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_inv_x.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/less_AbsIR.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/less_AbsIR.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_distr_AbsIR.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/leEq_distr_AbsIR.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_approach_zero.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_approach_zero.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_zero.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_zero.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Abs_Max.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Abs_Max.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_str_bnd.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_str_bnd.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con" as lemma.
(* UNEXPORTED
End Absolute
(* begin hide *)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/P.con" "Part_Function_Max__".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/P.con" "Part_Function_Max__" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/Q.con" "Part_Function_Max__".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/Q.con" "Part_Function_Max__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/part_function_Max_strext.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/part_function_Max_strext.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/FMax.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/FMax.con" as definition.
(* UNEXPORTED
End Part_Function_Max
(* begin hide *)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/P.con" "Part_Function_Abs__".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/P.con" "Part_Function_Abs__" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/Q.con" "Part_Function_Abs__".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/Q.con" "Part_Function_Abs__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/FMin.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/FMin.con" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs.con" as definition.
(* UNEXPORTED
Opaque Max.
*)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/FMin_char.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/FMin_char.con" as lemma.
(* UNEXPORTED
Transparent Max.
*)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_char.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_char.con" as lemma.
(* UNEXPORTED
End Part_Function_Abs
Hint Resolve FAbs_char: algebra.
*)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_char'.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_char'.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_nonneg.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/FAbs_nonneg.con" as lemma.
(* UNEXPORTED
Hint Resolve FAbs_char': algebra.
(* begin hide *)
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/P.con" "Inclusion__".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/P.con" "Inclusion__" as definition.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/Q.con" "Inclusion__".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/Inclusion/Q.con" "Inclusion__" as definition.
(* end hide *)
alias id "R" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/R.var".
-inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax'.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax'.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax''.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax''.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin'.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin'.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin''.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMin''.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FAbs.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FAbs.con" as lemma.
-inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con".
+inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con" as lemma.
(* UNEXPORTED
End Inclusion
(* begin hide *)
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot/p.con" "NRoot__".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot/p.con" "NRoot__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/NRootIR/CnrootIR.con".
+inline procedural "cic:/CoRN/reals/NRootIR/CnrootIR.con" as lemma.
(* UNEXPORTED
End NRoot
Section Nth_Root
*)
-inline procedural "cic:/CoRN/reals/NRootIR/nroot.con".
+inline procedural "cic:/CoRN/reals/NRootIR/nroot.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot.con" as definition.
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_power.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_power.con" as lemma.
(* UNEXPORTED
Hint Resolve NRoot_power: algebra.
*)
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_nonneg.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_pos.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_pos.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_power'.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_power'.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_pres_less.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_pres_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_less_one.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_less_one.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_cancel.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_cancel.con" as lemma.
(*#* %\begin{convention}% Let [x,y] be nonnegative real numbers.
%\end{convention}% *)
alias id "Hy" = "cic:/CoRN/reals/NRootIR/Nth_Root/Hy.var".
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_wd.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_unique.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_unique.con" as lemma.
(* UNEXPORTED
End Nth_Root
Hint Resolve NRoot_power NRoot_power': algebra.
*)
-inline procedural "cic:/CoRN/reals/NRootIR/NRoot_resp_leEq.con".
+inline procedural "cic:/CoRN/reals/NRootIR/NRoot_resp_leEq.con" as lemma.
(*#**********************************)
(*#* ** Square root *)
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt.con" as definition.
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_sqr.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_sqr.con" as lemma.
(* UNEXPORTED
Hint Resolve sqrt_sqr: algebra.
*)
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_nonneg.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_wd.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_wd.con" as lemma.
(* UNEXPORTED
Hint Resolve sqrt_wd: algebra_c.
*)
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_to_nonneg.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_to_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_to_nonpos.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_to_nonpos.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_mult.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_mult.con" as lemma.
(* UNEXPORTED
Hint Resolve sqrt_mult: algebra.
*)
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_mult_wd.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_mult_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_less.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_less'.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_less'.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_resp_leEq.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/sqrt_resp_less.con".
+inline procedural "cic:/CoRN/reals/NRootIR/sqrt_resp_less.con" as lemma.
(* UNEXPORTED
End Square_root
values in [IR].
*)
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_sqrt_sqr.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_sqrt_sqr.con" as lemma.
(* UNEXPORTED
Hint Resolve AbsIR_sqrt_sqr: algebra.
*)
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_resp_mult.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_resp_mult.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos'.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_mult_pos'.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_nexp.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_nexp.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_nexp_op.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_nexp_op.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_less_square.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_less_square.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_leEq_square.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_leEq_square.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_division.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_division.con" as lemma.
(*#* Some special cases. *)
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_recip.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_recip.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_div_two.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_div_two.con" as lemma.
(*#* Cauchy-Schwartz for IR and variants on that subject. *)
-inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR.con".
+inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/triangle_SumIR.con".
+inline procedural "cic:/CoRN/reals/NRootIR/triangle_SumIR.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR_minus.con".
+inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR_minus.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/weird_triangleIR.con".
+inline procedural "cic:/CoRN/reals/NRootIR/weird_triangleIR.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR_minus'.con".
+inline procedural "cic:/CoRN/reals/NRootIR/triangle_IR_minus'.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/triangle_SumxIR.con".
+inline procedural "cic:/CoRN/reals/NRootIR/triangle_SumxIR.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/triangle_Sum2IR.con".
+inline procedural "cic:/CoRN/reals/NRootIR/triangle_Sum2IR.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_str_bnd_AbsIR.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_str_bnd_AbsIR.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_bnd_AbsIR.con".
+inline procedural "cic:/CoRN/reals/NRootIR/AbsIR_bnd_AbsIR.con" as lemma.
(* UNEXPORTED
End Absolute_Props
Cauchy sequence.
*)
-inline procedural "cic:/CoRN/reals/NRootIR/Cauchy_Lim_recip.con".
+inline procedural "cic:/CoRN/reals/NRootIR/Cauchy_Lim_recip.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/Cauchy_recip.con".
+inline procedural "cic:/CoRN/reals/NRootIR/Cauchy_recip.con" as lemma.
-inline procedural "cic:/CoRN/reals/NRootIR/Lim_recip.con".
+inline procedural "cic:/CoRN/reals/NRootIR/Lim_recip.con" as lemma.
(* UNEXPORTED
End Consequences
(* begin hide *)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/Cbigger.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/Cbigger.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_big.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/cpoly_pos.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con" as lemma.
(* UNEXPORTED
End CPoly_Big
(* begin hide *)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip.con" as definition.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_poly.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_coefficient.con" as lemma.
(* UNEXPORTED
Hint Resolve flip_coefficient: algebra.
*)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con" as lemma.
(* UNEXPORTED
End Flip_Poly
(* begin hide *)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_pos'.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con" as lemma.
(* UNEXPORTED
End OddPoly_Signs
(* begin hide *)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_aux.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm.con" as definition.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_monic.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con" as lemma.
(* UNEXPORTED
End Poly_Norm
(*#* ** Roots of polynomials of odd degree
Polynomials of odd degree over the reals always have a root. *)
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root'.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/oddpoly_root.con" as lemma.
-inline procedural "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con".
+inline procedural "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con" as lemma.
(* UNEXPORTED
End OddPoly_Root
(*#***** Opaque_algebra.v will be loaded in line 151 ******)
-inline procedural "cic:/CoRN/reals/Q_dense/or_not_and.con".
+inline procedural "cic:/CoRN/reals/Q_dense/or_not_and.con" as lemma.
(* UNEXPORTED
Section Interval_definition
cic:/matita/CoRN-Procedural/reals/Q_dense/pair_crr.con
*)
-inline procedural "cic:/CoRN/reals/Q_dense/Length.con".
+inline procedural "cic:/CoRN/reals/Q_dense/Length.con" as definition.
(* UNEXPORTED
End Interval_definition
*)
-inline procedural "cic:/CoRN/reals/Q_dense/Rat_Interval.con".
+inline procedural "cic:/CoRN/reals/Q_dense/Rat_Interval.con" as definition.
(* we have this in Q_COrdField... *)
-inline procedural "cic:/CoRN/reals/Q_dense/Qlt_eq_gt_dec'.con".
+inline procedural "cic:/CoRN/reals/Q_dense/Qlt_eq_gt_dec'.con" as lemma.
(*
Lemma ex_informative_on_Q:(P:Q_as_COrdField->Prop)(Ex [q:Q_as_COrdField](P q))
alias id "OF" = "cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var".
-inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con".
+inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_neg_reflexive.con".
+inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_neg_reflexive.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con".
+inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con" as lemma.
(* UNEXPORTED
End COrdField_extra
alias id "R1" = "cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var".
-inline procedural "cic:/CoRN/reals/Q_dense/start_l.con".
+inline procedural "cic:/CoRN/reals/Q_dense/start_l.con" as definition.
-inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence2.con".
+inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence2.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/start_r.con".
+inline procedural "cic:/CoRN/reals/Q_dense/start_r.con" as definition.
-inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence_property.con".
+inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence_property.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/l_less_r.con".
+inline procedural "cic:/CoRN/reals/Q_dense/l_less_r.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/shrink23.con".
+inline procedural "cic:/CoRN/reals/Q_dense/shrink23.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/shrink13.con".
+inline procedural "cic:/CoRN/reals/Q_dense/shrink13.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/shrink24.con".
+inline procedural "cic:/CoRN/reals/Q_dense/shrink24.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze.con".
+inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze.con" as definition.
-inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze_strong.con".
+inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze_strong.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/trichotomy.con".
+inline procedural "cic:/CoRN/reals/Q_dense/trichotomy.con" as definition.
-inline procedural "cic:/CoRN/reals/Q_dense/trichotomy_strong1.con".
+inline procedural "cic:/CoRN/reals/Q_dense/trichotomy_strong1.con" as lemma.
(* NOTATION
Notation "( A , B )" := (pairT A B).
*)
-inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans.con".
+inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans.con" as definition.
-inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans_strong.con".
+inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans_strong.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/Intrvl.con".
+inline procedural "cic:/CoRN/reals/Q_dense/Intrvl.con" as definition.
-inline procedural "cic:/CoRN/reals/Q_dense/G.con".
+inline procedural "cic:/CoRN/reals/Q_dense/G.con" as definition.
(* UNEXPORTED
Opaque Q_as_CField.
*)
-inline procedural "cic:/CoRN/reals/Q_dense/delta_Intrvl.con".
+inline procedural "cic:/CoRN/reals/Q_dense/delta_Intrvl.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/Length_Intrvl.con".
+inline procedural "cic:/CoRN/reals/Q_dense/Length_Intrvl.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_l_n.con".
+inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_l_n.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_r_n.con".
+inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_r_n.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_lower.con".
+inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_lower.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_upper.con".
+inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_upper.con" as lemma.
(* UNEXPORTED
Opaque Q_as_COrdField.
*)
-inline procedural "cic:/CoRN/reals/Q_dense/a_simple_inequality.con".
+inline procedural "cic:/CoRN/reals/Q_dense/a_simple_inequality.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate2.con".
+inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate2.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_G.con".
+inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_G.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/G_as_CauchySeq.con".
+inline procedural "cic:/CoRN/reals/Q_dense/G_as_CauchySeq.con" as definition.
-inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_inj_Q_G.con".
+inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_inj_Q_G.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/inj_Q_G_as_CauchySeq.con".
+inline procedural "cic:/CoRN/reals/Q_dense/inj_Q_G_as_CauchySeq.con" as definition.
-inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_l.con".
+inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_l.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_r.con".
+inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_r.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate_resp_x.con".
+inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate_resp_x.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con".
+inline procedural "cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con" as lemma.
(* UNEXPORTED
End Rational_sequence
(* begin hide *)
-inline procedural "cic:/CoRN/reals/Q_in_CReals/CReals_is_CReals.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/CReals_is_CReals.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/Lim_Cauchy.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/Lim_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/Archimedes.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/Archimedes.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/Archimedes'.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/Archimedes'.con" as lemma.
(*#**************************************)
To define the injection we need one elemntary lemma about the denominator:
*)
-inline procedural "cic:/CoRN/reals/Q_in_CReals/den_is_nonzero.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/den_is_nonzero.con" as lemma.
(*#* 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 procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q.con" as definition.
(*#* Next we need some properties of [nring], on the setoid of natural numbers: *)
-inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_strext.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_strext.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_wd.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_eq.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_eq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_leEq.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/nring_leEq.con" as lemma.
(* begin hide *)
(*#* Similarly we prove some properties of [zring] on the ring of integers: *)
-inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_strext.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_strext.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_wd.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_less.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/zring_less.con" as lemma.
(*#* 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 procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_strext.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_strext.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_wd.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_plus.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_plus.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_mult.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_mult.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_less.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/less_inj_Q.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/less_inj_Q.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/leEq_inj_Q.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/leEq_inj_Q.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_leEq.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_min.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_min.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_minus.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_minus.con" as lemma.
(*#* Moreover, and as expected, the [AbsSmall] predicate is also
preserved under the [inj_Q] *)
-inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_AbsSmall.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_AbsSmall.con" as lemma.
-inline procedural "cic:/CoRN/reals/Q_in_CReals/AbsSmall_inj_Q.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/AbsSmall_inj_Q.con" as lemma.
(*#* ** 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 procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_Cauchy.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_Cauchy.con" as theorem.
(*#* 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 procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_nring.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/inj_Q_nring.con" as lemma.
(*#* ** Injection of [Q] is dense
Finally we are able to prove the density of image of [Q] in [R1]. We
trisection" argument, which is ubiquitous in constructive analysis.
*)
-inline procedural "cic:/CoRN/reals/Q_in_CReals/start_of_sequence.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/start_of_sequence.con" as theorem.
(*#* 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 procedural "cic:/CoRN/reals/Q_in_CReals/Q_dense_in_CReals.con".
+inline procedural "cic:/CoRN/reals/Q_in_CReals/Q_dense_in_CReals.con" as lemma.
(* UNEXPORTED
End Rational_sequence_prelogue
(* This comes from CReals1.v *)
-inline procedural "cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con".
+inline procedural "cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con" as definition.
(* UNEXPORTED
Section morphism
alias id "g2" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g2.var".
-inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_relation.con".
+inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_relation.con" as definition.
-inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_un_fun.con".
+inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_un_fun.con" as definition.
-inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_bin_fun.con".
+inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_bin_fun.con" as definition.
(*
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 procedural "cic:/CoRN/reals/R_morphism/fun_pres_Lim.con".
+inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_Lim.con" as definition.
(* UNEXPORTED
End morphism_details
).
*****************)
-inline procedural "cic:/CoRN/reals/R_morphism/map_strext_unfolded.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_strext_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_wd_unfolded.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_wd_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_less_unfolded.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_less_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_plus_unfolded.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_plus_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_mult_unfolded.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_mult_unfolded.con" as lemma.
(* Now we start to derive some useful properties of a Homomorphism *)
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_zero.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_zero.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_zero_unfolded.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_zero_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_minus.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_minus.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_minus_unfolded.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_minus_unfolded.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_apartness.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_apartness.con" as lemma.
(* Merely a useful special case *)
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_ap_zero.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_one.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_one.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_one_unfolded.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_one_unfolded.con" as lemma.
(* I will not use the following lemma *)
-inline procedural "cic:/CoRN/reals/R_morphism/map_pres_inv_unfolded.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_pres_inv_unfolded.con" as lemma.
(* UNEXPORTED
End morphism
alias id "g" = "cic:/CoRN/reals/R_morphism/composition/g.var".
-inline procedural "cic:/CoRN/reals/R_morphism/compose.con".
+inline procedural "cic:/CoRN/reals/R_morphism/compose.con" as definition.
-inline procedural "cic:/CoRN/reals/R_morphism/compose_strext.con".
+inline procedural "cic:/CoRN/reals/R_morphism/compose_strext.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_less.con".
+inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_plus.con".
+inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_plus.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_mult.con".
+inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_mult.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_Lim.con".
+inline procedural "cic:/CoRN/reals/R_morphism/compose_pres_Lim.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/Compose.con".
+inline procedural "cic:/CoRN/reals/R_morphism/Compose.con" as definition.
(* UNEXPORTED
End composition
alias id "f" = "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/f.var".
-inline procedural "cic:/CoRN/reals/R_morphism/map_is_id.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_is_id.con" as definition.
(* UNEXPORTED
End identity_map
alias id "f" = "cic:/CoRN/reals/R_morphism/surjective_map/f.var".
-inline procedural "cic:/CoRN/reals/R_morphism/map_is_surjective.con".
+inline procedural "cic:/CoRN/reals/R_morphism/map_is_surjective.con" as definition.
(* UNEXPORTED
End surjective_map
alias id "H1" = "cic:/CoRN/reals/R_morphism/simplification/H1.var".
-inline procedural "cic:/CoRN/reals/R_morphism/f_well_def.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_well_def.con" as lemma.
(* UNEXPORTED
Section with_less
alias id "H2" = "cic:/CoRN/reals/R_morphism/simplification/with_less/H2.var".
-inline procedural "cic:/CoRN/reals/R_morphism/less_pres_f.con".
+inline procedural "cic:/CoRN/reals/R_morphism/less_pres_f.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/leEq_pres_f.con".
+inline procedural "cic:/CoRN/reals/R_morphism/leEq_pres_f.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/f_pres_leEq.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_pres_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/f_pres_apartness.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_pres_apartness.con" as lemma.
(* UNEXPORTED
End with_less
alias id "H3" = "cic:/CoRN/reals/R_morphism/simplification/with_plus/H3.var".
-inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Zero.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Zero.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/f_pres_minus.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_pres_minus.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/f_pres_min.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_pres_min.con" as lemma.
(* UNEXPORTED
End with_plus
alias id "H3" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H3.var".
-inline procedural "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con" as lemma.
(* UNEXPORTED
Section surjectivity_helps
alias id "f_surj" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/surjectivity_helps/f_surj.var".
-inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Lim.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Lim.con" as lemma.
(* UNEXPORTED
End surjectivity_helps
alias id "H4" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/with_mult_plus_less/H4.var".
-inline procedural "cic:/CoRN/reals/R_morphism/f_pres_one.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_pres_one.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/f_pres_inv.con".
+inline procedural "cic:/CoRN/reals/R_morphism/f_pres_inv.con" as lemma.
-inline procedural "cic:/CoRN/reals/R_morphism/simplified_Homomorphism.con".
+inline procedural "cic:/CoRN/reals/R_morphism/simplified_Homomorphism.con" as definition.
(* UNEXPORTED
End with_mult_plus_less
$\emptyset$#∅# for [a [>] b]).
*)
-inline procedural "cic:/CoRN/reals/RealFuncts/Intclr.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/Intclr.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/Intolr.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/Intolr.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/Intol.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/Intol.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/Intcl.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/Intcl.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/Intcr.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/Intcr.con" as definition.
(*#* The limit of [f(x)] as [x] goes to [p = l], for both unary and binary
functions:
]]
*)
-inline procedural "cic:/CoRN/reals/RealFuncts/funLim.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/funLim.con" as definition.
(*#* The definition of limit of [f] in [p] using Cauchy sequences. *)
-inline procedural "cic:/CoRN/reals/RealFuncts/funLim_Cauchy.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/funLim_Cauchy.con" as definition.
(*#* The first definition implies the second one. *)
]]
*)
-inline procedural "cic:/CoRN/reals/RealFuncts/funLim2.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/funLim2.con" as definition.
(*#* 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 procedural "cic:/CoRN/reals/RealFuncts/continAt.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/continAt.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/continAtCauchy.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/continAtCauchy.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/continAt2.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/continAt2.con" as definition.
(*
Ax_iom continAt_prop1 :(p:IR)(continAt p)->(continAtCauchy p).
*)
-inline procedural "cic:/CoRN/reals/RealFuncts/contin.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/contin.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/continCauchy.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/continCauchy.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/contin2.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/contin2.con" as definition.
(*#*
Continuous on a closed, resp.%\% open, resp.%\% left open, resp.%\% left closed
interval *)
-inline procedural "cic:/CoRN/reals/RealFuncts/continOnc.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/continOnc.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/continOno.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/continOno.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/continOnol.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/continOnol.con" as definition.
-inline procedural "cic:/CoRN/reals/RealFuncts/continOncl.con".
+inline procedural "cic:/CoRN/reals/RealFuncts/continOncl.con" as definition.
(*
Section Sequence_and_function_limits.
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 procedural "cic:/CoRN/reals/RealLists/maxlist.con".
+inline procedural "cic:/CoRN/reals/RealLists/maxlist.con" as definition.
-inline procedural "cic:/CoRN/reals/RealLists/minlist.con".
+inline procedural "cic:/CoRN/reals/RealLists/minlist.con" as definition.
-inline procedural "cic:/CoRN/reals/RealLists/member.con".
+inline procedural "cic:/CoRN/reals/RealLists/member.con" as definition.
(*#*
Sometimes the length of the list has to be restricted; the next definition provides an easy way to do that. *)
-inline procedural "cic:/CoRN/reals/RealLists/length_leEq.con".
+inline procedural "cic:/CoRN/reals/RealLists/length_leEq.con" as definition.
(*#* Length is preserved by mapping. *)
Implicit Arguments map [A B].
*)
-inline procedural "cic:/CoRN/reals/RealLists/map_pres_length.con".
+inline procedural "cic:/CoRN/reals/RealLists/map_pres_length.con" as lemma.
(*#*
Often we want to map partial functions through a list; this next operator provides a way to do that, and is proved to be correct. *)
Implicit Arguments cons [A].
*)
-inline procedural "cic:/CoRN/reals/RealLists/map2.con".
+inline procedural "cic:/CoRN/reals/RealLists/map2.con" as definition.
-inline procedural "cic:/CoRN/reals/RealLists/map2_wd.con".
+inline procedural "cic:/CoRN/reals/RealLists/map2_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/RealLists/map2_pres_member.con".
+inline procedural "cic:/CoRN/reals/RealLists/map2_pres_member.con" as lemma.
(*#*
As [maxlist] and [minlist] are generalizations of [Max] and [Min] to finite sets of real numbers, they have the expected properties: *)
-inline procedural "cic:/CoRN/reals/RealLists/maxlist_greater.con".
+inline procedural "cic:/CoRN/reals/RealLists/maxlist_greater.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/reals/RealLists/Lists/maxlist_aux.con" "Lists__".
+inline procedural "cic:/CoRN/reals/RealLists/Lists/maxlist_aux.con" "Lists__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/RealLists/maxlist_leEq_eps.con".
+inline procedural "cic:/CoRN/reals/RealLists/maxlist_leEq_eps.con" as lemma.
-inline procedural "cic:/CoRN/reals/RealLists/maxlist_less.con".
+inline procedural "cic:/CoRN/reals/RealLists/maxlist_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/RealLists/maxlist_leEq.con".
+inline procedural "cic:/CoRN/reals/RealLists/maxlist_leEq.con" as lemma.
-inline procedural "cic:/CoRN/reals/RealLists/minlist_smaller.con".
+inline procedural "cic:/CoRN/reals/RealLists/minlist_smaller.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/reals/RealLists/Lists/minlist_aux.con" "Lists__".
+inline procedural "cic:/CoRN/reals/RealLists/Lists/minlist_aux.con" "Lists__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/RealLists/minlist_leEq_eps.con".
+inline procedural "cic:/CoRN/reals/RealLists/minlist_leEq_eps.con" as lemma.
-inline procedural "cic:/CoRN/reals/RealLists/less_minlist.con".
+inline procedural "cic:/CoRN/reals/RealLists/less_minlist.con" as lemma.
-inline procedural "cic:/CoRN/reals/RealLists/leEq_minlist.con".
+inline procedural "cic:/CoRN/reals/RealLists/leEq_minlist.con" as lemma.
(* UNEXPORTED
End Lists
alias id "x" = "cic:/CoRN/reals/Series/Definitions/x.var".
-inline procedural "cic:/CoRN/reals/Series/seq_part_sum.con".
+inline procedural "cic:/CoRN/reals/Series/seq_part_sum.con" as definition.
(*#*
For subsequent purposes it will be very useful to be able to write the
sums as a sum of elements of the original sequence.
*)
-inline procedural "cic:/CoRN/reals/Series/seq_part_sum_n.con".
+inline procedural "cic:/CoRN/reals/Series/seq_part_sum_n.con" as lemma.
(*#* A series is convergent iff its sequence of partial Sums is a
Cauchy sequence. To each convergent series we can assign a Sum.
*)
-inline procedural "cic:/CoRN/reals/Series/convergent.con".
+inline procedural "cic:/CoRN/reals/Series/convergent.con" as definition.
-inline procedural "cic:/CoRN/reals/Series/series_sum.con".
+inline procedural "cic:/CoRN/reals/Series/series_sum.con" as definition.
(*#* Divergence can be characterized in a positive way, which will sometimes
be useful. We thus define divergence of sequences and series and prove the
considered either as a sequence or as a series.
*)
-inline procedural "cic:/CoRN/reals/Series/divergent_seq.con".
+inline procedural "cic:/CoRN/reals/Series/divergent_seq.con" as definition.
-inline procedural "cic:/CoRN/reals/Series/divergent.con".
+inline procedural "cic:/CoRN/reals/Series/divergent.con" as definition.
-inline procedural "cic:/CoRN/reals/Series/conv_imp_not_div.con".
+inline procedural "cic:/CoRN/reals/Series/conv_imp_not_div.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/div_imp_not_conv.con".
+inline procedural "cic:/CoRN/reals/Series/div_imp_not_conv.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/convergent_imp_not_divergent.con".
+inline procedural "cic:/CoRN/reals/Series/convergent_imp_not_divergent.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/divergent_imp_not_convergent.con".
+inline procedural "cic:/CoRN/reals/Series/divergent_imp_not_convergent.con" as lemma.
(*#* Finally we have the well known fact that every convergent series converges
to zero as a sequence.
*)
-inline procedural "cic:/CoRN/reals/Series/series_seq_Lim.con".
+inline procedural "cic:/CoRN/reals/Series/series_seq_Lim.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/series_seq_Lim'.con".
+inline procedural "cic:/CoRN/reals/Series/series_seq_Lim'.con" as lemma.
(* UNEXPORTED
End Definitions
(*#* We also define absolute convergence. *)
-inline procedural "cic:/CoRN/reals/Series/abs_convergent.con".
+inline procedural "cic:/CoRN/reals/Series/abs_convergent.con" as definition.
(* UNEXPORTED
End More_Definitions
Power series are an important special case.
*)
-inline procedural "cic:/CoRN/reals/Series/power_series.con".
+inline procedural "cic:/CoRN/reals/Series/power_series.con" as definition.
(*#*
Specially important is the case when [c] is a positive real number
alias id "Hc1" = "cic:/CoRN/reals/Series/Power_Series/Hc1.var".
-inline procedural "cic:/CoRN/reals/Series/c_exp_Lim.con".
+inline procedural "cic:/CoRN/reals/Series/c_exp_Lim.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/power_series_Lim1.con".
+inline procedural "cic:/CoRN/reals/Series/power_series_Lim1.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/power_series_conv.con".
+inline procedural "cic:/CoRN/reals/Series/power_series_conv.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/power_series_sum.con".
+inline procedural "cic:/CoRN/reals/Series/power_series_sum.con" as lemma.
(* UNEXPORTED
End Power_Series
the series that is zero everywhere.
*)
-inline procedural "cic:/CoRN/reals/Series/conv_zero_series.con".
+inline procedural "cic:/CoRN/reals/Series/conv_zero_series.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/series_sum_zero.con".
+inline procedural "cic:/CoRN/reals/Series/series_sum_zero.con" as lemma.
(*#* Next we consider extensionality, as well as the sum and difference
of two convergent series.
alias id "convY" = "cic:/CoRN/reals/Series/Operations/convY.var".
-inline procedural "cic:/CoRN/reals/Series/convergent_wd.con".
+inline procedural "cic:/CoRN/reals/Series/convergent_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/series_sum_wd.con".
+inline procedural "cic:/CoRN/reals/Series/series_sum_wd.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/conv_series_plus.con".
+inline procedural "cic:/CoRN/reals/Series/conv_series_plus.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/series_sum_plus.con".
+inline procedural "cic:/CoRN/reals/Series/series_sum_plus.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/conv_series_minus.con".
+inline procedural "cic:/CoRN/reals/Series/conv_series_minus.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/series_sum_minus.con".
+inline procedural "cic:/CoRN/reals/Series/series_sum_minus.con" as lemma.
(*#* Multiplication by a scalar [c] is also permitted. *)
alias id "c" = "cic:/CoRN/reals/Series/Operations/c.var".
-inline procedural "cic:/CoRN/reals/Series/conv_series_mult_scal.con".
+inline procedural "cic:/CoRN/reals/Series/conv_series_mult_scal.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/series_sum_mult_scal.con".
+inline procedural "cic:/CoRN/reals/Series/series_sum_mult_scal.con" as lemma.
(* UNEXPORTED
End Operations
(*#* As a corollary, we get the series of the inverses. *)
-inline procedural "cic:/CoRN/reals/Series/conv_series_inv.con".
+inline procedural "cic:/CoRN/reals/Series/conv_series_inv.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/series_sum_inv.con".
+inline procedural "cic:/CoRN/reals/Series/series_sum_inv.con" as lemma.
(* UNEXPORTED
End More_Operations
alias id "y" = "cic:/CoRN/reals/Series/Almost_Everywhere/y.var".
-inline procedural "cic:/CoRN/reals/Series/aew_eq.con".
+inline procedural "cic:/CoRN/reals/Series/aew_eq.con" as definition.
alias id "aew_equal" = "cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var".
-inline procedural "cic:/CoRN/reals/Series/aew_Cauchy.con".
+inline procedural "cic:/CoRN/reals/Series/aew_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/aew_Cauchy2.con".
+inline procedural "cic:/CoRN/reals/Series/aew_Cauchy2.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/aew_series_conv.con".
+inline procedural "cic:/CoRN/reals/Series/aew_series_conv.con" as lemma.
(* UNEXPORTED
End Almost_Everywhere
alias id "aew_equal" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var".
-inline procedural "cic:/CoRN/reals/Series/aew_Lim.con".
+inline procedural "cic:/CoRN/reals/Series/aew_Lim.con" as lemma.
(* UNEXPORTED
End Cauchy_Almost_Everywhere
general (but simpler) form.
*)
-inline procedural "cic:/CoRN/reals/Series/str_comparison.con".
+inline procedural "cic:/CoRN/reals/Series/str_comparison.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/comparison.con".
+inline procedural "cic:/CoRN/reals/Series/comparison.con" as lemma.
(*#* As a corollary, we get that every absolutely convergent series converges. *)
-inline procedural "cic:/CoRN/reals/Series/abs_imp_conv.con".
+inline procedural "cic:/CoRN/reals/Series/abs_imp_conv.con" as lemma.
(*#* Next we have the ratio test, both as a positive and negative result. *)
-inline procedural "cic:/CoRN/reals/Series/divergent_crit.con".
+inline procedural "cic:/CoRN/reals/Series/divergent_crit.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/tail_series.con".
+inline procedural "cic:/CoRN/reals/Series/tail_series.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/join_series.con".
+inline procedural "cic:/CoRN/reals/Series/join_series.con" as lemma.
(* UNEXPORTED
End Convergence_Criteria
alias id "x" = "cic:/CoRN/reals/Series/More_CC/x.var".
-inline procedural "cic:/CoRN/reals/Series/ratio_test_conv.con".
+inline procedural "cic:/CoRN/reals/Series/ratio_test_conv.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/ratio_test_div.con".
+inline procedural "cic:/CoRN/reals/Series/ratio_test_div.con" as lemma.
(* UNEXPORTED
End More_CC
(* begin hide *)
-inline procedural "cic:/CoRN/reals/Series/Alternate_Series/y.con" "Alternate_Series__".
+inline procedural "cic:/CoRN/reals/Series/Alternate_Series/y.con" "Alternate_Series__" as definition.
-inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma1.con" "Alternate_Series__".
+inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma1.con" "Alternate_Series__" as definition.
-inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma2.con" "Alternate_Series__".
+inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma2.con" "Alternate_Series__" as definition.
-inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma3.con" "Alternate_Series__".
+inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma3.con" "Alternate_Series__" as definition.
-inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma4.con" "Alternate_Series__".
+inline procedural "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma4.con" "Alternate_Series__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/reals/Series/alternate_series_conv.con".
+inline procedural "cic:/CoRN/reals/Series/alternate_series_conv.con" as lemma.
(* UNEXPORTED
End Alternate_Series
and $e$#e#, both as sums of convergent series.
*)
-inline procedural "cic:/CoRN/reals/Series/e_series.con".
+inline procedural "cic:/CoRN/reals/Series/e_series.con" as definition.
-inline procedural "cic:/CoRN/reals/Series/e_series_conv.con".
+inline procedural "cic:/CoRN/reals/Series/e_series_conv.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/E.con".
+inline procedural "cic:/CoRN/reals/Series/E.con" as definition.
-inline procedural "cic:/CoRN/reals/Series/pi_series.con".
+inline procedural "cic:/CoRN/reals/Series/pi_series.con" as definition.
-inline procedural "cic:/CoRN/reals/Series/pi_series_conv.con".
+inline procedural "cic:/CoRN/reals/Series/pi_series_conv.con" as lemma.
-inline procedural "cic:/CoRN/reals/Series/pi.con".
+inline procedural "cic:/CoRN/reals/Series/pi.con" as definition.
(* UNEXPORTED
End Important_Numbers
include "reals/R_morphism.ma".
-inline procedural "cic:/CoRN/reals/iso_CReals/less_pres_Lim.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/less_pres_Lim.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_less.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_less.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_less.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/less_inj_seq.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/less_inj_seq.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/SeqLimit_unique.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/SeqLimit_unique.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/Lim_well_def.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/Lim_well_def.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/Lim_one_one.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/Lim_one_one.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_well_def.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_well_def.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/inj_Q_one_one.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/inj_Q_one_one.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_plus.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_plus.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_plus.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_plus.con" as lemma.
(* This theorem can be avoided but it is interesting *)
-inline procedural "cic:/CoRN/reals/iso_CReals/nonarchemaedian_bound_for_Lim.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/nonarchemaedian_bound_for_Lim.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_mult.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_mult.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_mult.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_mult.con" as lemma.
(* UNEXPORTED
Section Concrete_iso_between_Creals
alias id "R2" = "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R2.var".
-inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy21.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy21.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq12.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq12.con" as definition.
-inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq21.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq21.con" as definition.
-inline procedural "cic:/CoRN/reals/iso_CReals/f12.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/f12.con" as definition.
-inline procedural "cic:/CoRN/reals/iso_CReals/g21.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/g21.con" as definition.
(*#****** ISO FROM R1 TO R2 ********)
-inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_inverse_g21.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_inverse_g21.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_surjective.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_surjective.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/f12_strong_ext.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/f12_strong_ext.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_less.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_less.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_plus.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_plus.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_mult.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_mult.con" as theorem.
(*#********* ISO FROM R2 TO R1 **********)
-inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_inverse_f12.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_inverse_f12.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_surjective.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_surjective.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/g21_strong_ext.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/g21_strong_ext.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_less.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_less.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_plus.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_plus.con" as theorem.
-inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_mult.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_mult.con" as theorem.
(*#** Building Homomorphisms out of f12 and g21 ***)
-inline procedural "cic:/CoRN/reals/iso_CReals/f12_as_Homomorphism.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/f12_as_Homomorphism.con" as definition.
-inline procedural "cic:/CoRN/reals/iso_CReals/g21_as_Homomorphism.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/g21_as_Homomorphism.con" as definition.
-inline procedural "cic:/CoRN/reals/iso_CReals/f12_inverse_lft.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/f12_inverse_lft.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/g21_inverse_rht.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/g21_inverse_rht.con" as lemma.
-inline procedural "cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con".
+inline procedural "cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con" as definition.
(* UNEXPORTED
End Concrete_iso_between_Creals
Section Syntactic_Expressions
*)
-inline procedural "cic:/CoRN/tactics/AlgReflection/varindex.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/varindex.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/pfunindex.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/pfunindex.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/unopindex.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/unopindex.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/binopindex.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/binopindex.con" as definition.
inline procedural "cic:/CoRN/tactics/AlgReflection/expr.ind".
-inline procedural "cic:/CoRN/tactics/AlgReflection/expr_zero.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/expr_zero.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/expr_one.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/expr_one.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/expr_nat.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/expr_nat.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/expr_inv.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/expr_inv.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/expr_minus.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/expr_minus.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/expr_power.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/expr_power.con" as definition.
(* UNEXPORTED
End Syntactic_Expressions
Section Normalization_Function
*)
-inline procedural "cic:/CoRN/tactics/AlgReflection/eq_nat.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/eq_nat.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/lt_nat.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/lt_nat.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/le_nat.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/le_nat.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/eq_int.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/eq_int.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/lt_int.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/lt_int.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/le_int.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/le_int.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/eq_expr.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/eq_expr.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/lt_expr.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/lt_expr.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/le_expr.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/le_expr.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/eq_monom.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/eq_monom.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/lt_monom.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/lt_monom.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/MI_mult.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/MI_mult.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/MV_mult.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/MV_mult.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/MM_mult.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/MM_mult.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/MM_plus.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/MM_plus.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/PM_plus.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/PM_plus.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/PP_plus.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/PP_plus.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/PM_mult.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/PM_mult.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/PP_mult.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/PP_mult.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/FF_plus.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/FF_plus.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/FF_mult.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/FF_mult.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/FF_div.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/FF_div.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/NormR.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/NormR.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/NormG.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/NormG.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/NormF.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/NormF.con" as definition.
-inline procedural "cic:/CoRN/tactics/AlgReflection/expr_is_zero.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/expr_is_zero.con" as definition.
(* UNEXPORTED
End Normalization_Function
Section Correctness_Results
*)
-inline procedural "cic:/CoRN/tactics/AlgReflection/eq_nat_corr.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/eq_nat_corr.con" as lemma.
-inline procedural "cic:/CoRN/tactics/AlgReflection/eq_int_corr.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/eq_int_corr.con" as lemma.
-inline procedural "cic:/CoRN/tactics/AlgReflection/eq_expr_corr.con".
+inline procedural "cic:/CoRN/tactics/AlgReflection/eq_expr_corr.con" as lemma.
(* UNEXPORTED
End Correctness_Results
inline procedural "cic:/CoRN/tactics/DiffTactics2/cont_function.ind".
-inline procedural "cic:/CoRN/tactics/DiffTactics2/cont_to_pfunct.con".
+inline procedural "cic:/CoRN/tactics/DiffTactics2/cont_to_pfunct.con" as definition.
-inline procedural "cic:/CoRN/tactics/DiffTactics2/continuous_cont.con".
+inline procedural "cic:/CoRN/tactics/DiffTactics2/continuous_cont.con" as lemma.
(* UNEXPORTED
End Automatizing_Continuity
inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_function.ind".
-inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_to_pfunct.con".
+inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_to_pfunct.con" as definition.
-inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_deriv.con".
+inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_deriv.con" as definition.
-inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_restr.con".
+inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_restr.con" as lemma.
-inline procedural "cic:/CoRN/tactics/DiffTactics2/diffble_restr.con".
+inline procedural "cic:/CoRN/tactics/DiffTactics2/diffble_restr.con" as lemma.
(* UNEXPORTED
End Automatizing_Derivatives
| ssum : nat->nat->(nat->symbPF)->symbPF
*)
-inline procedural "cic:/CoRN/tactics/DiffTactics3/symb_to_PartIR.con".
+inline procedural "cic:/CoRN/tactics/DiffTactics3/symb_to_PartIR.con" as definition.
-inline procedural "cic:/CoRN/tactics/DiffTactics3/symbPF_deriv.con".
+inline procedural "cic:/CoRN/tactics/DiffTactics3/symbPF_deriv.con" as definition.
(* UNEXPORTED
Ltac PartIR_to_symbPF f :=
inline procedural "cic:/CoRN/tactics/FieldReflection/interpF.ind".
-inline procedural "cic:/CoRN/tactics/FieldReflection/wfF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/wfF.con" as definition.
inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF.ind".
-inline procedural "cic:/CoRN/tactics/FieldReflection/xforgetF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/xforgetF.con" as definition.
-inline procedural "cic:/CoRN/tactics/FieldReflection/xinterpF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/xinterpF.con" as definition.
-inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF2interpF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF2interpF.con" as lemma.
-inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF_diagram_commutes.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF_diagram_commutes.con" as definition.
-inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF2wfF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/xexprF2wfF.con" as lemma.
inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF.ind".
-inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_var.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_var.con" as definition.
-inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_int.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_int.con" as definition.
-inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_plus.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_plus.con" as definition.
-inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_mult.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF_mult.con" as definition.
-inline procedural "cic:/CoRN/tactics/FieldReflection/fforgetF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/fforgetF.con" as definition.
-inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF2interpF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF2interpF.con" as lemma.
-inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF2wfF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/fexprF2wfF.con" as lemma.
include "tactics/Opaque_algebra.ma".
-inline procedural "cic:/CoRN/tactics/FieldReflection/refl_interpF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/refl_interpF.con" as lemma.
-inline procedural "cic:/CoRN/tactics/FieldReflection/interpF_wd.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/interpF_wd.con" as lemma.
(* UNEXPORTED
End Field_Interpretation_Function
Opaque Zmult.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/MI_mult_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/MI_mult_corr_F.con" as lemma.
(* UNEXPORTED
Transparent Zmult.
Opaque MI_mult.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/MV_mult_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/MV_mult_corr_F.con" as lemma.
(* UNEXPORTED
Transparent MI_mult.
Opaque MV_mult MI_mult.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/MM_mult_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/MM_mult_corr_F.con" as lemma.
(* UNEXPORTED
Transparent MV_mult MI_mult.
Opaque MV_mult.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/MM_plus_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/MM_plus_corr_F.con" as lemma.
(* UNEXPORTED
Transparent MV_mult.
Opaque MM_plus.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/PM_plus_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/PM_plus_corr_F.con" as lemma.
(* UNEXPORTED
Transparent MM_plus.
Opaque PM_plus.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/PP_plus_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/PP_plus_corr_F.con" as lemma.
(* UNEXPORTED
Transparent PM_plus.
Opaque PM_plus MM_mult MI_mult.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/PM_mult_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/PM_mult_corr_F.con" as lemma.
(* UNEXPORTED
Opaque PM_mult.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/PP_mult_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/PP_mult_corr_F.con" as lemma.
(* UNEXPORTED
Transparent PP_plus PM_mult PP_mult PM_plus MI_mult.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/FF_plus_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/FF_plus_corr_F.con" as lemma.
-inline procedural "cic:/CoRN/tactics/FieldReflection/FF_mult_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/FF_mult_corr_F.con" as lemma.
(* UNEXPORTED
Transparent FF_div.
*)
-inline procedural "cic:/CoRN/tactics/FieldReflection/FF_div_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/FF_div_corr_F.con" as lemma.
-inline procedural "cic:/CoRN/tactics/FieldReflection/NormF_corr.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/NormF_corr.con" as lemma.
-inline procedural "cic:/CoRN/tactics/FieldReflection/Norm_wfF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/Norm_wfF.con" as lemma.
-inline procedural "cic:/CoRN/tactics/FieldReflection/expr_is_zero_corr_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/expr_is_zero_corr_F.con" as lemma.
-inline procedural "cic:/CoRN/tactics/FieldReflection/Tactic_lemma_zero_F.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/Tactic_lemma_zero_F.con" as lemma.
-inline procedural "cic:/CoRN/tactics/FieldReflection/Tactic_lemmaF.con".
+inline procedural "cic:/CoRN/tactics/FieldReflection/Tactic_lemmaF.con" as lemma.
(* UNEXPORTED
End Field_NormCorrect
inline procedural "cic:/CoRN/tactics/GroupReflection/interpG.ind".
-inline procedural "cic:/CoRN/tactics/GroupReflection/wfG.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/wfG.con" as definition.
inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG.ind".
-inline procedural "cic:/CoRN/tactics/GroupReflection/xforgetG.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/xforgetG.con" as definition.
-inline procedural "cic:/CoRN/tactics/GroupReflection/xinterpG.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/xinterpG.con" as definition.
-inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG2interpG.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG2interpG.con" as lemma.
-inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG_diagram_commutes.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG_diagram_commutes.con" as definition.
-inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG2wfG.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/xexprG2wfG.con" as lemma.
inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG.ind".
-inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_var.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_var.con" as definition.
-inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_zero.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_zero.con" as definition.
-inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_plus.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_plus.con" as definition.
-inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_mult_int.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG_mult_int.con" as definition.
-inline procedural "cic:/CoRN/tactics/GroupReflection/fforgetG.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/fforgetG.con" as definition.
-inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG2interp.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG2interp.con" as lemma.
-inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG2wf.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/fexprG2wf.con" as lemma.
(* UNEXPORTED
Opaque csg_crr.
Opaque cg_minus.
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/refl_interpG.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/refl_interpG.con" as lemma.
-inline procedural "cic:/CoRN/tactics/GroupReflection/interpG_wd.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/interpG_wd.con" as lemma.
(* UNEXPORTED
End Group_Interpretation_Function
P: sorted on M, all M's not an I
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/MI_mult_comm_int.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/MI_mult_comm_int.con" as lemma.
(* UNEXPORTED
Opaque Zmult.
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/MI_mult_corr_G.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/MI_mult_corr_G.con" as lemma.
(* UNEXPORTED
Transparent Zmult.
Opaque MI_mult.
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/MV_mult_corr_G.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/MV_mult_corr_G.con" as lemma.
(* UNEXPORTED
Opaque MV_mult.
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/MM_mult_corr_G.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/MM_mult_corr_G.con" as lemma.
(* UNEXPORTED
Transparent MV_mult MI_mult.
Opaque MV_mult.
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/MM_plus_corr_G.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/MM_plus_corr_G.con" as lemma.
(* UNEXPORTED
Transparent MV_mult.
Opaque MM_plus.
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/PM_plus_corr_G.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/PM_plus_corr_G.con" as lemma.
(* UNEXPORTED
Transparent MM_plus.
Opaque PM_plus.
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/PP_plus_corr_G.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/PP_plus_corr_G.con" as lemma.
(* UNEXPORTED
Transparent PM_plus.
Opaque PM_plus MM_mult MI_mult.
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/PM_mult_corr_G.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/PM_mult_corr_G.con" as lemma.
(* UNEXPORTED
Opaque PM_mult.
*)
-inline procedural "cic:/CoRN/tactics/GroupReflection/PP_mult_corr_G.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/PP_mult_corr_G.con" as lemma.
-inline procedural "cic:/CoRN/tactics/GroupReflection/NormG_corr_G.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/NormG_corr_G.con" as lemma.
-inline procedural "cic:/CoRN/tactics/GroupReflection/Tactic_lemmaG.con".
+inline procedural "cic:/CoRN/tactics/GroupReflection/Tactic_lemmaG.con" as lemma.
(* UNEXPORTED
End Group_NormCorrect
inline procedural "cic:/CoRN/tactics/RingReflection/interpR.ind".
-inline procedural "cic:/CoRN/tactics/RingReflection/wfR.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/wfR.con" as definition.
inline procedural "cic:/CoRN/tactics/RingReflection/xexprR.ind".
-inline procedural "cic:/CoRN/tactics/RingReflection/xforgetR.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/xforgetR.con" as definition.
-inline procedural "cic:/CoRN/tactics/RingReflection/xinterpR.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/xinterpR.con" as definition.
-inline procedural "cic:/CoRN/tactics/RingReflection/xexprR2interpR.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/xexprR2interpR.con" as lemma.
-inline procedural "cic:/CoRN/tactics/RingReflection/xexprR_diagram_commutes.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/xexprR_diagram_commutes.con" as definition.
-inline procedural "cic:/CoRN/tactics/RingReflection/xexprR2wfR.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/xexprR2wfR.con" as lemma.
inline procedural "cic:/CoRN/tactics/RingReflection/fexprR.ind".
-inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_var.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_var.con" as definition.
-inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_int.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_int.con" as definition.
-inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_plus.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_plus.con" as definition.
-inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_mult.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/fexprR_mult.con" as definition.
-inline procedural "cic:/CoRN/tactics/RingReflection/fforgetR.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/fforgetR.con" as definition.
-inline procedural "cic:/CoRN/tactics/RingReflection/fexprR2interp.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/fexprR2interp.con" as lemma.
-inline procedural "cic:/CoRN/tactics/RingReflection/fexprR2wf.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/fexprR2wf.con" as lemma.
(* UNEXPORTED
Opaque csg_crr.
Opaque nexp_op.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/refl_interpR.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/refl_interpR.con" as lemma.
-inline procedural "cic:/CoRN/tactics/RingReflection/interpR_wd.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/interpR_wd.con" as lemma.
(* UNEXPORTED
End Ring_Interpretation_Function
Opaque Zmult.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/MI_mult_corr_R.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/MI_mult_corr_R.con" as lemma.
(* UNEXPORTED
Transparent Zmult.
Opaque MI_mult.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/MV_mult_corr_R.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/MV_mult_corr_R.con" as lemma.
(* UNEXPORTED
Transparent MI_mult.
Opaque MV_mult MI_mult.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/MM_mult_corr_R.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/MM_mult_corr_R.con" as lemma.
(* UNEXPORTED
Transparent MV_mult MI_mult.
Opaque MV_mult.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/MM_plus_corr_R.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/MM_plus_corr_R.con" as lemma.
(* UNEXPORTED
Transparent MV_mult.
Opaque MM_plus.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/PM_plus_corr_R.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/PM_plus_corr_R.con" as lemma.
(* UNEXPORTED
Transparent MM_plus.
Opaque PM_plus.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/PP_plus_corr_R.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/PP_plus_corr_R.con" as lemma.
(* UNEXPORTED
Transparent PM_plus.
Opaque PM_plus MM_mult MI_mult.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/PM_mult_corr_R.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/PM_mult_corr_R.con" as lemma.
(* UNEXPORTED
Opaque PM_mult.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/PP_mult_corr_R.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/PP_mult_corr_R.con" as lemma.
(*
Transparent PP_plus PM_mult PP_mult PM_plus MI_mult.
Qed.
*)
-inline procedural "cic:/CoRN/tactics/RingReflection/NormR_corr.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/NormR_corr.con" as lemma.
-inline procedural "cic:/CoRN/tactics/RingReflection/Tactic_lemmaR.con".
+inline procedural "cic:/CoRN/tactics/RingReflection/Tactic_lemmaR.con" as lemma.
(* UNEXPORTED
End Ring_NormCorrect
Exponential is strongly extensional and well defined.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_strext.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_strext.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_wd.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_wd.con" as lemma.
(* UNEXPORTED
Hint Resolve Exp_wd: algebra.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_zero.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_zero.con" as lemma.
(*#* $e^1=e$#e<sup>1</sup>=e#, where [e] was defined a long time ago.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_one.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_one.con" as lemma.
(* UNEXPORTED
Hint Resolve Exp_zero Exp_one: algebra.
The exponential function is its own derivative, and continuous.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Derivative_Exp.con".
+inline procedural "cic:/CoRN/transc/Exponential/Derivative_Exp.con" as lemma.
(* UNEXPORTED
Hint Resolve Derivative_Exp: derivate.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Continuous_Exp.con".
+inline procedural "cic:/CoRN/transc/Exponential/Continuous_Exp.con" as lemma.
(* UNEXPORTED
Hint Resolve Continuous_Exp: continuous.
Negative numbers are projected into the interval [[0,1]].
*)
-inline procedural "cic:/CoRN/transc/Exponential/One_less_Exp.con".
+inline procedural "cic:/CoRN/transc/Exponential/One_less_Exp.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/One_leEq_Exp.con".
+inline procedural "cic:/CoRN/transc/Exponential/One_leEq_Exp.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_pos'.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_pos'.con" as lemma.
(*#*
Exponential is the unique function which evaluates to 1 at 0 and is
its own derivative.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_unique_lemma.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_unique_lemma.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_bnd.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_bnd.con" as lemma.
(* UNEXPORTED
Opaque Expon.
Transparent Expon.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_unique.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_unique.con" as lemma.
(* UNEXPORTED
Opaque Expon.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_plus_pos.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_plus_pos.con" as lemma.
(*#* The usual rules for computing the exponential of a sum. *)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_plus.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_plus.con" as lemma.
(* UNEXPORTED
Hint Resolve Exp_plus: algebra.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_plus'.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_plus'.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_inv_char.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_inv_char.con" as lemma.
(* UNEXPORTED
Hint Resolve Exp_inv_char: algebra.
from zero.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_pos.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_pos.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_ap_zero.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_ap_zero.con" as lemma.
(*#*
And the rules for the exponential of differences.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_inv.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve Exp_inv: algebra.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_minus.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_minus.con" as lemma.
(* UNEXPORTED
Hint Resolve Exp_minus: algebra.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_inv'.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_inv'.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_minus'.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_minus'.con" as lemma.
(*#* Exponential is a monotonous function. *)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_less_One.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_less_One.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_leEq_One.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_leEq_One.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_resp_less.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_resp_leEq.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_resp_leEq.con" as lemma.
(*#* **Properties of Logarithm
The logarithm is a continuous function with derivative [One[/]x].
*)
-inline procedural "cic:/CoRN/transc/Exponential/Derivative_Log.con".
+inline procedural "cic:/CoRN/transc/Exponential/Derivative_Log.con" as lemma.
(* UNEXPORTED
Hint Resolve Derivative_Log: derivate.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Continuous_Log.con".
+inline procedural "cic:/CoRN/transc/Exponential/Continuous_Log.con" as lemma.
(* UNEXPORTED
Hint Resolve Continuous_Log: continuous.
(*#* Logarithm of [One]. *)
-inline procedural "cic:/CoRN/transc/Exponential/Log_one.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_one.con" as lemma.
(* UNEXPORTED
Hint Resolve Log_one: algebra.
(*#* The logarithm is (strongly) extensional. *)
-inline procedural "cic:/CoRN/transc/Exponential/Log_strext.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_strext.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_wd.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_wd.con" as lemma.
(* UNEXPORTED
Hint Resolve Log_wd: algebra.
Transparent Logarithm.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Log_mult.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_mult.con" as lemma.
(* UNEXPORTED
Hint Resolve Log_mult: algebra.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Log_mult'.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_mult'.con" as lemma.
(*#* A characterization of the domain of the logarithm. *)
-inline procedural "cic:/CoRN/transc/Exponential/Log_domain.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_domain.con" as lemma.
(* UNEXPORTED
Opaque Expon Logarithm.
numerical and as a functional equation.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Log_Exp_inv.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_Exp_inv.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_Exp.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_Exp.con" as lemma.
(* UNEXPORTED
Transparent Logarithm.
Hint Resolve Log_Exp: algebra.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_Log_lemma.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_Log_lemma.con" as lemma.
(*#* The converse expression. *)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_Log.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_Log.con" as lemma.
(* UNEXPORTED
Hint Resolve Exp_Log: algebra.
(*#* Exponential and logarithm are injective. *)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_cancel.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_cancel.con" as lemma.
(* UNEXPORTED
Opaque Logarithm.
(*#* And the final characterization as inverse functions. *)
-inline procedural "cic:/CoRN/transc/Exponential/Exp_Log_inv.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_Log_inv.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_E.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_E.con" as lemma.
(* UNEXPORTED
Hint Resolve Log_E: algebra.
(*#* Several rules regarding inequalities. *)
-inline procedural "cic:/CoRN/transc/Exponential/Log_cancel_less.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_cancel_less.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_cancel_leEq.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_cancel_leEq.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_resp_less.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_resp_leEq.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel_less.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel_less.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel_leEq.con".
+inline procedural "cic:/CoRN/transc/Exponential/Exp_cancel_leEq.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_less_Zero.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_less_Zero.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_leEq_Zero.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_leEq_Zero.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Zero_less_Log.con".
+inline procedural "cic:/CoRN/transc/Exponential/Zero_less_Log.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Zero_leEq_Log.con".
+inline procedural "cic:/CoRN/transc/Exponential/Zero_leEq_Log.con" as lemma.
(*#* Finally, rules for logarithm of quotients. *)
-inline procedural "cic:/CoRN/transc/Exponential/Log_recip_char.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_recip_char.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_recip.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_recip.con" as lemma.
(* UNEXPORTED
Hint Resolve Log_recip: algebra.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Log_recip'.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_recip'.con" as lemma.
-inline procedural "cic:/CoRN/transc/Exponential/Log_div.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_div.con" as lemma.
(* UNEXPORTED
Hint Resolve Log_div: algebra.
*)
-inline procedural "cic:/CoRN/transc/Exponential/Log_div'.con".
+inline procedural "cic:/CoRN/transc/Exponential/Log_div'.con" as lemma.
Opaque Sine Cosine Expon Logarithm.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_def_lemma.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_def_lemma.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_def_zero.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_def_zero.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin.con" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_domain.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_domain.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcSin.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcSin.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcSin.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcSin.con" as lemma.
(* UNEXPORTED
Hint Resolve Derivative_ArcSin: derivate.
(*#* ***Arccosine
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos.con" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_domain.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_domain.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcCos.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcCos.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcCos.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcCos.con" as lemma.
(*#* ***Arctangent
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_def_lemma.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_def_lemma.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTang.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTang.con" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_domain.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_domain.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan.con" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcTan.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Continuous_ArcTan.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcTan.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Derivative_ArcTan.con" as lemma.
(* UNEXPORTED
Hint Resolve Derivative_ArcCos Derivative_ArcTan: derivate.
***Sine and Arcsine
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/maps_Sin.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/maps_Sin.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin_inv.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin_inv.con" as lemma.
(* UNEXPORTED
Opaque ArcSin.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_Sin.con" as lemma.
(* UNEXPORTED
Transparent ArcSin.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_range.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_range.con" as lemma.
(* UNEXPORTED
Transparent ArcSin.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin_inv.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Sin_ArcSin_inv.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_resp_leEq.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcSin_resp_leEq.con" as lemma.
(*#* ***Cosine and Arcosine
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos_inv.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_Cos_inv.con" as lemma.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos_inv.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Cos_ArcCos_inv.con" as lemma.
(* UNEXPORTED
Opaque ArcSin.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_resp_leEq.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcCos_resp_leEq.con" as lemma.
(*#* ***Tangent and Arctangent
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/maps_Tan.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/maps_Tan.con" as lemma.
(* UNEXPORTED
Opaque Tang.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan_inv.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan_inv.con" as lemma.
(* UNEXPORTED
Transparent Tang.
Opaque ArcTang.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_Tan.con" as lemma.
(* UNEXPORTED
Opaque iprop.
Opaque Cos.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ilim.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ilim.con" as lemma.
(* UNEXPORTED
Opaque Min.
(* begin hide *)
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min1.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min1.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min2.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min2.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min3.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min3.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min4.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min4.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max1.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max1.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max2.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max2.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max3.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max3.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max4.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max4.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min5.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min5.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min6.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min6.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max5.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max5.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max6.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max6.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a1.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a1.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a2.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a2.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a3.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a3.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a4.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a4.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a5.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a5.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b1.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b1.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b2.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b2.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b3.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b3.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b4.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b4.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b5.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b5.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/ab.con" "Inverses__ArcTan_Range__".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/ab.con" "Inverses__ArcTan_Range__" as definition.
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con" as lemma.
(* end hide *)
Transparent ArcTang.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_range.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/ArcTan_range.con" as lemma.
(* UNEXPORTED
End ArcTan_Range
Transparent ArcTang.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan.con" as lemma.
(* UNEXPORTED
Opaque ArcTang.
*)
-inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con".
+inline procedural "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con" as lemma.
(* UNEXPORTED
End Inverses
[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 procedural "cic:/CoRN/transc/Pi/pi_seq.con".
+inline procedural "cic:/CoRN/transc/Pi/pi_seq.con" as definition.
(* UNEXPORTED
Opaque Cosine.
Opaque Sine.
*)
-inline procedural "cic:/CoRN/transc/Pi/pi_seq_lemma.con".
+inline procedural "cic:/CoRN/transc/Pi/pi_seq_lemma.con" as lemma.
(* end hide *)
sequence is strictly increasing.
*)
-inline procedural "cic:/CoRN/transc/Pi/pi_seq_nonneg.con".
+inline procedural "cic:/CoRN/transc/Pi/pi_seq_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/cos_pi_seq_pos.con".
+inline procedural "cic:/CoRN/transc/Pi/cos_pi_seq_pos.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/pi_seq_incr.con".
+inline procedural "cic:/CoRN/transc/Pi/pi_seq_incr.con" as lemma.
(*#* Trivial---but useful---consequences. *)
-inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_mon.con".
+inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_mon.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_nonneg.con".
+inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_gt_one.con".
+inline procedural "cic:/CoRN/transc/Pi/sin_pi_seq_gt_one.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/cos_pi_seq_mon.con".
+inline procedural "cic:/CoRN/transc/Pi/cos_pi_seq_mon.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/transc/Pi/pi_seq_gt_one.con".
+inline procedural "cic:/CoRN/transc/Pi/pi_seq_gt_one.con" as lemma.
(* UNEXPORTED
Opaque Sine Cosine.
*)
-inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd.con".
+inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd'.con".
+inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd'.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd''.con".
+inline procedural "cic:/CoRN/transc/Pi/pi_seq_bnd''.con" as lemma.
(* end hide *)
(*#* An auxiliary result. *)
-inline procedural "cic:/CoRN/transc/Pi/Sin_One_pos.con".
+inline procedural "cic:/CoRN/transc/Pi/Sin_One_pos.con" as lemma.
(*#* We can now prove that this is a Cauchy sequence. We define [Pi] as
twice its limit.
*)
-inline procedural "cic:/CoRN/transc/Pi/pi_seq_Cauchy.con".
+inline procedural "cic:/CoRN/transc/Pi/pi_seq_Cauchy.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/Pi.con" as definition.
(*#*
For $x\in[0,\frac{\pi}2)$#x∈[0,π/2)#, [(Cos x) [>] 0];
$\cos(\frac{pi}2)=0$#cos(π/2)=0#.
*)
-inline procedural "cic:/CoRN/transc/Pi/pos_cos.con".
+inline procedural "cic:/CoRN/transc/Pi/pos_cos.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Cos_HalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/Cos_HalfPi.con" as lemma.
(*#* Convergence to [Pi [/] Two] is increasing; therefore, [Pi] is positive. *)
-inline procedural "cic:/CoRN/transc/Pi/HalfPi_gt_pi_seq.con".
+inline procedural "cic:/CoRN/transc/Pi/HalfPi_gt_pi_seq.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/pos_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/pos_Pi.con" as lemma.
(* UNEXPORTED
End Properties_of_Pi
[PiSolve] will prove any of these inequalities.
*)
-inline procedural "cic:/CoRN/transc/Pi/pos_HalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/pos_HalfPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/pos_QuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/pos_QuarterPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/QuarterPi_less_HalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/QuarterPi_less_HalfPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/HalfPi_less_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/HalfPi_less_Pi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/QuarterPi_less_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/QuarterPi_less_Pi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/neg_invPi.con".
+inline procedural "cic:/CoRN/transc/Pi/neg_invPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/neg_invHalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/neg_invHalfPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/neg_invQuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/neg_invQuarterPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_invQuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_invQuarterPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invPi_less_invHalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/invPi_less_invHalfPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invPi_less_invQuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/invPi_less_invQuarterPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invPi_less_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/invPi_less_Pi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invPi_less_HalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/invPi_less_HalfPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invPi_less_QuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/invPi_less_QuarterPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_Pi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_HalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_HalfPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_QuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/invHalfPi_less_QuarterPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_Pi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_HalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_HalfPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_QuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/invQuarterPi_less_QuarterPi.con" as lemma.
(* UNEXPORTED
End Pi_and_Order
the double.
*)
-inline procedural "cic:/CoRN/transc/Pi/Cos_double.con".
+inline procedural "cic:/CoRN/transc/Pi/Cos_double.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Sin_double.con".
+inline procedural "cic:/CoRN/transc/Pi/Sin_double.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Tan_double.con".
+inline procedural "cic:/CoRN/transc/Pi/Tan_double.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/transc/Pi/sqrt_lemma.con".
+inline procedural "cic:/CoRN/transc/Pi/sqrt_lemma.con" as lemma.
(* end hide *)
(*#* Value of trigonometric functions at [Pi[/]Four]. *)
-inline procedural "cic:/CoRN/transc/Pi/Cos_QuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/Cos_QuarterPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Sin_QuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/Sin_QuarterPi.con" as lemma.
(* UNEXPORTED
Hint Resolve Sin_QuarterPi Cos_QuarterPi: algebra.
Opaque Sine Cosine.
*)
-inline procedural "cic:/CoRN/transc/Pi/Tan_QuarterPi.con".
+inline procedural "cic:/CoRN/transc/Pi/Tan_QuarterPi.con" as lemma.
(*#* Shifting sine and cosine by [Pi[/]Two] and [Pi]. *)
-inline procedural "cic:/CoRN/transc/Pi/Sin_HalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/Sin_HalfPi.con" as lemma.
(* UNEXPORTED
Hint Resolve Sin_HalfPi: algebra.
*)
-inline procedural "cic:/CoRN/transc/Pi/Sin_plus_HalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/Sin_plus_HalfPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Sin_HalfPi_minus.con".
+inline procedural "cic:/CoRN/transc/Pi/Sin_HalfPi_minus.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Cos_plus_HalfPi.con".
+inline procedural "cic:/CoRN/transc/Pi/Cos_plus_HalfPi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Cos_HalfPi_minus.con".
+inline procedural "cic:/CoRN/transc/Pi/Cos_HalfPi_minus.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Sin_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/Sin_Pi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Cos_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/Cos_Pi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Sin_plus_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/Sin_plus_Pi.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Cos_plus_Pi.con".
+inline procedural "cic:/CoRN/transc/Pi/Cos_plus_Pi.con" as lemma.
(* UNEXPORTED
Hint Resolve Sin_plus_Pi Cos_plus_Pi: algebra.
(*#* Sine and cosine have period [Two Pi], tangent has period [Pi]. *)
-inline procedural "cic:/CoRN/transc/Pi/Sin_periodic.con".
+inline procedural "cic:/CoRN/transc/Pi/Sin_periodic.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Cos_periodic.con".
+inline procedural "cic:/CoRN/transc/Pi/Cos_periodic.con" as lemma.
-inline procedural "cic:/CoRN/transc/Pi/Tan_periodic.con".
+inline procedural "cic:/CoRN/transc/Pi/Tan_periodic.con" as lemma.
(* UNEXPORTED
End Sin_And_Cos
alias id "a" = "cic:/CoRN/transc/PowerSeries/Power_Series/a.var".
-inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries.con" as definition.
(*#*
The most important convergence criterium specifically for power series
alias id "Ha" = "cic:/CoRN/transc/PowerSeries/Power_Series/Ha.var".
-inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/r.con" "Power_Series__".
+inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/r.con" "Power_Series__" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/Hr.con" "Power_Series__".
+inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/Hr.con" "Power_Series__" as definition.
(* end show *)
-inline procedural "cic:/CoRN/transc/PowerSeries/Dirichlet_crit.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Dirichlet_crit.con" as lemma.
(*#*
When defining a function using its Taylor series as a motivation, the following operator can be of use.
*)
-inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'.con" as definition.
(*#*
This function is also continuous and has a good convergence ratio.
*)
-inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_cont.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_cont.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/included_FPowerSeries'.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/included_FPowerSeries'.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv'.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv'.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv.con" as lemma.
(* UNEXPORTED
End Power_Series
(* begin hide *)
-inline procedural "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/F.con" "More_on_PowerSeries__".
+inline procedural "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/F.con" "More_on_PowerSeries__" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/G.con" "More_on_PowerSeries__".
+inline procedural "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/G.con" "More_on_PowerSeries__" as definition.
(* end hide *)
(*#* We get a comparison test for power series. *)
-inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries'_comp.con" as lemma.
(*#* And a rule for differentiation. *)
Opaque nring fac.
*)
-inline procedural "cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con" as lemma.
(* UNEXPORTED
End More_on_PowerSeries
quotient of sine over cosine.
*)
-inline procedural "cic:/CoRN/transc/PowerSeries/Exp_ps.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Exp_ps.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/sin_seq.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/sin_seq.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/sin_ps.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/sin_ps.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/cos_seq.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/cos_seq.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/cos_ps.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/cos_ps.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/Exp_conv'.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Exp_conv'.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/Exp_conv.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Exp_conv.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/sin_conv.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/sin_conv.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/cos_conv.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/cos_conv.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/Expon.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Expon.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/Sine.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Sine.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/Cosine.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Cosine.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/Tang.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Tang.con" as definition.
(*#*
Some auxiliary domain results.
*)
-inline procedural "cic:/CoRN/transc/PowerSeries/Exp_domain.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Exp_domain.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/sin_domain.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/sin_domain.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/cos_domain.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/cos_domain.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/included_Exp.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/included_Exp.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/included_Sin.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/included_Sin.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/included_Cos.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/included_Cos.con" as lemma.
(*#*
Definition of the logarithm.
*)
-inline procedural "cic:/CoRN/transc/PowerSeries/log_defn_lemma.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/log_defn_lemma.con" as lemma.
-inline procedural "cic:/CoRN/transc/PowerSeries/Logarithm.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Logarithm.con" as definition.
(* UNEXPORTED
End Definitions
As most of these functions are total, it makes sense to treat them as setoid functions on the reals. In the case of logarithm and tangent, this is not possible; however, we still define some abbreviations for aesthetical reasons.
*)
-inline procedural "cic:/CoRN/transc/PowerSeries/Exp.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Exp.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/Sin.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Sin.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/Cos.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Cos.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/Log.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Log.con" as definition.
-inline procedural "cic:/CoRN/transc/PowerSeries/Tan.con".
+inline procedural "cic:/CoRN/transc/PowerSeries/Tan.con" as definition.
[x [>] 0], inspired by the rules for manipulating these expressions.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/power.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power.con" as definition.
(* NOTATION
Notation "x [!] y [//] Hy" := (power x y Hy) (at level 20).
coincides with the exponential function.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/power_wd.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_wd.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/power_strext.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_strext.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/power_plus.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_plus.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/power_inv.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_inv.con" as lemma.
(* UNEXPORTED
Hint Resolve power_wd power_plus power_inv: algebra.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/power_minus.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_minus.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/power_nat.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_nat.con" as lemma.
(* UNEXPORTED
Hint Resolve power_minus power_nat: algebra.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/power_zero.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_zero.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/power_one.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_one.con" as lemma.
(* UNEXPORTED
Hint Resolve power_zero power_one: algebra.
Opaque nexp_op.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/power_int.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_int.con" as lemma.
(* UNEXPORTED
Hint Resolve power_int: algebra.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/Exp_power.con".
+inline procedural "cic:/CoRN/transc/RealPowers/Exp_power.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/mult_power.con".
+inline procedural "cic:/CoRN/transc/RealPowers/mult_power.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/recip_power.con".
+inline procedural "cic:/CoRN/transc/RealPowers/recip_power.con" as lemma.
(* UNEXPORTED
Hint Resolve Exp_power mult_power recip_power: algebra.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/div_power.con".
+inline procedural "cic:/CoRN/transc/RealPowers/div_power.con" as lemma.
(* UNEXPORTED
Hint Resolve div_power: algebra.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/power_ap_zero.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_ap_zero.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/power_mult.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_mult.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/power_pos.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_pos.con" as lemma.
(* UNEXPORTED
Hint Resolve power_mult: algebra.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/power_recip.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_recip.con" as lemma.
(* UNEXPORTED
Hint Resolve power_recip: algebra.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/power_div.con".
+inline procedural "cic:/CoRN/transc/RealPowers/power_div.con" as lemma.
(* UNEXPORTED
Hint Resolve power_div: algebra.
alias id "G" = "cic:/CoRN/transc/RealPowers/Power_Function/G.var".
-inline procedural "cic:/CoRN/transc/RealPowers/FPower.con".
+inline procedural "cic:/CoRN/transc/RealPowers/FPower.con" as definition.
-inline procedural "cic:/CoRN/transc/RealPowers/FPower_domain.con".
+inline procedural "cic:/CoRN/transc/RealPowers/FPower_domain.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/Continuous_power.con".
+inline procedural "cic:/CoRN/transc/RealPowers/Continuous_power.con" as lemma.
(* UNEXPORTED
End Power_Function
(*#* From global continuity we can obviously get local continuity: *)
-inline procedural "cic:/CoRN/transc/RealPowers/continuous_I_power.con".
+inline procedural "cic:/CoRN/transc/RealPowers/continuous_I_power.con" as lemma.
(*#* The rule for differentiation is a must. *)
Opaque Logarithm.
*)
-inline procedural "cic:/CoRN/transc/RealPowers/Derivative_power.con".
+inline procedural "cic:/CoRN/transc/RealPowers/Derivative_power.con" as lemma.
-inline procedural "cic:/CoRN/transc/RealPowers/Diffble_power.con".
+inline procedural "cic:/CoRN/transc/RealPowers/Diffble_power.con" as lemma.
(* UNEXPORTED
End More_on_Power_Function
(* begin hide *)
-inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/F.con" "Sum_and_so_on__".
+inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/F.con" "Sum_and_so_on__" as definition.
-inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/G.con" "Sum_and_so_on__".
+inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/G.con" "Sum_and_so_on__" as definition.
-inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/F'.con" "Sum_and_so_on__".
+inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/F'.con" "Sum_and_so_on__" as definition.
-inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/G'.con" "Sum_and_so_on__".
+inline procedural "cic:/CoRN/transc/SinCos/Sum_and_so_on/G'.con" "Sum_and_so_on__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/transc/SinCos/Sin_plus.con".
+inline procedural "cic:/CoRN/transc/SinCos/Sin_plus.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/Cos_plus.con".
+inline procedural "cic:/CoRN/transc/SinCos/Cos_plus.con" as lemma.
(* UNEXPORTED
Opaque Sine Cosine.
(*#* As a corollary we get the rule for the tangent of the sum. *)
-inline procedural "cic:/CoRN/transc/SinCos/Tan_plus.con".
+inline procedural "cic:/CoRN/transc/SinCos/Tan_plus.con" as lemma.
(* UNEXPORTED
Transparent Sine Cosine.
(*#* Sine, cosine and tangent of [[--]x]. *)
-inline procedural "cic:/CoRN/transc/SinCos/Cos_inv.con".
+inline procedural "cic:/CoRN/transc/SinCos/Cos_inv.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/Sin_inv.con".
+inline procedural "cic:/CoRN/transc/SinCos/Sin_inv.con" as lemma.
(* UNEXPORTED
Opaque Sine Cosine.
Hint Resolve Cos_inv Sin_inv: algebra.
*)
-inline procedural "cic:/CoRN/transc/SinCos/Tan_inv.con".
+inline procedural "cic:/CoRN/transc/SinCos/Tan_inv.con" as lemma.
(* UNEXPORTED
Transparent Sine Cosine.
Hint Resolve Cos_zero: algebra.
*)
-inline procedural "cic:/CoRN/transc/SinCos/FFT.con".
+inline procedural "cic:/CoRN/transc/SinCos/FFT.con" as theorem.
(* UNEXPORTED
Opaque Sine Cosine.
Hint Resolve FFT: algebra.
*)
-inline procedural "cic:/CoRN/transc/SinCos/FFT'.con".
+inline procedural "cic:/CoRN/transc/SinCos/FFT'.con" as lemma.
(* UNEXPORTED
End Sum_and_so_on
Sine, cosine and tangent are strongly extensional and well defined.
*)
-inline procedural "cic:/CoRN/transc/SinCos/Sin_strext.con".
+inline procedural "cic:/CoRN/transc/SinCos/Sin_strext.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/Cos_strext.con".
+inline procedural "cic:/CoRN/transc/SinCos/Cos_strext.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/Tan_strext.con".
+inline procedural "cic:/CoRN/transc/SinCos/Tan_strext.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/Sin_wd.con".
+inline procedural "cic:/CoRN/transc/SinCos/Sin_wd.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/Cos_wd.con".
+inline procedural "cic:/CoRN/transc/SinCos/Cos_wd.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/Tan_wd.con".
+inline procedural "cic:/CoRN/transc/SinCos/Tan_wd.con" as lemma.
(*#*
The sine and cosine produce values in [[-1,1]].
*)
-inline procedural "cic:/CoRN/transc/SinCos/AbsIR_Sin_leEq_One.con".
+inline procedural "cic:/CoRN/transc/SinCos/AbsIR_Sin_leEq_One.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/AbsIR_Cos_leEq_One.con".
+inline procedural "cic:/CoRN/transc/SinCos/AbsIR_Cos_leEq_One.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/Sin_leEq_One.con".
+inline procedural "cic:/CoRN/transc/SinCos/Sin_leEq_One.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/Cos_leEq_One.con".
+inline procedural "cic:/CoRN/transc/SinCos/Cos_leEq_One.con" as lemma.
(*#*
If the cosine is positive then the sine is in [(-1,1)].
*)
-inline procedural "cic:/CoRN/transc/SinCos/Sin_less_One.con".
+inline procedural "cic:/CoRN/transc/SinCos/Sin_less_One.con" as lemma.
-inline procedural "cic:/CoRN/transc/SinCos/AbsIR_Sin_less_One.con".
+inline procedural "cic:/CoRN/transc/SinCos/AbsIR_Sin_less_One.con" as lemma.
(* UNEXPORTED
End Basic_Properties
alias id "Ha" = "cic:/CoRN/transc/TaylorSeries/Definitions/Ha.var".
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con" as definition.
(*#*
%\begin{convention}% Assume also that [f] is the sequence of
alias id "derF" = "cic:/CoRN/transc/TaylorSeries/Definitions/derF.var".
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series.con" as definition.
(* UNEXPORTED
Opaque N_Deriv.
(*#* Characterizations of the Taylor remainder. *)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Rem_char.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Rem_char.con" as lemma.
-inline procedural "cic:/CoRN/transc/TaylorSeries/abs_Taylor_Rem_char.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/abs_Taylor_Rem_char.con" as lemma.
(* UNEXPORTED
End Definitions
alias id "derF" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/derF.var".
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con" as lemma.
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_lemma_cont.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_lemma_cont.con" as lemma.
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_bnd.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_bnd.con" as definition.
(* begin show *)
(* begin hide *)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H1.con" "Convergence_in_IR__".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H1.con" "Convergence_in_IR__" as definition.
(* UNEXPORTED
Transparent nexp_op.
*)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma1.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma1.con" as lemma.
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma2.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma2.con" as lemma.
(* end hide *)
Opaque nexp_op.
*)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_IR.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_IR.con" as lemma.
(* begin hide *)
Transparent nexp_op.
*)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_majoration_lemma.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_majoration_lemma.con" as lemma.
(* UNEXPORTED
Opaque N_Deriv fac.
*)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma3.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_lemma3.con" as lemma.
(* end hide *)
Opaque mult.
*)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_to_fun.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_to_fun.con" as lemma.
(* UNEXPORTED
End Convergence_in_IR
give some helpful lemmas.
*)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_bnd_trans.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_bnd_trans.con" as lemma.
(* begin hide *)
Opaque nexp_op.
*)
-inline procedural "cic:/CoRN/transc/TaylorSeries/convergence_lemma.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/convergence_lemma.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/transc/TaylorSeries/bnd_imp_Taylor_bnd.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/bnd_imp_Taylor_bnd.con" as lemma.
(*#*
Finally, a uniqueness criterium: two functions [F] and [G] are equal,
(* begin hide *)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Other_Results/Hf.con" "Other_Results__".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Other_Results/Hf.con" "Other_Results__" as definition.
(* end hide *)
-inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_unique_crit.con".
+inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_unique_crit.con" as lemma.
(* UNEXPORTED
End Other_Results
$(0,\pi)$#(0,π)# and tangent in $(0,\frac{\pi}2)$#0,π/2)#.
*)
-inline procedural "cic:/CoRN/transc/TrigMon/Cos_pos.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Cos_pos.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Sin_pos.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Sin_pos.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Tan_pos.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Tan_pos.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Cos_nonneg.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Cos_nonneg.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Sin_nonneg.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Sin_nonneg.con" as lemma.
(*#* Consequences. *)
-inline procedural "cic:/CoRN/transc/TrigMon/Abs_Sin_less_One.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Abs_Sin_less_One.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Abs_Cos_less_One.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Abs_Cos_less_One.con" as lemma.
(*#*
Sine is (strictly) increasing in [[ [--]Pi[/]Two,Pi[/]Two]]; cosine
is (strictly) decreasing in [[Zero,Pi]].
*)
-inline procedural "cic:/CoRN/transc/TrigMon/Sin_resp_leEq.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Sin_resp_leEq.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Cos_resp_leEq.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Cos_resp_leEq.con" as lemma.
(* begin hide *)
-inline procedural "cic:/CoRN/transc/TrigMon/Cos_resp_less_aux.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Cos_resp_less_aux.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Cos_resp_less_aux'.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Cos_resp_less_aux'.con" as lemma.
(* end hide *)
-inline procedural "cic:/CoRN/transc/TrigMon/Cos_resp_less.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Cos_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Sin_resp_less.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Sin_resp_less.con" as lemma.
(* UNEXPORTED
Section Tangent
monotonicity properties.
*)
-inline procedural "cic:/CoRN/transc/TrigMon/bnd_Cos.con".
+inline procedural "cic:/CoRN/transc/TrigMon/bnd_Cos.con" as lemma.
(* UNEXPORTED
Opaque Sine Cosine.
*)
-inline procedural "cic:/CoRN/transc/TrigMon/Derivative_Tan_1.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Derivative_Tan_1.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Derivative_Tan_2.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Derivative_Tan_2.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Tan_resp_less.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Tan_resp_less.con" as lemma.
-inline procedural "cic:/CoRN/transc/TrigMon/Tan_resp_leEq.con".
+inline procedural "cic:/CoRN/transc/TrigMon/Tan_resp_leEq.con" as lemma.
(* UNEXPORTED
End Tangent
(*#* First, we need a lemma on mappings. *)
-inline procedural "cic:/CoRN/transc/Trigonometric/maps_translation.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/maps_translation.con" as lemma.
(* UNEXPORTED
End Lemmas
(*#* Sine, cosine and tangent at [Zero]. *)
-inline procedural "cic:/CoRN/transc/Trigonometric/Sin_zero.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sin_zero.con" as lemma.
-inline procedural "cic:/CoRN/transc/Trigonometric/Cos_zero.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Cos_zero.con" as lemma.
(* UNEXPORTED
Hint Resolve Sin_zero Cos_zero: algebra.
Opaque Sine Cosine.
*)
-inline procedural "cic:/CoRN/transc/Trigonometric/Tan_zero.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Tan_zero.con" as lemma.
(* UNEXPORTED
Transparent Sine Cosine.
Continuity of sine and cosine are trivial.
*)
-inline procedural "cic:/CoRN/transc/Trigonometric/Continuous_Sin.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Continuous_Sin.con" as lemma.
-inline procedural "cic:/CoRN/transc/Trigonometric/Continuous_Cos.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Continuous_Cos.con" as lemma.
(*#*
The rules for the derivative of the sine and cosine function; we begin by proving that their defining sequences can be expressed in terms of one another.
*)
-inline procedural "cic:/CoRN/transc/Trigonometric/cos_sin_seq.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/cos_sin_seq.con" as lemma.
-inline procedural "cic:/CoRN/transc/Trigonometric/sin_cos_seq.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/sin_cos_seq.con" as lemma.
-inline procedural "cic:/CoRN/transc/Trigonometric/Derivative_Sin.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Derivative_Sin.con" as lemma.
-inline procedural "cic:/CoRN/transc/Trigonometric/Derivative_Cos.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Derivative_Cos.con" as lemma.
(* UNEXPORTED
Hint Resolve Derivative_Sin Derivative_Cos: derivate.
(* begin hide *)
-inline procedural "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F.con" "Sine_and_Cosine__Sine_of_Sum__".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F.con" "Sine_and_Cosine__Sine_of_Sum__" as definition.
-inline procedural "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G.con" "Sine_and_Cosine__Sine_of_Sum__".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G.con" "Sine_and_Cosine__Sine_of_Sum__" as definition.
-inline procedural "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F'.con" "Sine_and_Cosine__Sine_of_Sum__".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F'.con" "Sine_and_Cosine__Sine_of_Sum__" as definition.
-inline procedural "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G'.con" "Sine_and_Cosine__Sine_of_Sum__".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G'.con" "Sine_and_Cosine__Sine_of_Sum__" as definition.
(* end hide *)
Transparent FAbs.
*)
-inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_lft.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_lft.con" as lemma.
(* UNEXPORTED
Opaque FAbs.
Transparent FAbs.
*)
-inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_rht.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_Taylor_bnd_rht.con" as lemma.
-inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_eq.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_eq.con" as lemma.
-inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_der_lft.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_der_lft.con" as lemma.
-inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_der_rht.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_der_rht.con" as lemma.
-inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_fun.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Sin_plus_fun.con" as lemma.
(* UNEXPORTED
End Sine_of_Sum
Opaque Sine Cosine.
*)
-inline procedural "cic:/CoRN/transc/Trigonometric/Cos_plus_fun.con".
+inline procedural "cic:/CoRN/transc/Trigonometric/Cos_plus_fun.con" as lemma.
(* UNEXPORTED
End Sine_and_Cosine
projects / helm.git / commitdiff