| 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_unexported och "UNEXPORTED" src
+(* FG: we do not export variables because we cook the other object
+ * let name = UriManager.name_of_uri (UriManager.uri_of_string src) in
+ * out_alias och name 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
let cat x = String.concat " " x
let mk_vars local idents =
- let map ident = T.Inline (local, T.Var, trim ident, "", None) in
+ let kind = if local then T.Var else T.Con in
+ let map ident = T.Inline (local, kind, trim ident, "", None) in
List.map map idents
let strip2 s =
$(H)echo no files to clean
endif
-mma: CoRN.conf.xml
+mma: CoRN.conf.xml clean.ma
$(H)$(TRANSCRIPT) -C $(BIN) CoRN
Section Well_foundedT
*)
-alias id "A" = "cic:/CoRN/algebra/Basics/Well_foundedT/A.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/Well_foundedT/A.var
+*)
-alias id "R" = "cic:/CoRN/algebra/Basics/Well_foundedT/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/Well_foundedT/R.var
+*)
(*#* The accessibility predicate is defined to be non-informative *)
Section AccT
*)
-alias id "A" = "cic:/CoRN/algebra/Basics/AccT/A.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/AccT/A.var
+*)
inline procedural "cic:/CoRN/algebra/Basics/well_founded.con" as definition.
Section IndT
*)
-alias id "A" = "cic:/CoRN/algebra/Basics/IndT/A.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/IndT/A.var
+*)
-alias id "R" = "cic:/CoRN/algebra/Basics/IndT/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/IndT/R.var
+*)
(* UNEXPORTED
Section AccIter
*)
-alias id "P" = "cic:/CoRN/algebra/Basics/IndT/AccIter/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/IndT/AccIter/P.var
+*)
-alias id "F" = "cic:/CoRN/algebra/Basics/IndT/AccIter/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/IndT/AccIter/F.var
+*)
inline procedural "cic:/CoRN/algebra/Basics/Acc_inv.con" as lemma.
End AccIter
*)
-alias id "Rwf" = "cic:/CoRN/algebra/Basics/IndT/Rwf.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/IndT/Rwf.var
+*)
inline procedural "cic:/CoRN/algebra/Basics/well_founded_induction_type.con" as theorem.
Section InductionT
*)
-alias id "A" = "cic:/CoRN/algebra/Basics/InductionT/A.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/InductionT/A.var
+*)
-alias id "f" = "cic:/CoRN/algebra/Basics/InductionT/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Basics/InductionT/f.var
+*)
inline procedural "cic:/CoRN/algebra/Basics/ltof.con" as definition.
Section AbGroup_Axioms
*)
-alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/AbGroup_Axioms/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Abelian_Groups/AbGroup_Axioms/G.var
+*)
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
** Subgroups of an Abelian Group
*)
-alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/G.var
+*)
-alias id "P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/P.var
+*)
-alias id "Punit" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/Punit.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/Punit.var
+*)
-alias id "op_pres_P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/op_pres_P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/op_pres_P.var
+*)
-alias id "inv_pres_P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/inv_pres_P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/inv_pres_P.var
+*)
(*#*
%\begin{convention}%
Hint Resolve cag_commutes_unfolded: algebra.
*)
-alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/Various/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Abelian_Groups/Various/G.var
+*)
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
function [inv] which inverts elements respective to [plus].
*)
-alias id "S" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Nice_Char/S.var
+*)
-alias id "unit" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/unit.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Nice_Char/unit.var
+*)
-alias id "plus" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Nice_Char/plus.var
+*)
(*#*
%\begin{convention}%
%\end{convention}%
*)
-alias id "plus_lext" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lext.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lext.var
+*)
-alias id "plus_lunit" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lunit.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lunit.var
+*)
-alias id "plus_comm" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_comm.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_comm.var
+*)
-alias id "plus_assoc" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_assoc.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_assoc.var
+*)
-alias id "inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Nice_Char/inv.var
+*)
-alias id "inv_inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var
+*)
inline procedural "cic:/CoRN/algebra/CAbGroups/plus_rext.con" as lemma.
Section Group_Extras
*)
-alias id "G" = "cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var
+*)
inline procedural "cic:/CoRN/algebra/CAbGroups/nmult.con" as definition.
Section AbMonoid_Axioms
*)
-alias id "M" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.var
+*)
(*#*
%\begin{convention}% Let [M] be an abelian monoid.
** Subgroups of an Abelian Monoid
*)
-alias id "M" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/M.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/M.var
+*)
-alias id "P" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/P.var
+*)
-alias id "Punit" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/Punit.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/Punit.var
+*)
-alias id "op_pres_P" = "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/op_pres_P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/op_pres_P.var
+*)
(*#*
%\begin{convention}%
Section Field_axioms
*)
-alias id "F" = "cic:/CoRN/algebra/CFields/Field_axioms/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/Field_axioms/F.var
+*)
inline procedural "cic:/CoRN/algebra/CFields/CField_is_CField.con" as lemma.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/algebra/CFields/Field_basics/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/Field_basics/F.var
+*)
inline procedural "cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con" as lemma.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/algebra/CFields/Field_multiplication/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/Field_multiplication/F.var
+*)
inline procedural "cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con" as lemma.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/algebra/CFields/Rcpcl_properties/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/Rcpcl_properties/F.var
+*)
inline procedural "cic:/CoRN/algebra/CFields/inv_one.con" as lemma.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/algebra/CFields/MultipGroup/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/MultipGroup/F.var
+*)
(*#*
The multiplicative monoid of NonZeros.
%\end{nameconvention}%
*)
-alias id "F" = "cic:/CoRN/algebra/CFields/Div_properties/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/Div_properties/F.var
+*)
inline procedural "cic:/CoRN/algebra/CFields/div_prop.con" as lemma.
Section Mult_Cancel_Ap_Zero
*)
-alias id "F" = "cic:/CoRN/algebra/CFields/Mult_Cancel_Ap_Zero/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/Mult_Cancel_Ap_Zero/F.var
+*)
inline procedural "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con" as lemma.
%\end{convention}%
*)
-alias id "X" = "cic:/CoRN/algebra/CFields/CField_Ops/X.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/CField_Ops/X.var
+*)
-alias id "F" = "cic:/CoRN/algebra/CFields/CField_Ops/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/CField_Ops/F.var
+*)
-alias id "G" = "cic:/CoRN/algebra/CFields/CField_Ops/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/CField_Ops/G.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CFields/CField_Ops/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CFields/CField_Ops/R.var
+*)
inline procedural "cic:/CoRN/algebra/CFields/included_FRecip.con" as lemma.
Section CGroup_axioms
*)
-alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_axioms/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/CGroup_axioms/G.var
+*)
inline procedural "cic:/CoRN/algebra/CGroups/cg_inverse.con" as lemma.
Section CGroup_basics
*)
-alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_basics/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/CGroup_basics/G.var
+*)
inline procedural "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con" as lemma.
Section SubCGroups
*)
-alias id "P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/P.var
+*)
-alias id "Punit" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/Punit.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/Punit.var
+*)
-alias id "op_pres_P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/op_pres_P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/op_pres_P.var
+*)
-alias id "inv_pres_P" = "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/inv_pres_P.var".
+(* UNEXPORTED
+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__" as definition.
Section Assoc_properties
*)
-alias id "G" = "cic:/CoRN/algebra/CGroups/Assoc_properties/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/Assoc_properties/G.var
+*)
inline procedural "cic:/CoRN/algebra/CGroups/assoc_2.con" as lemma.
Section cgroups_apartness
*)
-alias id "G" = "cic:/CoRN/algebra/CGroups/cgroups_apartness/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/cgroups_apartness/G.var
+*)
inline procedural "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con" as lemma.
%\end{convention}%
*)
-alias id "G" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/CGroup_Ops/G.var
+*)
-alias id "F" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/CGroup_Ops/F.var
+*)
-alias id "F'" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/F'.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/CGroup_Ops/F'.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CGroups/CGroup_Ops/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CGroups/CGroup_Ops/R.var
+*)
inline procedural "cic:/CoRN/algebra/CGroups/included_FInv.con" as lemma.
Let [P] be a predicate on $\NN^2$#N times N#.
*)
-alias id "P" = "cic:/CoRN/algebra/CLogic/Choice/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CLogic/Choice/P.var
+*)
inline procedural "cic:/CoRN/algebra/CLogic/choice.con" as lemma.
%\end{convention}%
*)
-alias id "A" = "cic:/CoRN/algebra/CLogic/CRelation_Definition/A.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CLogic/CRelation_Definition/A.var
+*)
inline procedural "cic:/CoRN/algebra/CLogic/Crelation.con" as definition.
-alias id "R" = "cic:/CoRN/algebra/CLogic/CRelation_Definition/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CLogic/CRelation_Definition/R.var
+*)
inline procedural "cic:/CoRN/algebra/CLogic/Creflexive.con" as definition.
%\end{convention}%
*)
-alias id "A" = "cic:/CoRN/algebra/CLogic/TRelation_Definition/A.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CLogic/TRelation_Definition/A.var
+*)
inline procedural "cic:/CoRN/algebra/CLogic/Trelation.con" as definition.
-alias id "R" = "cic:/CoRN/algebra/CLogic/TRelation_Definition/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CLogic/TRelation_Definition/R.var
+*)
inline procedural "cic:/CoRN/algebra/CLogic/Treflexive.con" as definition.
%\end{convention}%
*)
-alias id "h" = "cic:/CoRN/algebra/CLogic/Natural_Numbers/h.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CLogic/Natural_Numbers/h.var
+*)
(*#*
First we characterize monotonicity by a local condition: if [h(n) < h(n+1)]
Section CMonoid_axioms
*)
-alias id "M" = "cic:/CoRN/algebra/CMonoids/CMonoid_axioms/M.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CMonoids/CMonoid_axioms/M.var
+*)
inline procedural "cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con" as lemma.
Section CMonoid_basics
*)
-alias id "M" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/M.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CMonoids/CMonoid_basics/M.var
+*)
inline procedural "cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con" as lemma.
Section SubCMonoids
*)
-alias id "P" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/P.var
+*)
-alias id "Punit" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/Punit.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/Punit.var
+*)
-alias id "op_pres_P" = "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/op_pres_P.var".
+(* UNEXPORTED
+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__" as definition.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/COrdAbs/AbsSmall_properties/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdAbs/AbsSmall_properties/R.var
+*)
inline procedural "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/COrdAbs/absBig_wd_properties/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdAbs/absBig_wd_properties/R.var
+*)
inline procedural "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/R.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "f" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f.var
+*)
-alias id "g" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/g.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/g.var
+*)
-alias id "Hf" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hf.var
+*)
-alias id "Hg" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hg.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hg.var
+*)
inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con" as lemma.
%\end{convention}%
*)
-alias id "e" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/e.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/e.var
+*)
-alias id "He" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/He.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/He.var
+*)
-alias id "N" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/N.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/N.var
+*)
-alias id "f_bnd" = "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f_bnd.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f_bnd.var
+*)
inline procedural "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con" as lemma.
Section Mult_AbsSmall
*)
-alias id "R" = "cic:/CoRN/algebra/COrdCauchy/Mult_AbsSmall/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/Mult_AbsSmall/R.var
+*)
(*#*
** [AbsSmall] revisited
Section Mult_Continuous
*)
-alias id "R" = "cic:/CoRN/algebra/COrdCauchy/Mult_Continuous/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/Mult_Continuous/R.var
+*)
(*#*
** Multiplication is continuous
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/COrdCauchy/Monotonous_functions/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdCauchy/Monotonous_functions/R.var
+*)
(*#*
We begin by characterizing the preservation of less (less or equal)
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/algebra/COrdFields/COrdField_axioms/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields/COrdField_axioms/F.var
+*)
inline procedural "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/COrdFields/OrdField_basics/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields/OrdField_basics/R.var
+*)
inline procedural "cic:/CoRN/algebra/COrdFields/less_imp_ap.con" as lemma.
(*#* ** Basic properties of [ [<=] ]
*)
-alias id "R" = "cic:/CoRN/algebra/COrdFields/Basic_Properties_of_leEq/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields/Basic_Properties_of_leEq/R.var
+*)
inline procedural "cic:/CoRN/algebra/COrdFields/leEq_wdr.con" as lemma.
e.g.%\% [x[/]TwoNZ].
*)
-alias id "R" = "cic:/CoRN/algebra/COrdFields/infinity_of_cordfields/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields/infinity_of_cordfields/R.var
+*)
inline procedural "cic:/CoRN/algebra/COrdFields/pos_one.con" as lemma.
*** Consequences of infinity
*)
-alias id "F" = "cic:/CoRN/algebra/COrdFields/consequences_of_infinity/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields/consequences_of_infinity/F.var
+*)
inline procedural "cic:/CoRN/algebra/COrdFields/square_eq.con" as lemma.
** Properties of [[<]]
*)
-alias id "R" = "cic:/CoRN/algebra/COrdFields/Properties_of_Ordering/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields/Properties_of_Ordering/R.var
+*)
(*#*
We do not use a special predicate for positivity,
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/COrdFields2/Properties_of_leEq/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields2/Properties_of_leEq/R.var
+*)
(* UNEXPORTED
Section addition
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/COrdFields2/PosP_properties/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields2/PosP_properties/R.var
+*)
(* begin hide *)
Section One_div_succ_properties
*)
-alias id "R" = "cic:/CoRN/algebra/COrdFields2/One_div_succ_properties/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields2/One_div_succ_properties/R.var
+*)
inline procedural "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/COrdFields2/Half_properties/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/COrdFields2/Half_properties/R.var
+*)
inline procedural "cic:/CoRN/algebra/COrdFields2/half_1.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/R.var
+*)
-alias id "a_" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/a_.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/a_.var
+*)
-alias id "distinct_a_" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/distinct_a_.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/distinct_a_.var
+*)
-alias id "f" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/f.var
+*)
-alias id "n" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/n.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/n.var
+*)
-alias id "degree_f" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/degree_f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/degree_f.var
+*)
(* begin hide *)
strengthened.
*)
-alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/R.var
+*)
(* begin show *)
-alias id "H" = "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/H.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/H.var
+*)
(* end show *)
Section Poly_ApZero_Interval
*)
-alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_ApZero_Interval/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_ApZero/Poly_ApZero_Interval/R.var
+*)
(* begin hide *)
Section Degree_def
*)
-alias id "R" = "cic:/CoRN/algebra/CPoly_Degree/Degree_def/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_Degree/Degree_def/R.var
+*)
(* begin hide *)
Section Degree_props
*)
-alias id "R" = "cic:/CoRN/algebra/CPoly_Degree/Degree_props/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_Degree/Degree_props/R.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/algebra/CPoly_Degree/degree_props_Field/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_Degree/degree_props_Field/F.var
+*)
(* begin hide *)
Section NthCoeff_def
*)
-alias id "R" = "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_def/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_def/R.var
+*)
(* begin hide *)
(*#* ** Properties of [nth_coeff] *)
-alias id "R" = "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_props/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_props/R.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "CR" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/CR.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPolynomials/CPoly_CRing/CR.var
+*)
(*#*
The intuition behind the type [cpoly] is the following
%\end{convention}%
*)
-alias id "CR" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/CR.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/CR.var
+*)
(* NOTATION
Notation RX := (cpoly_cring CR).
Section helpful_section
*)
-alias id "p" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/p.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/p.var
+*)
-alias id "q" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/q.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/q.var
+*)
-alias id "c" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/c.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/c.var
+*)
-alias id "d" = "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/d.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/d.var
+*)
inline procedural "cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con" as lemma.
Section Poly_properties
*)
-alias id "R" = "cic:/CoRN/algebra/CPolynomials/Poly_properties/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPolynomials/Poly_properties/R.var
+*)
(* NOTATION
Notation RX := (cpoly_cring R).
Section Poly_Prop_Induction
*)
-alias id "CR" = "cic:/CoRN/algebra/CPolynomials/Poly_Prop_Induction/CR.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CPolynomials/Poly_Prop_Induction/CR.var
+*)
(* NOTATION
Notation Cpoly := (cpoly CR).
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/CRing_axioms/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/CRing_axioms/R.var
+*)
inline procedural "cic:/CoRN/algebra/CRings/CRing_is_CRing.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/Ring_constructions/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/Ring_constructions/R.var
+*)
(*#*
The multiplicative monoid of a ring is defined as follows.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/Ring_unfolded/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/Ring_unfolded/R.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/Ring_basics/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/Ring_basics/R.var
+*)
inline procedural "cic:/CoRN/algebra/CRings/one_ap_zero.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/exponentiation/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/exponentiation/R.var
+*)
(* End_SpecReals *)
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/nat_injection/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/nat_injection/R.var
+*)
(*#*
The injection of Coq natural numbers into a ring is called [nring].
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/int_injection/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/int_injection/R.var
+*)
(*#*
The injection of Coq integers into a ring is called [zring]. Again,
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/Ring_sums/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/Ring_sums/R.var
+*)
(*#*
*** Infinite Ring sums
Section Dist_properties
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/Dist_properties/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/Dist_properties/R.var
+*)
inline procedural "cic:/CoRN/algebra/CRings/dist_1b.con" as lemma.
Section NExp_properties
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/NExp_properties/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/NExp_properties/R.var
+*)
inline procedural "cic:/CoRN/algebra/CRings/nexp_wd.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/CRing_Ops/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/CRing_Ops/R.var
+*)
-alias id "F" = "cic:/CoRN/algebra/CRings/CRing_Ops/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/CRing_Ops/F.var
+*)
-alias id "G" = "cic:/CoRN/algebra/CRings/CRing_Ops/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/CRing_Ops/G.var
+*)
(* begin hide *)
Section Part_Function_Nth_Power
*)
-alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var
+*)
inline procedural "cic:/CoRN/algebra/CRings/part_function_nth_strext.con" as lemma.
%\end{convention}%
*)
-alias id "R'" = "cic:/CoRN/algebra/CRings/CRing_Ops/R'.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/CRing_Ops/R'.var
+*)
inline procedural "cic:/CoRN/algebra/CRings/included_FMult.con" as lemma.
inline procedural "cic:/CoRN/algebra/CRings/included_FMult''.con" as lemma.
-alias id "n" = "cic:/CoRN/algebra/CRings/CRing_Ops/n.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/CRing_Ops/n.var
+*)
inline procedural "cic:/CoRN/algebra/CRings/included_FNth.con" as lemma.
Section ScalarMultiplication
*)
-alias id "R" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/ScalarMultiplication/R.var
+*)
-alias id "F" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/ScalarMultiplication/F.var
+*)
(* begin hide *)
(* end hide *)
-alias id "R'" = "cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var
+*)
inline procedural "cic:/CoRN/algebra/CRings/included_FScalMult.con" as lemma.
Section CSemiGroup_axioms
*)
-alias id "G" = "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_axioms/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSemiGroups/CSemiGroup_axioms/G.var
+*)
inline procedural "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con" as lemma.
Section CSemiGroup_basics
*)
-alias id "G" = "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_basics/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSemiGroups/CSemiGroup_basics/G.var
+*)
(* End_SpecReals *)
Section Part_Function_Plus
*)
-alias id "G" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/G.var
+*)
-alias id "F" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F.var
+*)
-alias id "F'" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F'.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F'.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/R.var
+*)
inline procedural "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con" as lemma.
Section SubCSemiGroups
*)
-alias id "csg" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/csg.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/csg.var
+*)
-alias id "P" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/P.var
+*)
-alias id "op_pres_P" = "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/op_pres_P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/op_pres_P.var
+*)
inline procedural "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/subcrr.con" "SubCSemiGroups__" as definition.
setoid function from [S1] to [S2], and [g] from [S2]
to [S3] in the following definition of composition. *)
-alias id "S1" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S1.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S1.var
+*)
-alias id "S2" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S2.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S2.var
+*)
-alias id "S3" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S3.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S3.var
+*)
-alias id "f" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/unary_function_composition/f.var
+*)
-alias id "g" = "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/g.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/unary_function_composition/g.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con" as definition.
Section BinProj
*)
-alias id "S" = "cic:/CoRN/algebra/CSetoidFun/BinProj/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/BinProj/S.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoidFun/binproj1.con" as definition.
Section CombiningOperations
*)
-alias id "S1" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S1.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S1.var
+*)
-alias id "S2" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S2.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S2.var
+*)
-alias id "S3" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S3.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S3.var
+*)
(*#*
In the following definition, we assume [f] is a setoid function from
Section CombiningUnaryOperations
*)
-alias id "f" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/f.var
+*)
-alias id "op" = "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/op.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/op.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoidFun/opOnFun.con" as definition.
%\end{convention}%
*)
-alias id "S" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/S.var
+*)
(* UNEXPORTED
Section Conjunction
*)
-alias id "P" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/P.var
+*)
-alias id "Q" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/Q.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/Q.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoidFun/conjP.con" as definition.
Section Disjunction
*)
-alias id "P" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/P.var
+*)
-alias id "Q" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/Q.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/Q.var
+*)
(*#*
Although at this stage we never use it, for completeness's sake we also treat disjunction (corresponding to union of subsets).
The next definition is a bit tricky, and is useful for choosing among the elements that satisfy a predicate [P] those that also satisfy [R] in the case where [R] is only defined for elements satisfying [P]---consider [R] to be a condition on the image of an object via a function with domain [P]. We chose to call this operation [extension].
*)
-alias id "P" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/P.var
+*)
-alias id "R" = "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/R.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoidFun/extend.con" as definition.
Section CSetoid_Ops
*)
-alias id "S" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/S.var
+*)
(*#*
To begin with, we want to be able to ``see'' each total function as a partial function.
%\end{convention}%
*)
-alias id "c" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Const/c.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Const/c.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoidFun/Fconst.con" as definition.
Section Part_Function_Composition
*)
-alias id "G" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/G.var
+*)
-alias id "F" = "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/F.var
+*)
(* begin hide *)
Section BinPart_Function_Composition
*)
-alias id "S1" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S1.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S1.var
+*)
-alias id "S2" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S2.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S2.var
+*)
-alias id "S3" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S3.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S3.var
+*)
-alias id "G" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/G.var
+*)
-alias id "F" = "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/F.var
+*)
(* begin hide *)
Let [S] be a setoid, and [P], [Q], [R] be predicates on [S]. *)
-alias id "S" = "cic:/CoRN/algebra/CSetoidInc/inclusion/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidInc/inclusion/S.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoidInc/included.con" as definition.
Section Basics
*)
-alias id "P" = "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/P.var
+*)
-alias id "Q" = "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/Q.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/Q.var
+*)
-alias id "R" = "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoidInc/included_refl.con" as lemma.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/algebra/CSetoidInc/inclusion/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidInc/inclusion/F.var
+*)
-alias id "G" = "cic:/CoRN/algebra/CSetoidInc/inclusion/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidInc/inclusion/G.var
+*)
(* begin hide *)
(* end hide *)
-alias id "R" = "cic:/CoRN/algebra/CSetoidInc/inclusion/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoidInc/inclusion/R.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoidInc/included_FComp.con" as lemma.
Section Properties_of_relations
*)
-alias id "A" = "cic:/CoRN/algebra/CSetoids/Properties_of_relations/A.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/Properties_of_relations/A.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/irreflexive.con" as definition.
Section CSetoid_axioms
*)
-alias id "S" = "cic:/CoRN/algebra/CSetoids/CSetoid_axioms/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_axioms/S.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con" as lemma.
Section CSetoid_basics
*)
-alias id "S" = "cic:/CoRN/algebra/CSetoids/CSetoid_basics/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_basics/S.var
+*)
(* End_SpecReals *)
Section CSetoid_relations_and_predicates
*)
-alias id "S" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/S.var
+*)
(* End_SpecReals *)
Section CSetoidPredicates
*)
-alias id "P" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPredicates/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPredicates/P.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext.con" as definition.
Section CSetoidPPredicates
*)
-alias id "P" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPPredicates/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPPredicates/P.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con" as definition.
Section CsetoidRelations
*)
-alias id "R" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CsetoidRelations/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CsetoidRelations/R.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/rel_wdr.con" as definition.
Section CCsetoidRelations
*)
-alias id "R" = "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CCsetoidRelations/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CCsetoidRelations/R.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/Crel_wdr.con" as definition.
Section CSetoid_functions
*)
-alias id "S1" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S1.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_functions/S1.var
+*)
-alias id "S2" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S2.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_functions/S2.var
+*)
-alias id "S3" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S3.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_functions/S3.var
+*)
(* UNEXPORTED
Section unary_functions
[f] is a function from (the carrier of) [S1] to
(the carrier of) [S2]. *)
-alias id "f" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/unary_functions/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_functions/unary_functions/f.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/fun_wd.con" as definition.
[f] is a function from [S1] and [S2] to [S3].
*)
-alias id "f" = "cic:/CoRN/algebra/CSetoids/CSetoid_functions/binary_functions/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/CSetoid_functions/binary_functions/f.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/bin_fun_wd.con" as definition.
Section csetoid_inner_ops
*)
-alias id "S" = "cic:/CoRN/algebra/CSetoids/csetoid_inner_ops/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/csetoid_inner_ops/S.var
+*)
(*#* Properties of binary operations *)
Section csetoid_outer_ops
*)
-alias id "S1" = "cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S1.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S1.var
+*)
-alias id "S2" = "cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S2.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S2.var
+*)
(*#*
Well-defined outer operations on a setoid.
Section SubCSetoids
*)
-alias id "S" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/S.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/SubCSetoids/S.var
+*)
-alias id "P" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/P.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/SubCSetoids/P.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/subcsetoid_crr.ind".
Section SubCSetoid_unary_operations
*)
-alias id "f" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/f.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con" as definition.
Assume [pr:un_op_pres_pred].
%\end{convention}% *)
-alias id "pr" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/pr.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/pr.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/restr_un_op.con" as definition.
Section SubCSetoid_binary_operations
*)
-alias id "f" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/f.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con" as definition.
%\end{convention}%
*)
-alias id "pr" = "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/pr.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/pr.var
+*)
inline procedural "cic:/CoRN/algebra/CSetoids/restr_bin_op.con" as definition.
Section Sums
*)
-alias id "G" = "cic:/CoRN/algebra/CSums/Sums/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSums/Sums/G.var
+*)
(* Sum1 and Sum use subtraction *)
Section More_Sums
*)
-alias id "G" = "cic:/CoRN/algebra/CSums/More_Sums/G.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CSums/More_Sums/G.var
+*)
inline procedural "cic:/CoRN/algebra/CSums/Mengolli_Sum.con" as lemma.
Section VS_basics
*)
-alias id "F" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var
+*)
-alias id "V" = "cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var
+*)
inline procedural "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con" as lemma.
Section Structure
*)
-alias id "F" = "cic:/CoRN/algebra/Cauchy_COF/Structure/F.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Cauchy_COF/Structure/F.var
+*)
(*#*
** Setoid Structure
Section More_Nexp
*)
-alias id "R" = "cic:/CoRN/algebra/Expon/More_Nexp/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Expon/More_Nexp/R.var
+*)
inline procedural "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con" as lemma.
Section Zexp_def
*)
-alias id "R" = "cic:/CoRN/algebra/Expon/Zexp_def/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Expon/Zexp_def/R.var
+*)
(*#*
It would be nicer to define [zexp] using [caseZdiff], but we already
Section Zexp_properties
*)
-alias id "R" = "cic:/CoRN/algebra/Expon/Zexp_properties/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Expon/Zexp_properties/R.var
+*)
inline procedural "cic:/CoRN/algebra/Expon/zexp_zero.con" as lemma.
Section Root_Unique
*)
-alias id "R" = "cic:/CoRN/algebra/Expon/Root_Unique/R.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/Expon/Root_Unique/R.var
+*)
inline procedural "cic:/CoRN/algebra/Expon/root_unique.con" as lemma.
Section List
*)
-alias id "A" = "cic:/CoRN/algebra/ListType/List/A.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/ListType/List/A.var
+*)
inline procedural "cic:/CoRN/algebra/ListType/list.ind".
Hint Unfold lel: list.
*)
-alias id "a" = "cic:/CoRN/algebra/ListType/List/length_order/a.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/ListType/List/length_order/a.var
+*)
-alias id "b" = "cic:/CoRN/algebra/ListType/List/length_order/b.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/ListType/List/length_order/b.var
+*)
-alias id "l" = "cic:/CoRN/algebra/ListType/List/length_order/l.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/ListType/List/length_order/l.var
+*)
-alias id "m" = "cic:/CoRN/algebra/ListType/List/length_order/m.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/ListType/List/length_order/m.var
+*)
-alias id "n" = "cic:/CoRN/algebra/ListType/List/length_order/n.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/ListType/List/length_order/n.var
+*)
inline procedural "cic:/CoRN/algebra/ListType/lel_refl.con" as lemma.
Section Map
*)
-alias id "A" = "cic:/CoRN/algebra/ListType/Map/A.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/ListType/Map/A.var
+*)
-alias id "B" = "cic:/CoRN/algebra/ListType/Map/B.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/ListType/Map/B.var
+*)
-alias id "f" = "cic:/CoRN/algebra/ListType/Map/f.var".
+(* UNEXPORTED
+cic:/CoRN/algebra/ListType/Map/f.var
+*)
inline procedural "cic:/CoRN/algebra/ListType/map.con" as definition.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a.var
+*)
-alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b.var
+*)
-alias id "b_" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b_.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a.var
+*)
-alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b.var
+*)
-alias id "a_" = "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a_.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_2/n.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_2/n.var
+*)
-alias id "c" = "cic:/CoRN/complex/NRootCC/NRootCC_2/c.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_2/c.var
+*)
-alias id "z" = "cic:/CoRN/complex/NRootCC/NRootCC_2/z.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_2/z.var
+*)
-alias id "c_" = "cic:/CoRN/complex/NRootCC/NRootCC_2/c_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_2/c_.var
+*)
inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_2'.con" as lemma.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_3/a.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_3/a.var
+*)
-alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_3/b.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_3/b.var
+*)
-alias id "b_" = "cic:/CoRN/complex/NRootCC/NRootCC_3/b_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_3/b_.var
+*)
-alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_3/n.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_3/n.var
+*)
inline procedural "cic:/CoRN/complex/NRootCC/nrCC3_poly''.con" as definition.
%\end{convention}%
*)
-alias id "c" = "cic:/CoRN/complex/NRootCC/NRootCC_3'/c.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_3'/c.var
+*)
-alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_3'/n.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_3'/n.var
+*)
-alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_3'/n_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_3'/n_.var
+*)
inline procedural "cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con" as definition.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/a.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/a.var
+*)
-alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b.var
+*)
-alias id "b_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b_.var
+*)
-alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n.var
+*)
-alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n_.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "r2'" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'.var
+*)
-alias id "c2" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/c2.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/c2.var
+*)
-alias id "r2'_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'_.var
+*)
(* UNEXPORTED
Hint Resolve nrootCC_3': algebra.
%\end{convention}%
*)
-alias id "r" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r.var
+*)
-alias id "r_property" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r_property.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r_property.var
+*)
-alias id "y2" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2.var
+*)
-alias id "y2_property" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2_property.var".
+(* UNEXPORTED
+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" as lemma.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a.var
+*)
-alias id "b" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b.var
+*)
-alias id "a_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a_.var
+*)
-alias id "n" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n.var
+*)
-alias id "n_" = "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n_.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "c" = "cic:/CoRN/complex/NRootCC/NRootCC_5/c.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_5/c.var
+*)
-alias id "c_" = "cic:/CoRN/complex/NRootCC/NRootCC_5/c_.var".
+(* UNEXPORTED
+cic:/CoRN/complex/NRootCC/NRootCC_5/c_.var
+*)
inline procedural "cic:/CoRN/complex/NRootCC/nrCC_5a4.con" as lemma.
Section p66E2
*)
-alias id "X" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/X.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/X.var
+*)
-alias id "f" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/f.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/f.var
+*)
-alias id "g" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/g.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/g.var
+*)
-alias id "h" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/h.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/h.var
+*)
(* Check comp_as_bin_op.*)
Section p66E2b4
*)
-alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2b4/A.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p66E2b4/A.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con" as definition.
Section p67R2
*)
-alias id "X" = "cic:/CoRN/devel/loeb/IDA/Ch6/p67R2/X.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p67R2/X.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con" as lemma.
Section D9S
*)
-alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M1.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M1.var
+*)
-alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M2.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M2.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con" as definition.
Section D9M
*)
-alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M1.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M1.var
+*)
-alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M2.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M2.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con" as lemma.
Section Th11
*)
-alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/M.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th11/M.var
+*)
-alias id "I" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/I.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th11/I.var
+*)
-alias id "C" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/C.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th11/C.var
+*)
-alias id "Cunit" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/Cunit.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th11/Cunit.var
+*)
-alias id "op_pres_C" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/op_pres_C.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th11/op_pres_C.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/K.con" as definition.
Section Th12
*)
-alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th12/A.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th12/A.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con" as lemma.
Section Th13
*)
-alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M1.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M1.var
+*)
-alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M2.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M2.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con" as definition.
Section p71E1
*)
-alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/M.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/M.var
+*)
-alias id "c" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/c.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/c.var
+*)
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" as definition.
-alias id "is_generated_by" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/is_generated_by.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/is_generated_by.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/f.con" "p71E1__" as definition.
Section p71E2
*)
-alias id "A" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/A.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/A.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/L.con" "p71E2__" as definition.
Section p71R1
*)
-alias id "S1" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S1.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S1.var
+*)
-alias id "S2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S2.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S2.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con" as definition.
Section p71R2
*)
-alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71R2/M.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p71R2/M.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con" as definition.
Section Th14
*)
-alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M1.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M1.var
+*)
-alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M2.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M2.var
+*)
-alias id "f" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/f.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th14/f.var
+*)
-alias id "isof" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/isof.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th14/isof.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con" as lemma.
Section p71E2b2
*)
-alias id "M1" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M1.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M1.var
+*)
-alias id "M2" = "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M2.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M2.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/f.con" "p71E2b2__" as definition.
Section Th15
*)
-alias id "M" = "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/M.var".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th15/M.var
+*)
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".
+(* UNEXPORTED
+cic:/CoRN/devel/loeb/IDA/Ch6/Th15/D.var
+*)
inline procedural "cic:/CoRN/devel/loeb/IDA/Ch6/member.con" as definition.
%\end{convention}%
*)
-alias id "f" = "cic:/CoRN/fta/CC_Props/Continuity_for_CC/f.var".
+(* UNEXPORTED
+cic:/CoRN/fta/CC_Props/Continuity_for_CC/f.var
+*)
(* (CSetoid_un_op CC). *)
%\end{convention}%
*)
-alias id "g" = "cic:/CoRN/fta/CPoly_Contin1/CPoly_CC_Continuous/g.var".
+(* UNEXPORTED
+cic:/CoRN/fta/CPoly_Contin1/CPoly_CC_Continuous/g.var
+*)
inline procedural "cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/fta/CPoly_Rev/Monomials/R.var".
+(* UNEXPORTED
+cic:/CoRN/fta/CPoly_Rev/Monomials/R.var
+*)
(* begin hide *)
Section Poly_Reverse
*)
-alias id "R" = "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/R.var".
+(* UNEXPORTED
+cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/R.var
+*)
(* begin hide *)
Section FTA_reg'
*)
-alias id "f" = "cic:/CoRN/fta/FTA/FTA_reg'/f.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTA/FTA_reg'/f.var
+*)
-alias id "n" = "cic:/CoRN/fta/FTA/FTA_reg'/n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTA/FTA_reg'/n.var
+*)
-alias id "f_degree" = "cic:/CoRN/fta/FTA/FTA_reg'/f_degree.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTA/FTA_reg'/f_degree.var
+*)
inline procedural "cic:/CoRN/fta/FTA/FTA_reg'.con" as lemma.
Section FTA_1
*)
-alias id "f" = "cic:/CoRN/fta/FTA/FTA_1/f.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTA/FTA_1/f.var
+*)
-alias id "n" = "cic:/CoRN/fta/FTA/FTA_1/n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTA/FTA_1/n.var
+*)
-alias id "f_degree" = "cic:/CoRN/fta/FTA/FTA_1/f_degree.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTA/FTA_1/f_degree.var
+*)
-alias id "c" = "cic:/CoRN/fta/FTA/FTA_1/c.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTA/FTA_1/c.var
+*)
-alias id "f_c" = "cic:/CoRN/fta/FTA/FTA_1/f_c.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTA/FTA_1/f_c.var
+*)
inline procedural "cic:/CoRN/fta/FTA/FTA_1a.con" as lemma.
Section Seq_Exists
*)
-alias id "n" = "cic:/CoRN/fta/FTAreg/Seq_Exists/n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/n.var
+*)
-alias id "lt0n" = "cic:/CoRN/fta/FTAreg/Seq_Exists/lt0n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/lt0n.var
+*)
(*#*
%\begin{convention}% Let [qK] be a real between 0 and 1, with
Section Kneser_Sequence
*)
-alias id "qK" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qK.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qK.var
+*)
-alias id "zltq" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/zltq.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/zltq.var
+*)
-alias id "qlt1" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qlt1.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qlt1.var
+*)
-alias id "q_prop" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/q_prop.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/q_prop.var
+*)
-alias id "p" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p.var
+*)
-alias id "mp" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/mp.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/mp.var
+*)
-alias id "c0" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/c0.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/c0.var
+*)
-alias id "p0ltc0" = "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p0ltc0.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p0ltc0.var
+*)
inline procedural "cic:/CoRN/fta/FTAreg/Knes_tup.ind".
Section N_Exists
*)
-alias id "n" = "cic:/CoRN/fta/FTAreg/N_Exists/n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/N_Exists/n.var
+*)
-alias id "lt0n" = "cic:/CoRN/fta/FTAreg/N_Exists/lt0n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/N_Exists/lt0n.var
+*)
-alias id "q" = "cic:/CoRN/fta/FTAreg/N_Exists/q.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/N_Exists/q.var
+*)
-alias id "zleq" = "cic:/CoRN/fta/FTAreg/N_Exists/zleq.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/N_Exists/zleq.var
+*)
-alias id "qlt1" = "cic:/CoRN/fta/FTAreg/N_Exists/qlt1.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/N_Exists/qlt1.var
+*)
-alias id "c" = "cic:/CoRN/fta/FTAreg/N_Exists/c.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/N_Exists/c.var
+*)
-alias id "zltc" = "cic:/CoRN/fta/FTAreg/N_Exists/zltc.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/N_Exists/zltc.var
+*)
(* begin hide *)
(* end hide *)
-alias id "e" = "cic:/CoRN/fta/FTAreg/N_Exists/e.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/N_Exists/e.var
+*)
-alias id "zlte" = "cic:/CoRN/fta/FTAreg/N_Exists/zlte.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/N_Exists/zlte.var
+*)
inline procedural "cic:/CoRN/fta/FTAreg/N_exists.con" as lemma.
(*#* ** The Kneser sequence is Cauchy in [CC] *)
-alias id "n" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/n.var
+*)
-alias id "lt0n" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/lt0n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/lt0n.var
+*)
-alias id "q" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q.var
+*)
-alias id "zleq" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zleq.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zleq.var
+*)
-alias id "qlt1" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/qlt1.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/qlt1.var
+*)
-alias id "c" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/c.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/c.var
+*)
-alias id "zltc" = "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zltc.var".
+(* UNEXPORTED
+cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zltc.var
+*)
(*#* %\begin{convention}% Let:
- [q_] prove [q[-]One [#] Zero]
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/a.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KeyLemma/Key_Lemma/a.var
+*)
-alias id "n" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KeyLemma/Key_Lemma/n.var
+*)
-alias id "gt_n_0" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/gt_n_0.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KeyLemma/Key_Lemma/gt_n_0.var
+*)
-alias id "eps" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KeyLemma/Key_Lemma/eps.var
+*)
-alias id "eps_pos" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_pos.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_pos.var
+*)
-alias id "a_nonneg" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_nonneg.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KeyLemma/Key_Lemma/a_nonneg.var
+*)
-alias id "a_n_1" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_n_1.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KeyLemma/Key_Lemma/a_n_1.var
+*)
-alias id "a_0" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_0.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KeyLemma/Key_Lemma/a_0.var
+*)
-alias id "eps_le_a_0" = "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_le_a_0.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_le_a_0.var
+*)
inline procedural "cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con" as lemma.
%\end{convention}%
*)
-alias id "b" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b.var
+*)
-alias id "n" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KneserLemma/Kneser_Lemma/n.var
+*)
-alias id "gt_n_0" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/gt_n_0.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KneserLemma/Kneser_Lemma/gt_n_0.var
+*)
(* begin hide *)
(* end hide *)
-alias id "b_n_1" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n_1.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n_1.var
+*)
-alias id "c" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/c.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KneserLemma/Kneser_Lemma/c.var
+*)
-alias id "b_0_lt_c" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0_lt_c.var".
+(* UNEXPORTED
+cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0_lt_c.var
+*)
(*#*
%\begin{convention}% We define the following local abbreviations:
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a.var".
+(* UNEXPORTED
+cic:/CoRN/fta/MainLemma/Main_Lemma/a.var
+*)
-alias id "n" = "cic:/CoRN/fta/MainLemma/Main_Lemma/n.var".
+(* UNEXPORTED
+cic:/CoRN/fta/MainLemma/Main_Lemma/n.var
+*)
-alias id "gt_n_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/gt_n_0.var".
+(* UNEXPORTED
+cic:/CoRN/fta/MainLemma/Main_Lemma/gt_n_0.var
+*)
-alias id "eps" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps.var".
+(* UNEXPORTED
+cic:/CoRN/fta/MainLemma/Main_Lemma/eps.var
+*)
-alias id "eps_pos" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_pos.var".
+(* UNEXPORTED
+cic:/CoRN/fta/MainLemma/Main_Lemma/eps_pos.var
+*)
-alias id "a_nonneg" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_nonneg.var".
+(* UNEXPORTED
+cic:/CoRN/fta/MainLemma/Main_Lemma/a_nonneg.var
+*)
-alias id "a_n_1" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_n_1.var".
+(* UNEXPORTED
+cic:/CoRN/fta/MainLemma/Main_Lemma/a_n_1.var
+*)
-alias id "a_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_0.var".
+(* UNEXPORTED
+cic:/CoRN/fta/MainLemma/Main_Lemma/a_0.var
+*)
-alias id "eps_le_a_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_le_a_0.var".
+(* UNEXPORTED
+cic:/CoRN/fta/MainLemma/Main_Lemma/eps_le_a_0.var
+*)
inline procedural "cic:/CoRN/fta/MainLemma/a_0_pos.con" as lemma.
refinement).
*)
-alias id "F" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/COrdLemmas/Lemmas/F.var
+*)
inline procedural "cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con" as lemma.
(* begin hide *)
-alias id "f" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/COrdLemmas/Lemmas/f.var
+*)
-alias id "f0" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/f0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/COrdLemmas/Lemmas/f0.var
+*)
-alias id "f_mon" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/f_mon.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/COrdLemmas/Lemmas/f_mon.var
+*)
-alias id "h" = "cic:/CoRN/ftc/COrdLemmas/Lemmas/h.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/COrdLemmas/Lemmas/h.var
+*)
(* end hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/COrdLemmas/More_Lemmas/F.var
+*)
(* begin show *)
partial functions, and prove some trivial results.
*)
-alias id "F" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/G.var
+*)
-alias id "a" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hab.var
+*)
-alias id "c" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/c.var
+*)
-alias id "d" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/d.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/d.var
+*)
-alias id "Hcd" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hcd.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hcd.var
+*)
(* begin hide *)
(* begin show *)
-alias id "Hf" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hf.var
+*)
(* end show *)
(* begin show *)
-alias id "maps" = "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/maps.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/maps.var
+*)
(* end show *)
completely characterizes the domain of the composite function.
*)
-alias id "F" = "cic:/CoRN/ftc/Composition/Mapping/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Composition/Mapping/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/G.var
+*)
-alias id "a" = "cic:/CoRN/ftc/Composition/Mapping/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Composition/Mapping/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Composition/Mapping/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/Hab.var
+*)
-alias id "c" = "cic:/CoRN/ftc/Composition/Mapping/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/c.var
+*)
-alias id "d" = "cic:/CoRN/ftc/Composition/Mapping/d.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/d.var
+*)
-alias id "Hcd" = "cic:/CoRN/ftc/Composition/Mapping/Hcd.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/Hcd.var
+*)
(* begin show *)
-alias id "Hf" = "cic:/CoRN/ftc/Composition/Mapping/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/Hf.var
+*)
-alias id "Hg" = "cic:/CoRN/ftc/Composition/Mapping/Hg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/Hg.var
+*)
-alias id "maps" = "cic:/CoRN/ftc/Composition/Mapping/maps.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Mapping/maps.var
+*)
(* end show *)
We now prove that the composition of two continuous partial functions is continuous.
*)
-alias id "a" = "cic:/CoRN/ftc/Composition/Interval_Continuity/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Composition/Interval_Continuity/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Composition/Interval_Continuity/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "c" = "cic:/CoRN/ftc/Composition/Interval_Continuity/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/c.var
+*)
-alias id "d" = "cic:/CoRN/ftc/Composition/Interval_Continuity/d.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/d.var
+*)
-alias id "Hcd" = "cic:/CoRN/ftc/Composition/Interval_Continuity/Hcd.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/Hcd.var
+*)
-alias id "F" = "cic:/CoRN/ftc/Composition/Interval_Continuity/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Composition/Interval_Continuity/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/G.var
+*)
(* begin show *)
-alias id "contF" = "cic:/CoRN/ftc/Composition/Interval_Continuity/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/Composition/Interval_Continuity/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/contG.var
+*)
-alias id "Hmap" = "cic:/CoRN/ftc/Composition/Interval_Continuity/Hmap.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Interval_Continuity/Hmap.var
+*)
(* end show *)
We now work with the derivative relation and prove the chain rule for partial functions.
*)
-alias id "F" = "cic:/CoRN/ftc/Composition/Derivative/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/Composition/Derivative/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/F'.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Composition/Derivative/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/G.var
+*)
-alias id "G'" = "cic:/CoRN/ftc/Composition/Derivative/G'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/G'.var
+*)
-alias id "a" = "cic:/CoRN/ftc/Composition/Derivative/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Composition/Derivative/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Composition/Derivative/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/Hab'.var
+*)
-alias id "c" = "cic:/CoRN/ftc/Composition/Derivative/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/c.var
+*)
-alias id "d" = "cic:/CoRN/ftc/Composition/Derivative/d.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/d.var
+*)
-alias id "Hcd'" = "cic:/CoRN/ftc/Composition/Derivative/Hcd'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/Hcd'.var
+*)
(* begin hide *)
(* begin show *)
-alias id "derF" = "cic:/CoRN/ftc/Composition/Derivative/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/derF.var
+*)
-alias id "derG" = "cic:/CoRN/ftc/Composition/Derivative/derG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/derG.var
+*)
-alias id "Hmap" = "cic:/CoRN/ftc/Composition/Derivative/Hmap.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Derivative/Hmap.var
+*)
(* end show *)
Finally, we move on to differentiability.
*)
-alias id "F" = "cic:/CoRN/ftc/Composition/Differentiability/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Composition/Differentiability/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/G.var
+*)
-alias id "a" = "cic:/CoRN/ftc/Composition/Differentiability/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Composition/Differentiability/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Composition/Differentiability/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/Hab'.var
+*)
-alias id "c" = "cic:/CoRN/ftc/Composition/Differentiability/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/c.var
+*)
-alias id "d" = "cic:/CoRN/ftc/Composition/Differentiability/d.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/d.var
+*)
-alias id "Hcd'" = "cic:/CoRN/ftc/Composition/Differentiability/Hcd'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/Hcd'.var
+*)
(* begin hide *)
(* begin show *)
-alias id "diffF" = "cic:/CoRN/ftc/Composition/Differentiability/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/diffF.var
+*)
-alias id "diffG" = "cic:/CoRN/ftc/Composition/Differentiability/diffG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/diffG.var
+*)
-alias id "Hmap" = "cic:/CoRN/ftc/Composition/Differentiability/Hmap.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Differentiability/Hmap.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "I" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/I.var
+*)
-alias id "J" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/J.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/pI.var
+*)
-alias id "pJ" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/pJ.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/pJ.var
+*)
inline procedural "cic:/CoRN/ftc/Composition/maps_compacts_into.con" as definition.
inline procedural "cic:/CoRN/ftc/Composition/comp_inc_lemma.con" as lemma.
-alias id "F" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/F'.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/G.var
+*)
-alias id "G'" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/G'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/G'.var
+*)
(* begin show *)
-alias id "Hmap" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap.var
+*)
(* end show *)
(* begin show *)
-alias id "Hmap'" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap'.var
+*)
(* end show *)
Here we define continuity and prove some basic properties of continuous functions.
*)
-alias id "a" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/F.var
+*)
(* begin hide *)
Assume [F] to be continuous in [I]. Then it has a least upper bound and a greater lower bound on [I].
*)
-alias id "contF" = "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/contF.var
+*)
(* begin hide *)
We now state and prove some results about continuous functions. Assume that [I] is included in the domain of both [F] and [G].
*)
-alias id "a" = "cic:/CoRN/ftc/Continuity/Local_Results/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Continuity/Local_Results/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Continuity/Local_Results/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/Continuity/Local_Results/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Continuity/Local_Results/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/G.var
+*)
(* begin hide *)
(* end hide *)
-alias id "incF" = "cic:/CoRN/ftc/Continuity/Local_Results/incF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/incF.var
+*)
-alias id "incG" = "cic:/CoRN/ftc/Continuity/Local_Results/incG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/incG.var
+*)
(*#*
The first result does not require the function to be continuous; however, its preconditions are easily verified by continuous functions, which justifies its inclusion in this section.
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 "contF" = "cic:/CoRN/ftc/Continuity/Local_Results/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/Continuity/Local_Results/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/contG.var
+*)
inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con" as lemma.
(* begin show *)
-alias id "Hg'" = "cic:/CoRN/ftc/Continuity/Local_Results/Hg'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/Hg'.var
+*)
-alias id "Hg''" = "cic:/CoRN/ftc/Continuity/Local_Results/Hg''.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Local_Results/Hg''.var
+*)
(* end show *)
Section Corolaries
*)
-alias id "a" = "cic:/CoRN/ftc/Continuity/Corolaries/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Corolaries/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Continuity/Corolaries/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Corolaries/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Continuity/Corolaries/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Corolaries/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/Continuity/Corolaries/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Corolaries/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Continuity/Corolaries/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Corolaries/G.var
+*)
(* begin hide *)
(* end hide *)
-alias id "contF" = "cic:/CoRN/ftc/Continuity/Corolaries/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Corolaries/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/Continuity/Corolaries/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Corolaries/contG.var
+*)
(*#*
The corresponding properties for subtraction, division and
inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con" as lemma.
-alias id "Hg'" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Corolaries/Hg'.var
+*)
-alias id "Hg''" = "cic:/CoRN/ftc/Continuity/Corolaries/Hg''.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Corolaries/Hg''.var
+*)
inline procedural "cic:/CoRN/ftc/Continuity/Continuous_I_div.con" as lemma.
We finally prove that the sum of an arbitrary family of continuous functions is still a continuous function.
*)
-alias id "a" = "cic:/CoRN/ftc/Continuity/Other/Sums/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Other/Sums/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Continuity/Other/Sums/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Other/Sums/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Continuity/Other/Sums/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Other/Sums/Hab.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Continuity/Other/Sums/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Continuity/Other/Sums/Hab'.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/Derivative/Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Derivative/Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Definitions/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Derivative/Definitions/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Definitions/Hab'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/Derivative/Definitions/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Definitions/F.var
+*)
(* begin hide *)
(*#* **Basic Properties
*)
-alias id "a" = "cic:/CoRN/ftc/Derivative/Basic_Properties/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Basic_Properties/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Derivative/Basic_Properties/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Basic_Properties/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Basic_Properties/Hab'.var
+*)
(* begin hide *)
Derivative is a well defined relation; we will make this explicit for both arguments:
*)
-alias id "F" = "cic:/CoRN/ftc/Derivative/Basic_Properties/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Basic_Properties/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Derivative/Basic_Properties/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Basic_Properties/G.var
+*)
-alias id "H" = "cic:/CoRN/ftc/Derivative/Basic_Properties/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Basic_Properties/H.var
+*)
(* begin hide *)
Any function that is or has a derivative is continuous.
*)
-alias id "Hab''" = "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab''.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Derivative/Basic_Properties/Hab''.var
+*)
inline procedural "cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con" as lemma.
We begin with some technical stuff that will be necessary for division.
*)
-alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Lemmas/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Lemmas/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var
+*)
(* begin hide *)
(* begin show *)
-alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var
+*)
(* end show *)
We can now derive all the usual rules for deriving constant and identity functions, sums, inverses and products of functions with a known derivative.
*)
-alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var
+*)
(* begin hide *)
inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con" as lemma.
-alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/F'.var
+*)
-alias id "G" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/G.var
+*)
-alias id "G'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/G'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/G'.var
+*)
-alias id "derF" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var
+*)
-alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var
+*)
inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con" as lemma.
(* begin show *)
-alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var
+*)
(* end show *)
Section Corolaries
*)
-alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/F'.var
+*)
-alias id "G" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/G.var
+*)
-alias id "G'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/G'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/G'.var
+*)
-alias id "derF" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/derF.var
+*)
-alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var
+*)
(*#*
From this lemmas the rules for the other algebraic operations follow directly.
inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con" as lemma.
-alias id "Gbnd" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var
+*)
inline procedural "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con" as lemma.
induction using the constant and addition rules.
*)
-alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var
+*)
(* begin hide *)
A function differentiable in an interval is everywhere defined in that interval.
*)
-alias id "a" = "cic:/CoRN/ftc/Differentiability/Local_Properties/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Local_Properties/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Differentiability/Local_Properties/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Local_Properties/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Local_Properties/Hab'.var
+*)
(* begin hide *)
All the algebraic results carry on.
*)
-alias id "a" = "cic:/CoRN/ftc/Differentiability/Operations/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Differentiability/Operations/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Operations/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/Hab'.var
+*)
(* begin hide *)
Section Well_Definedness
*)
-alias id "F" = "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/F.var
+*)
-alias id "H" = "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/H.var
+*)
-alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/diffF.var
+*)
inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con" as lemma.
End Well_Definedness
*)
-alias id "F" = "cic:/CoRN/ftc/Differentiability/Operations/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Differentiability/Operations/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/G.var
+*)
-alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Operations/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/diffF.var
+*)
-alias id "diffG" = "cic:/CoRN/ftc/Differentiability/Operations/diffG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/diffG.var
+*)
inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con" as lemma.
(* begin show *)
-alias id "Gbnd" = "cic:/CoRN/ftc/Differentiability/Operations/Gbnd.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Operations/Gbnd.var
+*)
(* end show *)
Section Corollaries
*)
-alias id "a" = "cic:/CoRN/ftc/Differentiability/Corollaries/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Corollaries/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Differentiability/Corollaries/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Corollaries/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Corollaries/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Corollaries/Hab'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/Differentiability/Corollaries/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Corollaries/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Differentiability/Corollaries/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Corollaries/G.var
+*)
-alias id "diffF" = "cic:/CoRN/ftc/Differentiability/Corollaries/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Corollaries/diffF.var
+*)
-alias id "diffG" = "cic:/CoRN/ftc/Differentiability/Corollaries/diffG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Corollaries/diffG.var
+*)
inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con" as lemma.
inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con" as lemma.
-alias id "Gbnd" = "cic:/CoRN/ftc/Differentiability/Corollaries/Gbnd.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Corollaries/Gbnd.var
+*)
inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con" as lemma.
induction using the constant and addition rules.
*)
-alias id "a" = "cic:/CoRN/ftc/Differentiability/Other_Properties/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Other_Properties/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Differentiability/Other_Properties/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Other_Properties/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Differentiability/Other_Properties/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Differentiability/Other_Properties/Hab'.var
+*)
inline procedural "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con" as lemma.
%\end{convention}%
*)
-alias id "I" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Indefinite_Integral/I.var
+*)
-alias id "F" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Indefinite_Integral/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Indefinite_Integral/contF.var
+*)
-alias id "a" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Indefinite_Integral/a.var
+*)
-alias id "Ha" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/Ha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Indefinite_Integral/Ha.var
+*)
inline procedural "cic:/CoRN/ftc/FTC/prim_lemma.con" as lemma.
%\end{convention}%
*)
-alias id "J" = "cic:/CoRN/ftc/FTC/FTC/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/FTC/J.var
+*)
-alias id "F" = "cic:/CoRN/ftc/FTC/FTC/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/FTC/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/FTC/FTC/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/FTC/contF.var
+*)
-alias id "x0" = "cic:/CoRN/ftc/FTC/FTC/x0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/FTC/x0.var
+*)
-alias id "Hx0" = "cic:/CoRN/ftc/FTC/FTC/Hx0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/FTC/Hx0.var
+*)
(* begin hide *)
The derivative of [G] is simply [F].
*)
-alias id "pJ" = "cic:/CoRN/ftc/FTC/FTC/pJ.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/FTC/pJ.var
+*)
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 "G0" = "cic:/CoRN/ftc/FTC/FTC/G0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/FTC/G0.var
+*)
-alias id "derG0" = "cic:/CoRN/ftc/FTC/FTC/derG0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/FTC/derG0.var
+*)
inline procedural "cic:/CoRN/ftc/FTC/FTC2.con" as theorem.
commutes with the indefinite integral.
*)
-alias id "J" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/f.var
+*)
-alias id "F" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/F.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contf.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contF.var
+*)
(* UNEXPORTED
Section Compact
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hab.var
+*)
-alias id "contIf" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIf.var
+*)
-alias id "contIF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIF.var
+*)
(* begin show *)
-alias id "convF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/convF.var
+*)
(* end show *)
-alias id "x0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/x0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/x0.var
+*)
-alias id "Hx0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0.var
+*)
-alias id "Hx0'" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0'.var
+*)
(* begin hide *)
(* begin show *)
-alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contg.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contG.var
+*)
(* end show *)
(* begin show *)
-alias id "convF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/convF.var
+*)
(* end show *)
-alias id "x0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/x0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/x0.var
+*)
-alias id "Hx0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/Hx0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/Hx0.var
+*)
(* begin hide *)
(* end hide *)
-alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contg.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contG.var
+*)
inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con" as lemma.
%\end{convention}%
*)
-alias id "J" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/J.var
+*)
-alias id "pJ" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/pJ.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/pJ.var
+*)
-alias id "f" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/g.var
+*)
-alias id "F" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/G.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contf.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contF.var
+*)
-alias id "convF" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convF.var
+*)
-alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contg.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contG.var
+*)
-alias id "convG" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convG.var
+*)
-alias id "derf" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/derf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/derf.var
+*)
inline procedural "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con" as lemma.
As a very important case of this result, we get a rule for deriving series.
*)
-alias id "J" = "cic:/CoRN/ftc/FTC/Derivative_Series/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Derivative_Series/J.var
+*)
-alias id "pJ" = "cic:/CoRN/ftc/FTC/Derivative_Series/pJ.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Derivative_Series/pJ.var
+*)
-alias id "f" = "cic:/CoRN/ftc/FTC/Derivative_Series/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Derivative_Series/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/FTC/Derivative_Series/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Derivative_Series/g.var
+*)
(* begin show *)
-alias id "convF" = "cic:/CoRN/ftc/FTC/Derivative_Series/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Derivative_Series/convF.var
+*)
-alias id "convG" = "cic:/CoRN/ftc/FTC/Derivative_Series/convG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Derivative_Series/convG.var
+*)
(* end show *)
-alias id "derF" = "cic:/CoRN/ftc/FTC/Derivative_Series/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FTC/Derivative_Series/derF.var
+*)
inline procedural "cic:/CoRN/ftc/FTC/Derivative_FSeries.con" as lemma.
see Bishop 1967.
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSequence/Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSequence/Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Definitions/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Definitions/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSequence/Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Definitions/f.var
+*)
-alias id "F" = "cic:/CoRN/ftc/FunctSequence/Definitions/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Definitions/F.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/FunctSequence/Definitions/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Definitions/contf.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/FunctSequence/Definitions/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Definitions/contF.var
+*)
(* begin hide *)
Section More_Definitions
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Definitions/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Definitions/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Definitions/f.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Definitions/contf.var
+*)
(*#*
We can also say that [f] is simply convergent if it converges to some
(* begin show *)
-alias id "H" = "cic:/CoRN/ftc/FunctSequence/More_Definitions/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Definitions/H.var
+*)
(* end show *)
This section contains a number of technical results stating mainly that being a Cauchy sequence or converging to some limit is a property of the sequence itself and independent of the proofs we supply of its continuity or the continuity of its limit.
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/f.var
+*)
(* begin show *)
-alias id "contf" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf.var
+*)
-alias id "contf0" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf0.var
+*)
(* end show *)
-alias id "F" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/F.var
+*)
(* begin show *)
-alias id "contF" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF.var
+*)
-alias id "contF0" = "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF0.var
+*)
(* end show *)
defined with respect to functional equality in the interval [[a,b]].
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSequence/More_Properties/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSequence/More_Properties/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/More_Properties/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSequence/More_Properties/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/FunctSequence/More_Properties/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/g.var
+*)
(* begin show *)
-alias id "contf" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/contf.var
+*)
-alias id "contf0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contf0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/contf0.var
+*)
-alias id "contg" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/contg.var
+*)
-alias id "contg0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contg0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/contg0.var
+*)
(* end show *)
inline procedural "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con" as lemma.
-alias id "F" = "cic:/CoRN/ftc/FunctSequence/More_Properties/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/FunctSequence/More_Properties/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/G.var
+*)
(* begin show *)
-alias id "contF" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/contF.var
+*)
-alias id "contF0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contF0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/contF0.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/contG.var
+*)
-alias id "contG0" = "cic:/CoRN/ftc/FunctSequence/More_Properties/contG0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Properties/contG0.var
+*)
(* end show *)
We now study how convergence is affected by algebraic operations, and some algebraic properties of the limit function.
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/g.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contf.var
+*)
-alias id "contg" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contg.var
+*)
(*#*
First, the limit function is unique.
We now prove that if two sequences converge than their sum (difference, product) also converge to the sum (difference, product) of their limits.
*)
-alias id "F" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/G.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contG.var
+*)
(* begin show *)
-alias id "convF" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convF.var
+*)
-alias id "convG" = "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convG.var
+*)
(* end show *)
Section More_Algebraic_Properties
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/g.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contf.var
+*)
-alias id "contg" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contg.var
+*)
(*#*
The same is true if we don't make the limits explicit.
(* begin hide *)
-alias id "Hf" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hf.var
+*)
-alias id "Hg" = "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hg.var
+*)
(* end hide *)
Section Still_More_Algebraic_Properties
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/f.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/contf.var
+*)
-alias id "Hf" = "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hf.var
+*)
(*#*
As a corollary, we get the analogous property for the sequence of algebraic inverse functions.
convergence is simply the convergence of the sequence of partial sums.
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/f.var
+*)
inline procedural "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con" as definition.
(* begin show *)
-alias id "H" = "cic:/CoRN/ftc/FunctSeries/Definitions/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Definitions/H.var
+*)
(* end show *)
Section More_Definitions
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var
+*)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var
+*)
(*#* A series can also be absolutely convergent. *)
All of these are analogous to the properties for series of real numbers, so we won't comment much about them.
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Operations/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Operations/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/Hab.var
+*)
(* begin hide *)
(* begin show *)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/FunctSeries/Operations/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/g.var
+*)
(* end show *)
(* begin show *)
-alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Operations/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/convF.var
+*)
-alias id "convG" = "cic:/CoRN/ftc/FunctSeries/Operations/convG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/convG.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "c" = "cic:/CoRN/ftc/FunctSeries/Operations/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/c.var
+*)
-alias id "H" = "cic:/CoRN/ftc/FunctSeries/Operations/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/H.var
+*)
-alias id "contH" = "cic:/CoRN/ftc/FunctSeries/Operations/contH.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Operations/contH.var
+*)
inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con" as lemma.
Section More_Operations
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/More_Operations/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/More_Operations/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/f.var
+*)
-alias id "convF" = "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var
+*)
inline procedural "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con" as lemma.
Section Other_Results
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Other_Results/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Other_Results/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var
+*)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Other_Results/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/f.var
+*)
-alias id "convF" = "cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var
+*)
(*#*
The following relate the sum series with the limit of the sequence of
Most of the convergence criteria for series of real numbers carry over to series of real-valued functions, so again we just present them without comments.
*)
-alias id "a" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var
+*)
(* UNEXPORTED
Opaque Frestr.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/Integral/Integral/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Integral/Integral/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Integral/Integral/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Hab.var
+*)
(* begin hide *)
inline procedural "cic:/CoRN/ftc/Integral/Integral/I.con" "Integral__" as definition.
-alias id "F" = "cic:/CoRN/ftc/Integral/Integral/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/Integral/Integral/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/contF.var
+*)
inline procedural "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__" as definition.
%\end{convention}%
*)
-alias id "n" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Integral_Thm/n.var
+*)
-alias id "P" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Integral_Thm/P.var
+*)
-alias id "e" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/e.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Integral_Thm/e.var
+*)
-alias id "He" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/He.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Integral_Thm/He.var
+*)
(* begin hide *)
(* end hide *)
-alias id "HmeshP" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HmeshP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HmeshP.var
+*)
-alias id "fP" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/fP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Integral_Thm/fP.var
+*)
-alias id "HfP" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP.var
+*)
-alias id "HfP'" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP'.var
+*)
-alias id "incF" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/incF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Integral/Integral_Thm/incF.var
+*)
inline procedural "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con" as lemma.
The usual extensionality and strong extensionality results hold.
*)
-alias id "a" = "cic:/CoRN/ftc/Integral/Basic_Properties/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Integral/Basic_Properties/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Integral/Basic_Properties/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Hab.var
+*)
(* begin hide *)
Section Well_Definedness
*)
-alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/G.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contG.var
+*)
inline procedural "cic:/CoRN/ftc/Integral/integral_strext.con" as lemma.
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".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/G.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contG.var
+*)
inline procedural "cic:/CoRN/ftc/Integral/integral_comm_scal.con" as lemma.
Section Linearity_and_Monotonicity'
*)
-alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/G.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contG.var
+*)
(*#*
%\begin{convention}% Let [alpha, beta : IR] and assume that
%\end{convention}%
*)
-alias id "alpha" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/alpha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/alpha.var
+*)
-alias id "beta" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/beta.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/beta.var
+*)
(* begin hide *)
(* end hide *)
-alias id "contH" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contH.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contH.var
+*)
inline procedural "cic:/CoRN/ftc/Integral/linear_integral.con" as lemma.
Section Corollaries
*)
-alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/G.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contG.var
+*)
(*#*
As corollaries we can calculate integrals of group operations applied to functions.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/F.var
+*)
-alias id "c" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/c.var
+*)
-alias id "Hac" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac.var
+*)
-alias id "Hcb" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hab'.var
+*)
-alias id "Hac'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac'.var
+*)
-alias id "Hcb'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb'.var
+*)
(* UNEXPORTED
Section Partition_Join
%\end{convention}%
*)
-alias id "n" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/n.var
+*)
-alias id "m" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/m.var
+*)
-alias id "P" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/P.var
+*)
-alias id "Q" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/Q.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/Q.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "fP" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fP.var
+*)
-alias id "HfP" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP.var
+*)
-alias id "HfP'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP'.var
+*)
-alias id "fQ" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fQ.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fQ.var
+*)
-alias id "HfQ" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ.var
+*)
-alias id "HfQ'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ'.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/IntervalFunct/Operations/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Operations/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/IntervalFunct/Operations/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Operations/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/IntervalFunct/Operations/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Operations/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/IntervalFunct/Operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Operations/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/IntervalFunct/Operations/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Operations/g.var
+*)
(* UNEXPORTED
Section Const
%\end{convention}%
*)
-alias id "c" = "cic:/CoRN/ftc/IntervalFunct/Operations/Const/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Operations/Const/c.var
+*)
inline procedural "cic:/CoRN/ftc/IntervalFunct/IConst_strext.con" as lemma.
Exponentiation to a natural power [n] is also useful.
*)
-alias id "n" = "cic:/CoRN/ftc/IntervalFunct/Operations/Nth_Power/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Operations/Nth_Power/n.var
+*)
inline procedural "cic:/CoRN/ftc/IntervalFunct/INth_strext.con" as lemma.
(* begin show *)
-alias id "Hg" = "cic:/CoRN/ftc/IntervalFunct/Operations/Recip_Div/Hg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Operations/Recip_Div/Hg.var
+*)
(* end show *)
Section Composition
*)
-alias id "a" = "cic:/CoRN/ftc/IntervalFunct/Composition/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Composition/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/IntervalFunct/Composition/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Composition/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Composition/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "a'" = "cic:/CoRN/ftc/IntervalFunct/Composition/a'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Composition/a'.var
+*)
-alias id "b'" = "cic:/CoRN/ftc/IntervalFunct/Composition/b'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Composition/b'.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Composition/Hab'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/IntervalFunct/Composition/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Composition/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/IntervalFunct/Composition/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Composition/g.var
+*)
-alias id "Hfg" = "cic:/CoRN/ftc/IntervalFunct/Composition/Hfg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/IntervalFunct/Composition/Hfg.var
+*)
inline procedural "cic:/CoRN/ftc/IntervalFunct/IComp_strext.con" as lemma.
but the ones which do we simply adapt in the usual way.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Definitions/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Definitions/f.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Definitions/F.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Definitions/contf.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con" as definition.
Limit is defined and works in the same way as before.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Definitions/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Definitions/f.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Definitions/contf.var
+*)
(* begin show *)
-alias id "conv" = "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/conv.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Definitions/conv.var
+*)
(* end show *)
Proofs are irrelevant as before---they just have to be present.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/f.var
+*)
(* begin show *)
-alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf.var
+*)
-alias id "contf0" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf0.var
+*)
(* end show *)
-alias id "F" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/F.var
+*)
(* begin show *)
-alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF.var
+*)
-alias id "contF0" = "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF0.var
+*)
(* end show *)
Section More_Properties
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/g.var
+*)
(* begin show *)
-alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf.var
+*)
-alias id "contf0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf0.var
+*)
-alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg.var
+*)
-alias id "contg0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg0.var
+*)
(* end show *)
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".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/G.var
+*)
(* begin show *)
-alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF.var
+*)
-alias id "contF0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF0.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG.var
+*)
-alias id "contG0" = "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG0.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG0.var
+*)
(* end show *)
Algebraic operations still work well.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/g.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contf.var
+*)
-alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con" as lemma.
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".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/G.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contG.var
+*)
(* begin show *)
-alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convF.var
+*)
-alias id "convG" = "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convG.var
+*)
(* end show *)
If we work with the limit function things fit in just as well.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/g.var
+*)
-alias id "contf" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contf.var
+*)
-alias id "contg" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contg.var
+*)
(* begin show *)
-alias id "Hf" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hf.var
+*)
-alias id "Hg" = "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hg.var
+*)
(* end show *)
Convergence is defined as expected---through convergence in every compact interval.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con" as definition.
(* begin show *)
-alias id "H" = "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/H.var
+*)
(* end show *)
Section More_Series_Definitions
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/f.var
+*)
(*#*
Absolute convergence still exists.
As before, any series converges to its sum.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con" as lemma.
Convergence is well defined and preserved by operations.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Operations/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Operations/J.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con" as lemma.
inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con" as lemma.
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Operations/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Operations/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/MoreFunSeries/Operations/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Operations/g.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con" as lemma.
(* begin show *)
-alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Operations/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Operations/convF.var
+*)
-alias id "convG" = "cic:/CoRN/ftc/MoreFunSeries/Operations/convG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Operations/convG.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "c" = "cic:/CoRN/ftc/MoreFunSeries/Operations/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Operations/c.var
+*)
-alias id "H" = "cic:/CoRN/ftc/MoreFunSeries/Operations/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Operations/H.var
+*)
-alias id "contH" = "cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con" as lemma.
comparison test (in both versions) and the ratio test.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/f.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con" as lemma.
position. This does not affect convergence or the sum of the series.
*)
-alias id "J" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/J.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Insert_Series/J.var
+*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Insert_Series/f.var
+*)
-alias id "convF" = "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunSeries/insert_series.con" as definition.
**Continuity
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Results/I.var
+*)
(*#*
Trivial stuff.
%\end{convention}%
*)
-alias id "cI" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/cI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Results/cI.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Results/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Results/contF.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con" as lemma.
(* begin show *)
-alias id "Hinc" = "cic:/CoRN/ftc/MoreFunctions/Basic_Results/Hinc.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Results/Hinc.var
+*)
(* end show *)
The usual stuff.
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Other_Results/I.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Other_Results/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Other_Results/G.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con" as lemma.
(* begin show *)
-alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Other_Results/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/MoreFunctions/Other_Results/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Other_Results/contG.var
+*)
(* end show *)
Section Corollaries
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Corollaries/I.var
+*)
-alias id "cI" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/cI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Corollaries/cI.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Corollaries/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Corollaries/G.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Corollaries/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/MoreFunctions/Corollaries/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Corollaries/contG.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con" as lemma.
Section Sums
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Sums/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Sums/I.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con" as lemma.
%\end{convention}%
*)
-alias id "f" = "cic:/CoRN/ftc/MoreFunctions/Sums/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Sums/f.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/MoreFunctions/Sums/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Sums/contF.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con" as lemma.
%\end{convention}%
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Properties/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Properties/pI.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Properties/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Properties/G.var
+*)
-alias id "H" = "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Basic_Properties/H.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con" as lemma.
Section More_Results
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Results/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Results/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Results/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Results/pI.var
+*)
(*#*
%\begin{convention}% Assume that [F'] and [G'] are derivatives of [F] and [G], respectively, in [I].
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/More_Results/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Results/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/MoreFunctions/More_Results/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Results/F'.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreFunctions/More_Results/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Results/G.var
+*)
-alias id "G'" = "cic:/CoRN/ftc/MoreFunctions/More_Results/G'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Results/G'.var
+*)
-alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Results/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Results/derF.var
+*)
-alias id "derG" = "cic:/CoRN/ftc/MoreFunctions/More_Results/derG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Results/derG.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con" as lemma.
Section More_Corollaries
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Corollaries/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Corollaries/pI.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F'.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G.var
+*)
-alias id "G'" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G'.var
+*)
-alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derF.var
+*)
-alias id "derG" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derG.var
+*)
(* begin show *)
-alias id "Gbnd" = "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/Gbnd.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Corollaries/Gbnd.var
+*)
(* end show *)
Section More_Sums
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Sums/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Sums/pI.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con" as lemma.
(* begin show *)
-alias id "f" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Sums/f.var
+*)
-alias id "f'" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/f'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Sums/f'.var
+*)
-alias id "derF" = "cic:/CoRN/ftc/MoreFunctions/More_Sums/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/More_Sums/derF.var
+*)
(* end show *)
Mutatis mutandis for differentiability.
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/pI.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con" as lemma.
inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con" as lemma.
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/G.var
+*)
-alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffF.var
+*)
-alias id "diffG" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffG.var
+*)
(*#*
%\begin{convention}% Assume [F] and [G] are differentiable in [I].
Section Diffble_Corollaries
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/pI.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/G.var
+*)
-alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffF.var
+*)
-alias id "diffG" = "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffG.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con" as lemma.
Higher order derivatives pose more interesting problems. It turns out that it really becomes necessary to generalize our [n_deriv] operator to any interval.
*)
-alias id "I" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/pI.var
+*)
(* UNEXPORTED
Section Definitions
%\end{convention}%
*)
-alias id "n" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/n.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/F.var
+*)
-alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/diffF.var
+*)
inline procedural "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con" as definition.
As a special case we get a differentiation operator%\ldots%#...#
*)
-alias id "F" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/F.var
+*)
(* begin show *)
-alias id "diffF" = "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/diffF.var
+*)
(* end show *)
Before we define the new integral we need to some trivial interval inclusions.
*)
-alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/Lemmas/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Lemmas/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/Lemmas/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Lemmas/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Lemmas/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Lemmas/Hab.var
+*)
inline procedural "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con" as lemma.
[<=] b].
*)
-alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Definitions/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Definitions/Hab.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Definitions/F.var
+*)
-alias id "HF" = "cic:/CoRN/ftc/MoreIntegrals/Definitions/HF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Definitions/HF.var
+*)
inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con" as lemma.
new ones, too. We begin with (strong) extensionality.
*)
-alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/Hab.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/G.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contF.var
+*)
-alias id "contG" = "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contG.var
+*)
inline procedural "cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con" as lemma.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/b.var
+*)
-alias id "c" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/c.var
+*)
(* begin show *)
-alias id "Hab'" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab'.var
+*)
-alias id "Hac'" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac'.var
+*)
-alias id "Hcb'" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb'.var
+*)
-alias id "Habc'" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc'.var
+*)
(* end show *)
-alias id "F" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/F.var
+*)
(* begin show *)
-alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab.var
+*)
-alias id "Hac" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac.var
+*)
-alias id "Hcb" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb.var
+*)
-alias id "Habc" = "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc.var
+*)
(* end show *)
Section Corollaries
*)
-alias id "a" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Corollaries/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Corollaries/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Corollaries/Hab.var
+*)
-alias id "F" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Corollaries/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/MoreIntegrals/Corollaries/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntegrals/Corollaries/contF.var
+*)
(*#* As a corollary, we get the following rule: *)
%\end{convention}%
*)
-alias id "P" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/P.var
+*)
-alias id "wdP" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/wdP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/wdP.var
+*)
-alias id "x" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/x.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/x.var
+*)
-alias id "Hx" = "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/Hx.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/Hx.var
+*)
inline procedural "cic:/CoRN/ftc/MoreIntervals/compact_single.con" as definition.
%\end{convention}%
*)
-alias id "n" = "cic:/CoRN/ftc/MoreIntervals/Functions/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntervals/Functions/n.var
+*)
-alias id "I" = "cic:/CoRN/ftc/MoreIntervals/Functions/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/MoreIntervals/Functions/I.var
+*)
inline procedural "cic:/CoRN/ftc/MoreIntervals/Continuous.con" as definition.
We first define what we mean by the derivative of order [n] of a function.
*)
-alias id "a" = "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Nth_Derivative/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Nth_Derivative/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab'.var
+*)
(* begin hide *)
These are the expected extensionality and uniqueness results.
*)
-alias id "a" = "cic:/CoRN/ftc/NthDerivative/Trivia/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Trivia/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/NthDerivative/Trivia/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Trivia/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/Trivia/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Trivia/Hab'.var
+*)
(* begin hide *)
definition of [Diffble_I_n].
*)
-alias id "a" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Basic_Results/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Basic_Results/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab'.var
+*)
(* begin hide *)
(* begin show *)
-alias id "F" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/F.var
+*)
-alias id "diffF" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffF.var
+*)
-alias id "diffFn" = "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffFn.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffFn.var
+*)
(* end show *)
Section More_Results
*)
-alias id "a" = "cic:/CoRN/ftc/NthDerivative/More_Results/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/More_Results/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/NthDerivative/More_Results/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/More_Results/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/NthDerivative/More_Results/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/NthDerivative/More_Results/Hab'.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "I" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Equality_Results/I.var
+*)
-alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Equality_Results/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Equality_Results/G.var
+*)
(* begin hide *)
(* end hide *)
-alias id "R" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/R.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Equality_Results/R.var
+*)
(*#*
We start with two lemmas which make it much easier to prove and use
%\end{convention}%
*)
-alias id "I" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/I.var
+*)
-alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/F.var
+*)
(* begin hide *)
(* begin show *)
-alias id "Hf" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/Hf.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/F.var
+*)
-alias id "P" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/P.var
+*)
-alias id "Q" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Q.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Q.var
+*)
inline procedural "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con" as lemma.
%\end{convention}%
*)
-alias id "I" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/More_on_Equality/I.var
+*)
(* UNEXPORTED
Section Feq_Equivalence
*)
-alias id "F" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/G.var
+*)
-alias id "H" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/H.var
+*)
inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con" as lemma.
Also it is preserved through application of functional constructors and restriction.
*)
-alias id "F" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F'.var
+*)
-alias id "G" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G.var
+*)
-alias id "G'" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G'.var
+*)
inline procedural "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con" as lemma.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Nth_Power/F.var
+*)
(* begin hide *)
(* end hide *)
-alias id "Q" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Q.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Nth_Power/Q.var
+*)
-alias id "H" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Nth_Power/H.var
+*)
-alias id "Hf" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Nth_Power/Hf.var
+*)
inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con" as lemma.
-alias id "n" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Nth_Power/n.var
+*)
-alias id "H'" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Nth_Power/H'.var
+*)
inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con" as lemma.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/F.var
+*)
-alias id "incF" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/incF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/incF.var
+*)
inline procedural "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con" as lemma.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/ftc/PartInterval/Conversion/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Conversion/F.var
+*)
-alias id "a" = "cic:/CoRN/ftc/PartInterval/Conversion/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Conversion/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/PartInterval/Conversion/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Conversion/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/PartInterval/Conversion/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Conversion/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "Hf" = "cic:/CoRN/ftc/PartInterval/Conversion/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Conversion/Hf.var
+*)
inline procedural "cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con" as lemma.
domain [[a,b]] and build the corresponding partial function.
*)
-alias id "a" = "cic:/CoRN/ftc/PartInterval/AntiConversion/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/AntiConversion/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/PartInterval/AntiConversion/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/AntiConversion/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/PartInterval/AntiConversion/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/AntiConversion/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/PartInterval/AntiConversion/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/AntiConversion/f.var
+*)
inline procedural "cic:/CoRN/ftc/PartInterval/PartInt_strext.con" as lemma.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/ftc/PartInterval/Equivalences/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/F.var
+*)
-alias id "G" = "cic:/CoRN/ftc/PartInterval/Equivalences/G.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/G.var
+*)
-alias id "a" = "cic:/CoRN/ftc/PartInterval/Equivalences/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/PartInterval/Equivalences/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/b.var
+*)
-alias id "c" = "cic:/CoRN/ftc/PartInterval/Equivalences/c.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/c.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/PartInterval/Equivalences/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "f" = "cic:/CoRN/ftc/PartInterval/Equivalences/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/f.var
+*)
-alias id "g" = "cic:/CoRN/ftc/PartInterval/Equivalences/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/g.var
+*)
-alias id "Ff" = "cic:/CoRN/ftc/PartInterval/Equivalences/Ff.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/Ff.var
+*)
-alias id "Gg" = "cic:/CoRN/ftc/PartInterval/Equivalences/Gg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/Gg.var
+*)
inline procedural "cic:/CoRN/ftc/PartInterval/part_int_const.con" as lemma.
(* begin show *)
-alias id "HG" = "cic:/CoRN/ftc/PartInterval/Equivalences/HG.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/HG.var
+*)
-alias id "Hg" = "cic:/CoRN/ftc/PartInterval/Equivalences/Hg.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/PartInterval/Equivalences/Hg.var
+*)
(* end show *)
Section Refinements
*)
-alias id "a" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Refinements/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Refinements/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Refinements/Hab.var
+*)
-alias id "m" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Refinements/m.var
+*)
-alias id "n" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Refinements/n.var
+*)
-alias id "P" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Refinements/P.var
+*)
-alias id "Q" = "cic:/CoRN/ftc/Partitions/Definitions/Refinements/Q.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Refinements/Q.var
+*)
(*#*
We now define what it means for a partition [Q] to be a refinement of
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/Partitions/Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Partitions/Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Partitions/Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Hab.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "m" = "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/m.var
+*)
-alias id "Q" = "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/Q.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/Q.var
+*)
inline procedural "cic:/CoRN/ftc/Partitions/Partition_imp_points.con" as definition.
As a corollary, given any continuous function [F] and a natural number we have an immediate choice of a sum of [F] in [[a,b]].
*)
-alias id "F" = "cic:/CoRN/ftc/Partitions/Definitions/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/Partitions/Definitions/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Definitions/contF.var
+*)
inline procedural "cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con" as definition.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/Partitions/Lemmas/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Lemmas/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Partitions/Lemmas/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Lemmas/b.var
+*)
(* begin hide *)
(* end hide *)
-alias id "Hab" = "cic:/CoRN/ftc/Partitions/Lemmas/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Lemmas/Hab.var
+*)
-alias id "n" = "cic:/CoRN/ftc/Partitions/Lemmas/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Lemmas/n.var
+*)
-alias id "P" = "cic:/CoRN/ftc/Partitions/Lemmas/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Lemmas/P.var
+*)
inline procedural "cic:/CoRN/ftc/Partitions/Mesh_lemma.con" as lemma.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/Partitions/Even_Partitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Even_Partitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Partitions/Even_Partitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Even_Partitions/b.var
+*)
(* begin hide *)
(* end hide *)
-alias id "Hab" = "cic:/CoRN/ftc/Partitions/Even_Partitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Even_Partitions/Hab.var
+*)
(*#*
An interesting property: in a partition, if [ai [<] aj] then [i < j].
Even partitions always have a common refinement.
*)
-alias id "m" = "cic:/CoRN/ftc/Partitions/Even_Partitions/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Even_Partitions/m.var
+*)
-alias id "n" = "cic:/CoRN/ftc/Partitions/Even_Partitions/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Even_Partitions/n.var
+*)
-alias id "Hm" = "cic:/CoRN/ftc/Partitions/Even_Partitions/Hm.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Even_Partitions/Hm.var
+*)
-alias id "Hn" = "cic:/CoRN/ftc/Partitions/Even_Partitions/Hn.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Even_Partitions/Hn.var
+*)
(* begin hide *)
Some auxiliary definitions. A partition is said to be separated if all its points are distinct.
*)
-alias id "a" = "cic:/CoRN/ftc/Partitions/More_Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/More_Definitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Partitions/More_Definitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/More_Definitions/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/Partitions/More_Definitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/More_Definitions/Hab.var
+*)
inline procedural "cic:/CoRN/ftc/Partitions/_Separated.con" as definition.
%\end{convention}%
*)
-alias id "n" = "cic:/CoRN/ftc/Partitions/More_Definitions/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/More_Definitions/n.var
+*)
-alias id "m" = "cic:/CoRN/ftc/Partitions/More_Definitions/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/More_Definitions/m.var
+*)
-alias id "P" = "cic:/CoRN/ftc/Partitions/More_Definitions/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/More_Definitions/P.var
+*)
-alias id "Q" = "cic:/CoRN/ftc/Partitions/More_Definitions/Q.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/More_Definitions/Q.var
+*)
inline procedural "cic:/CoRN/ftc/Partitions/Separated.con" as definition.
Section Sep_Partitions
*)
-alias id "a" = "cic:/CoRN/ftc/Partitions/Sep_Partitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Sep_Partitions/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Partitions/Sep_Partitions/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Sep_Partitions/b.var
+*)
(* begin hide *)
(* end hide *)
-alias id "Hab" = "cic:/CoRN/ftc/Partitions/Sep_Partitions/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Partitions/Sep_Partitions/Hab.var
+*)
(*#*
The antimesh of a separated partition is always positive.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF.var
+*)
-alias id "incF" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/incF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/incF.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/e.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/e.var
+*)
-alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/He.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/He.var
+*)
(* begin hide *)
(* end hide *)
-alias id "m" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/m.var
+*)
-alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/n.var
+*)
-alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/P.var
+*)
-alias id "HMesh" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HMesh.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HMesh.var
+*)
-alias id "Q" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Q.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Q.var
+*)
-alias id "Href" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Href.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Href.var
+*)
-alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fP.var
+*)
-alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP.var
+*)
-alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP'.var
+*)
-alias id "fQ" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fQ.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fQ.var
+*)
-alias id "HfQ" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ.var
+*)
-alias id "HfQ'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ'.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/n.var
+*)
-alias id "j" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/j.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/j.var
+*)
-alias id "k" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/k.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/k.var
+*)
-alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/P.var
+*)
-alias id "Q" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/Q.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/Q.var
+*)
-alias id "R" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/R.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/R.var
+*)
-alias id "HrefP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefP.var
+*)
-alias id "HrefR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefR.var
+*)
-alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e.var
+*)
-alias id "e'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e'.var
+*)
-alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He.var
+*)
-alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "HMeshP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshP.var
+*)
-alias id "HMeshR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshR.var
+*)
-alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fP.var
+*)
-alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP.var
+*)
-alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP'.var
+*)
-alias id "fR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fR.var
+*)
-alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR.var
+*)
-alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR'.var
+*)
inline procedural "cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con" as lemma.
%\end{convention}%
*)
-alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/n.var
+*)
-alias id "m" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/m.var
+*)
-alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P.var
+*)
-alias id "R" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R.var
+*)
-alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e.var
+*)
-alias id "e'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e'.var
+*)
-alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He.var
+*)
-alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "HMeshP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshP.var
+*)
-alias id "HMeshR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshR.var
+*)
-alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP.var
+*)
-alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP.var
+*)
-alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP'.var
+*)
-alias id "fR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR.var
+*)
-alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR.var
+*)
-alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR'.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hab'.var
+*)
-alias id "beta" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/beta.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/beta.var
+*)
-alias id "Hbeta" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hbeta.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hbeta.var
+*)
(* begin hide *)
above)
*)
-alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/n.var
+*)
-alias id "m" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/m.var
+*)
-alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/P.var
+*)
-alias id "R" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/R.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/R.var
+*)
-alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e.var
+*)
-alias id "e'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e'.var
+*)
-alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He.var
+*)
-alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "HMeshP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshP.var
+*)
-alias id "HMeshR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshR.var
+*)
-alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fP.var
+*)
-alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP.var
+*)
-alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP'.var
+*)
-alias id "fR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fR.var
+*)
-alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR.var
+*)
-alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR'.var
+*)
(* begin show *)
-alias id "Hab'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Hab'.var
+*)
(* end show *)
(*#* We finish by presenting Theorem 9. *)
-alias id "n" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/n.var
+*)
-alias id "m" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/m.var
+*)
-alias id "P" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/P.var
+*)
-alias id "R" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/R.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/R.var
+*)
-alias id "e" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e.var
+*)
-alias id "e'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e'.var
+*)
-alias id "He" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He.var
+*)
-alias id "He'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "HMeshP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshP.var
+*)
-alias id "HMeshR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshR.var
+*)
-alias id "fP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fP.var
+*)
-alias id "HfP" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP.var
+*)
-alias id "HfP'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP'.var
+*)
-alias id "fR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fR.var
+*)
-alias id "HfR" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR.var
+*)
-alias id "HfR'" = "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR'.var
+*)
inline procedural "cic:/CoRN/ftc/RefLemma/refinement_lemma.con" as lemma.
Section Refining_Separated
*)
-alias id "a" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/Hab.var
+*)
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".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/contF.var
+*)
-alias id "incF" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/incF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/incF.var
+*)
-alias id "m" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/m.var
+*)
-alias id "n" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/n.var
+*)
-alias id "P" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/P.var
+*)
-alias id "R" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/R.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/R.var
+*)
-alias id "HPR" = "cic:/CoRN/ftc/RefSepRef/Refining_Separated/HPR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSepRef/Refining_Separated/HPR.var
+*)
inline procedural "cic:/CoRN/ftc/RefSepRef/RSR_HP.con" as lemma.
Section Separating__Separated
*)
-alias id "a" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab.var
+*)
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".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF.var
+*)
-alias id "incF" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/incF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/incF.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab'.var
+*)
-alias id "m" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/m.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/m.var
+*)
-alias id "n" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/n.var
+*)
-alias id "P" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/P.var
+*)
-alias id "R" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/R.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/R.var
+*)
-alias id "HP" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/HP.var
+*)
-alias id "HR" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HR.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/HR.var
+*)
inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_n.con" as lemma.
inline procedural "cic:/CoRN/ftc/RefSeparated/RS_pos_m.con" as lemma.
-alias id "alpha" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/alpha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/alpha.var
+*)
-alias id "Halpha" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Halpha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/Halpha.var
+*)
inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/e.con" "Separating__Separated__" as definition.
inline procedural "cic:/CoRN/ftc/RefSeparated/RS_Hd'.con" as lemma.
-alias id "csi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/csi.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/csi.var
+*)
-alias id "Hcsi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hcsi.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hcsi.var
+*)
inline procedural "cic:/CoRN/ftc/RefSeparated/Separating__Separated/M.con" "Separating__Separated__" as definition.
Section Defining_ai'
*)
-alias id "i" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/i.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/i.var
+*)
-alias id "Hi" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi.var
+*)
inline procedural "cic:/CoRN/ftc/RefSeparated/separation_conseq.con" as lemma.
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".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi0.var
+*)
-alias id "Hin" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hin.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hin.var
+*)
inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con" as definition.
inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con" as lemma.
-alias id "g" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/g.var
+*)
-alias id "gP" = "cic:/CoRN/ftc/RefSeparated/Separating__Separated/gP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparated/Separating__Separated/gP.var
+*)
inline procedural "cic:/CoRN/ftc/RefSeparated/sep__sep_points.con" as definition.
Section Separating_Partition
*)
-alias id "a" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab.var
+*)
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".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/contF.var
+*)
-alias id "incF" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/incF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/incF.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab'.var
+*)
-alias id "n" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/n.var
+*)
-alias id "P" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/P.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/P.var
+*)
-alias id "alpha" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/alpha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/alpha.var
+*)
-alias id "Halpha" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Halpha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/Halpha.var
+*)
-alias id "csi" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/csi.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/csi.var
+*)
-alias id "Hcsi" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hcsi.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hcsi.var
+*)
inline procedural "cic:/CoRN/ftc/RefSeparating/Separating_Partition/M.con" "Separating_Partition__" as definition.
inline procedural "cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con" as lemma.
-alias id "Hab''" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab''.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab''.var
+*)
inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con" as lemma.
inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con" as lemma.
-alias id "g" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/g.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/g.var
+*)
-alias id "gP" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP.var
+*)
-alias id "gP'" = "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP'.var
+*)
inline procedural "cic:/CoRN/ftc/RefSeparating/sep__part_pts.con" as definition.
(* begin hide *)
-alias id "a" = "cic:/CoRN/ftc/Rolle/Rolle/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Rolle/Rolle/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Rolle/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/Hab'.var
+*)
inline procedural "cic:/CoRN/ftc/Rolle/Rolle/Hab.con" "Rolle__" as definition.
inline procedural "cic:/CoRN/ftc/Rolle/Rolle/I.con" "Rolle__" as definition.
-alias id "F" = "cic:/CoRN/ftc/Rolle/Rolle/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/Rolle/Rolle/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/F'.var
+*)
-alias id "derF" = "cic:/CoRN/ftc/Rolle/Rolle/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/derF.var
+*)
-alias id "Ha" = "cic:/CoRN/ftc/Rolle/Rolle/Ha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/Ha.var
+*)
-alias id "Hb" = "cic:/CoRN/ftc/Rolle/Rolle/Hb.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/Hb.var
+*)
(* end hide *)
(* begin show *)
-alias id "Fab" = "cic:/CoRN/ftc/Rolle/Rolle/Fab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/Fab.var
+*)
(* end show *)
(* begin hide *)
-alias id "e" = "cic:/CoRN/ftc/Rolle/Rolle/e.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/e.var
+*)
-alias id "He" = "cic:/CoRN/ftc/Rolle/Rolle/He.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Rolle/He.var
+*)
inline procedural "cic:/CoRN/ftc/Rolle/Rolle/contF'.con" "Rolle__" as definition.
The following is a simple corollary:
*)
-alias id "a" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Law_of_the_Mean/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Law_of_the_Mean/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F'.var
+*)
-alias id "HF" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HF.var
+*)
(* begin show *)
-alias id "HA" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HA.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HA.var
+*)
-alias id "HB" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HB.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HB.var
+*)
(* end show *)
We can also state these theorems without expliciting the derivative of [F].
*)
-alias id "a" = "cic:/CoRN/ftc/Rolle/Corollaries/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Corollaries/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Rolle/Corollaries/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Corollaries/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Corollaries/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Corollaries/Hab'.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/Rolle/Corollaries/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Corollaries/F.var
+*)
(* begin show *)
-alias id "HF" = "cic:/CoRN/ftc/Rolle/Corollaries/HF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Corollaries/HF.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "I" = "cic:/CoRN/ftc/Rolle/Generalizations/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Generalizations/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/Rolle/Generalizations/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Generalizations/pI.var
+*)
-alias id "F" = "cic:/CoRN/ftc/Rolle/Generalizations/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Generalizations/F.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/Rolle/Generalizations/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Generalizations/F'.var
+*)
(* begin show *)
-alias id "derF" = "cic:/CoRN/ftc/Rolle/Generalizations/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Rolle/Generalizations/derF.var
+*)
(* end show *)
The same notations and conventions apply as before.
*)
-alias id "a" = "cic:/CoRN/ftc/StrongIVT/IVT'/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/StrongIVT/IVT'/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/Hab'.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/StrongIVT/IVT'/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/StrongIVT/IVT'/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/contF.var
+*)
(* begin hide *)
(* begin show *)
-alias id "incrF" = "cic:/CoRN/ftc/StrongIVT/IVT'/incrF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/incrF.var
+*)
(* end show *)
(* begin show *)
-alias id "z" = "cic:/CoRN/ftc/StrongIVT/IVT'/z.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/z.var
+*)
-alias id "Haz" = "cic:/CoRN/ftc/StrongIVT/IVT'/Haz.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/Haz.var
+*)
-alias id "Hzb" = "cic:/CoRN/ftc/StrongIVT/IVT'/Hzb.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/StrongIVT/IVT'/Hzb.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "I" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/More_Taylor_Defs/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/More_Taylor_Defs/pI.var
+*)
-alias id "F" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/More_Taylor_Defs/F.var
+*)
(* begin show *)
(* end show *)
-alias id "a" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/More_Taylor_Defs/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/More_Taylor_Defs/b.var
+*)
-alias id "Ha" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Ha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Ha.var
+*)
-alias id "Hb" = "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Hb.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Hb.var
+*)
(* begin show *)
%\end{convention}%
*)
-alias id "I" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/I.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/I.var
+*)
-alias id "pI" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/pI.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/pI.var
+*)
-alias id "F" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/F.var
+*)
-alias id "n" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/n.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/n.var
+*)
-alias id "f" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/f.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/f.var
+*)
-alias id "goodF" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF.var
+*)
-alias id "goodF'" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF'.var
+*)
-alias id "derF" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF.var
+*)
-alias id "F'" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/F'.var
+*)
-alias id "derF'" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF'.var
+*)
-alias id "a" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/b.var
+*)
-alias id "Ha" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Ha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/Ha.var
+*)
-alias id "Hb" = "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Hb.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/Taylor/Taylor_Theorem/Hb.var
+*)
(* begin show *)
[[Min(a,b),Max(a,b)]].
*)
-alias id "a" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/b.var
+*)
-alias id "Hap" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hap.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hap.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/F.var
+*)
-alias id "Ha" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Ha.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Ha.var
+*)
-alias id "Hb" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hb.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hb.var
+*)
(* begin show *)
%\end{convention}%
*)
-alias id "e" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/e.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/e.var
+*)
-alias id "He" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/He.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/He.var
+*)
(* begin hide *)
Section Lemma1
*)
-alias id "a" = "cic:/CoRN/ftc/WeakIVT/Lemma1/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma1/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/WeakIVT/Lemma1/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma1/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/WeakIVT/Lemma1/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma1/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/WeakIVT/Lemma1/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma1/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/WeakIVT/Lemma1/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma1/contF.var
+*)
(*#* **First Lemmas
Section Lemma2
*)
-alias id "a" = "cic:/CoRN/ftc/WeakIVT/Lemma2/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma2/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/WeakIVT/Lemma2/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma2/b.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/WeakIVT/Lemma2/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma2/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/WeakIVT/Lemma2/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma2/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/WeakIVT/Lemma2/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/Lemma2/contF.var
+*)
(*#*
If [f(b) [<] f(a)], a similar result holds:
converge to [x0] such that [f(x0) [=] z].
*)
-alias id "a" = "cic:/CoRN/ftc/WeakIVT/IVT/a.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/a.var
+*)
-alias id "b" = "cic:/CoRN/ftc/WeakIVT/IVT/b.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/b.var
+*)
-alias id "Hab'" = "cic:/CoRN/ftc/WeakIVT/IVT/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/Hab'.var
+*)
-alias id "Hab" = "cic:/CoRN/ftc/WeakIVT/IVT/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "F" = "cic:/CoRN/ftc/WeakIVT/IVT/F.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/F.var
+*)
-alias id "contF" = "cic:/CoRN/ftc/WeakIVT/IVT/contF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/contF.var
+*)
(* begin hide *)
(* begin show *)
-alias id "incrF" = "cic:/CoRN/ftc/WeakIVT/IVT/incrF.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/incrF.var
+*)
(* end show *)
(* begin show *)
-alias id "z" = "cic:/CoRN/ftc/WeakIVT/IVT/z.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/z.var
+*)
-alias id "Haz" = "cic:/CoRN/ftc/WeakIVT/IVT/Haz.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/Haz.var
+*)
-alias id "Hzb" = "cic:/CoRN/ftc/WeakIVT/IVT/Hzb.var".
+(* UNEXPORTED
+cic:/CoRN/ftc/WeakIVT/IVT/Hzb.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "A" = "cic:/CoRN/metrics/CPseudoMSpaces/Relations/A.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/CPseudoMSpaces/Relations/A.var
+*)
-alias id "d" = "cic:/CoRN/metrics/CPseudoMSpaces/Relations/d.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/CPseudoMSpaces/Relations/d.var
+*)
(* UNEXPORTED
Set Implicit Arguments.
%\end{convention}%
*)
-alias id "A" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_axioms/A.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/CPseudoMSpaces/PsMS_axioms/A.var
+*)
inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con" as lemma.
%\end{convention}%
*)
-alias id "Y" = "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_basics/Y.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/CPseudoMSpaces/PsMS_basics/Y.var
+*)
inline procedural "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con" as lemma.
%\end{convention}%
*)
-alias id "A" = "cic:/CoRN/metrics/ContFunctions/Continuous_functions/A.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/ContFunctions/Continuous_functions/A.var
+*)
-alias id "B" = "cic:/CoRN/metrics/ContFunctions/Continuous_functions/B.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/ContFunctions/Continuous_functions/B.var
+*)
(*#*
We will look at some notions of continuous functions.
Hence it is uniformly continuous and continuous.
*)
-alias id "B" = "cic:/CoRN/metrics/ContFunctions/Constant/B.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/ContFunctions/Constant/B.var
+*)
-alias id "X" = "cic:/CoRN/metrics/ContFunctions/Constant/X.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/ContFunctions/Constant/X.var
+*)
inline procedural "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con" as lemma.
again Lipschitz/uniformly continuous/continuous.
*)
-alias id "X" = "cic:/CoRN/metrics/ContFunctions/Composition/X.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/ContFunctions/Composition/X.var
+*)
-alias id "B" = "cic:/CoRN/metrics/ContFunctions/Composition/B.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/ContFunctions/Composition/B.var
+*)
-alias id "f" = "cic:/CoRN/metrics/ContFunctions/Composition/f.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/ContFunctions/Composition/f.var
+*)
-alias id "C" = "cic:/CoRN/metrics/ContFunctions/Composition/C.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/ContFunctions/Composition/C.var
+*)
-alias id "g" = "cic:/CoRN/metrics/ContFunctions/Composition/g.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/ContFunctions/Composition/g.var
+*)
inline procedural "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con" as lemma.
inline procedural "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con" as definition.
-alias id "X" = "cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var".
+(* UNEXPORTED
+cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var
+*)
inline procedural "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con" as lemma.
Section LUBP
*)
-alias id "R1" = "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var
+*)
(* SUBSECTION ON GENRAL DEFINITIONS *)
Section lub_definitions
*)
-alias id "OF" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var
+*)
-alias id "SS" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var
+*)
inline procedural "cic:/CoRN/reals/Bridges_LUB/member.con" as definition.
Section upper_bound_sequence
*)
-alias id "A" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var
+*)
-alias id "is_inhabitted" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var
+*)
-alias id "bounded_above" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var
+*)
-alias id "located" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var".
+(* UNEXPORTED
+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__" as definition.
Section bridges_axioms_imply_ours
*)
-alias id "OF" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/OF.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/OF.var
+*)
-alias id "lubp" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/lubp.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/lubp.var
+*)
-alias id "is_Archimedes" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/is_Archimedes.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/is_Archimedes.var
+*)
inline procedural "cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con" as lemma.
Section supremum
*)
-alias id "P" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P.var
+*)
inline procedural "cic:/CoRN/reals/Bridges_iso/inequality1.con" as lemma.
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".
+(* UNEXPORTED
+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" as definition.
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".
+(* UNEXPORTED
+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" as lemma.
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".
+(* UNEXPORTED
+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" as lemma.
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".
+(* UNEXPORTED
+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__" as definition.
End Every_Cauchy_Sequence_is_bounded
*)
-alias id "g" = "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g.var".
+(* UNEXPORTED
+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__" as definition.
Section CMetric_Field_Cauchy
*)
-alias id "F" = "cic:/CoRN/reals/CMetricFields/CMetric_Field_Cauchy/F.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CMetricFields/CMetric_Field_Cauchy/F.var
+*)
(*#*
%\begin{convention}% Let [F:CMetricField].
[seq2] is monotonous.
*)
-alias id "seq1" = "cic:/CoRN/reals/CReals1/Subsequences/seq1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Subsequences/seq1.var
+*)
-alias id "seq2" = "cic:/CoRN/reals/CReals1/Subsequences/seq2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Subsequences/seq2.var
+*)
-alias id "f" = "cic:/CoRN/reals/CReals1/Subsequences/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Subsequences/f.var
+*)
-alias id "monF" = "cic:/CoRN/reals/CReals1/Subsequences/monF.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Subsequences/monF.var
+*)
-alias id "crescF" = "cic:/CoRN/reals/CReals1/Subsequences/crescF.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Subsequences/crescF.var
+*)
-alias id "subseq" = "cic:/CoRN/reals/CReals1/Subsequences/subseq.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Subsequences/subseq.var
+*)
-alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Subsequences/mon_seq2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Subsequences/mon_seq2.var
+*)
inline procedural "cic:/CoRN/reals/CReals1/unbnd_f.con" as lemma.
Section Cauchy_Subsequences
*)
-alias id "seq1" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq1.var
+*)
-alias id "seq2" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq2.var
+*)
-alias id "f" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Cauchy_Subsequences/f.var
+*)
-alias id "monF" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/monF.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Cauchy_Subsequences/monF.var
+*)
-alias id "crescF" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/crescF.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Cauchy_Subsequences/crescF.var
+*)
-alias id "subseq" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/subseq.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Cauchy_Subsequences/subseq.var
+*)
-alias id "mon_seq2" = "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/mon_seq2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CReals1/Cauchy_Subsequences/mon_seq2.var
+*)
inline procedural "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con" as lemma.
Section Sums_over_Reals
*)
-alias id "c" = "cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var".
+(* UNEXPORTED
+cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var
+*)
inline procedural "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con" as lemma.
Opaque IR.
*)
-alias id "IR" = "cic:/CoRN/reals/CauchySeq/IR.var".
+inline procedural "cic:/CoRN/reals/CauchySeq/IR.con".
(* NOTATION
Notation PartIR := (PartFunct IR).
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Cauchy_CReals/R_CReals/F.var
+*)
(* NOTATION
Notation "'R_COrdField''" := (R_COrdField F).
resulting one is, too.
*)
-alias id "F_is_archemaedian" = "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F_is_archemaedian.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Cauchy_CReals/R_CReals/F_is_archemaedian.var
+*)
inline procedural "cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con" as theorem.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/reals/IVT/Nested_Intervals/a.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/a.var
+*)
-alias id "b" = "cic:/CoRN/reals/IVT/Nested_Intervals/b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/b.var
+*)
-alias id "a_mon" = "cic:/CoRN/reals/IVT/Nested_Intervals/a_mon.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/a_mon.var
+*)
-alias id "b_mon" = "cic:/CoRN/reals/IVT/Nested_Intervals/b_mon.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/b_mon.var
+*)
-alias id "a_b" = "cic:/CoRN/reals/IVT/Nested_Intervals/a_b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/a_b.var
+*)
-alias id "b_a" = "cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var
+*)
inline procedural "cic:/CoRN/reals/IVT/a_mon'.con" as lemma.
%\end{convention}%
*)
-alias id "f" = "cic:/CoRN/reals/IVT/Nested_Intervals/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/f.var
+*)
-alias id "f_contin" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var
+*)
inline procedural "cic:/CoRN/reals/IVT/f_contin_pos.con" as lemma.
(*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *)
-alias id "f_a" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_a.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/f_a.var
+*)
-alias id "f_b" = "cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var
+*)
inline procedural "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con" as lemma.
(*#* ** Bissections *)
-alias id "f" = "cic:/CoRN/reals/IVT/Bisection/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Bisection/f.var
+*)
-alias id "f_apzero_interval" = "cic:/CoRN/reals/IVT/Bisection/f_apzero_interval.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Bisection/f_apzero_interval.var
+*)
-alias id "a" = "cic:/CoRN/reals/IVT/Bisection/a.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Bisection/a.var
+*)
-alias id "b" = "cic:/CoRN/reals/IVT/Bisection/b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Bisection/b.var
+*)
-alias id "a_b" = "cic:/CoRN/reals/IVT/Bisection/a_b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Bisection/a_b.var
+*)
-alias id "f_a" = "cic:/CoRN/reals/IVT/Bisection/f_a.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Bisection/f_a.var
+*)
-alias id "f_b" = "cic:/CoRN/reals/IVT/Bisection/f_b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Bisection/f_b.var
+*)
(*#*
%\begin{convention}% Let [Small] denote [Two[/]ThreeNZ], [lft] be [(Two[*]a[+]b) [/]ThreeNZ] and [rht] be [(a[+]Two[*]b) [/]ThreeNZ].
Section Bisect_Interval
*)
-alias id "f" = "cic:/CoRN/reals/IVT/Bisect_Interval/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Bisect_Interval/f.var
+*)
-alias id "C_f_apzero_interval" = "cic:/CoRN/reals/IVT/Bisect_Interval/C_f_apzero_interval.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/Bisect_Interval/C_f_apzero_interval.var
+*)
(* begin hide *)
Same conventions as before.
*)
-alias id "f" = "cic:/CoRN/reals/IVT/IVT_Op/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/IVT_Op/f.var
+*)
-alias id "f_contin" = "cic:/CoRN/reals/IVT/IVT_Op/f_contin.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/IVT_Op/f_contin.var
+*)
-alias id "f_apzero_interval" = "cic:/CoRN/reals/IVT/IVT_Op/f_apzero_interval.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/IVT_Op/f_apzero_interval.var
+*)
-alias id "a" = "cic:/CoRN/reals/IVT/IVT_Op/a.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/IVT_Op/a.var
+*)
-alias id "b" = "cic:/CoRN/reals/IVT/IVT_Op/b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/IVT_Op/b.var
+*)
-alias id "a_b" = "cic:/CoRN/reals/IVT/IVT_Op/a_b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/IVT_Op/a_b.var
+*)
-alias id "f_a" = "cic:/CoRN/reals/IVT/IVT_Op/f_a.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/IVT_Op/f_a.var
+*)
-alias id "f_b" = "cic:/CoRN/reals/IVT/IVT_Op/f_b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/IVT/IVT_Op/f_b.var
+*)
(* begin hide *)
members of the interval [[Min(a,b),Max(a,b)]].
*)
-alias id "a" = "cic:/CoRN/reals/Intervals/Intervals/a.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Intervals/Intervals/a.var
+*)
-alias id "b" = "cic:/CoRN/reals/Intervals/Intervals/b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Intervals/Intervals/b.var
+*)
-alias id "Hab" = "cic:/CoRN/reals/Intervals/Intervals/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Intervals/Intervals/Hab.var
+*)
inline procedural "cic:/CoRN/reals/Intervals/compact_inc_lft.con" as lemma.
%\end{convention}%
*)
-alias id "a" = "cic:/CoRN/reals/Intervals/Compact/a.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Intervals/Compact/a.var
+*)
-alias id "b" = "cic:/CoRN/reals/Intervals/Compact/b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Intervals/Compact/b.var
+*)
-alias id "Hab" = "cic:/CoRN/reals/Intervals/Compact/Hab.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Intervals/Compact/Hab.var
+*)
(* begin hide *)
(* end hide *)
-alias id "Hab'" = "cic:/CoRN/reals/Intervals/Compact/Hab'.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Intervals/Compact/Hab'.var
+*)
-alias id "e" = "cic:/CoRN/reals/Intervals/Compact/e.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Intervals/Compact/e.var
+*)
-alias id "He" = "cic:/CoRN/reals/Intervals/Compact/He.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Intervals/Compact/He.var
+*)
(*#*
We start by finding a natural number [n] such that [(b[-]a) [/] n [<] e].
%\end{convention}%
*)
-alias id "x" = "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/x.var
+*)
-alias id "y" = "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/y.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/y.var
+*)
inline procedural "cic:/CoRN/reals/Max_AbsIR/Max_seq.con" as definition.
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".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Minimum/a.var
+*)
-alias id "b" = "cic:/CoRN/reals/Max_AbsIR/Minimum/b.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Minimum/b.var
+*)
inline procedural "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con" as lemma.
%\end{convention}%
*)
-alias id "F" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/F.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/F.var
+*)
-alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/G.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/G.var
+*)
(* begin hide *)
Section Part_Function_Abs
*)
-alias id "F" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/F.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/F.var
+*)
-alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/G.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/G.var
+*)
(* begin hide *)
Section Inclusion
*)
-alias id "F" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/F.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Inclusion/F.var
+*)
-alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/G.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Inclusion/G.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/R.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Max_AbsIR/Inclusion/R.var
+*)
inline procedural "cic:/CoRN/reals/Max_AbsIR/included_FMax.con" as lemma.
%\end{convention}%
*)
-alias id "n" = "cic:/CoRN/reals/NRootIR/NRoot/n.var".
+(* UNEXPORTED
+cic:/CoRN/reals/NRootIR/NRoot/n.var
+*)
-alias id "n_pos" = "cic:/CoRN/reals/NRootIR/NRoot/n_pos.var".
+(* UNEXPORTED
+cic:/CoRN/reals/NRootIR/NRoot/n_pos.var
+*)
-alias id "c" = "cic:/CoRN/reals/NRootIR/NRoot/c.var".
+(* UNEXPORTED
+cic:/CoRN/reals/NRootIR/NRoot/c.var
+*)
-alias id "c_nonneg" = "cic:/CoRN/reals/NRootIR/NRoot/c_nonneg.var".
+(* UNEXPORTED
+cic:/CoRN/reals/NRootIR/NRoot/c_nonneg.var
+*)
(* begin hide *)
(*#* %\begin{convention}% Let [x,y] be nonnegative real numbers.
%\end{convention}% *)
-alias id "x" = "cic:/CoRN/reals/NRootIR/Nth_Root/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/NRootIR/Nth_Root/x.var
+*)
-alias id "y" = "cic:/CoRN/reals/NRootIR/Nth_Root/y.var".
+(* UNEXPORTED
+cic:/CoRN/reals/NRootIR/Nth_Root/y.var
+*)
-alias id "Hx" = "cic:/CoRN/reals/NRootIR/Nth_Root/Hx.var".
+(* UNEXPORTED
+cic:/CoRN/reals/NRootIR/Nth_Root/Hx.var
+*)
-alias id "Hy" = "cic:/CoRN/reals/NRootIR/Nth_Root/Hy.var".
+(* UNEXPORTED
+cic:/CoRN/reals/NRootIR/Nth_Root/Hy.var
+*)
inline procedural "cic:/CoRN/reals/NRootIR/NRoot_wd.con" as lemma.
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var".
+(* UNEXPORTED
+cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var".
+(* UNEXPORTED
+cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var".
+(* UNEXPORTED
+cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "R" = "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var".
+(* UNEXPORTED
+cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var
+*)
(* begin hide *)
Section Interval_definition
*)
-alias id "OF" = "cic:/CoRN/reals/Q_dense/Interval_definition/OF.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Q_dense/Interval_definition/OF.var
+*)
inline procedural "cic:/CoRN/reals/Q_dense/Interval.ind".
Section COrdField_extra
*)
-alias id "OF" = "cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var
+*)
inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con" as lemma.
(*#*** WARNING: A file is being loaded *****)
-alias id "R1" = "cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var
+*)
inline procedural "cic:/CoRN/reals/Q_dense/start_l.con" as definition.
%\end{convention}%
*)
-alias id "R1" = "cic:/CoRN/reals/Q_in_CReals/Rational_sequence_prelogue/R1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Q_in_CReals/Rational_sequence_prelogue/R1.var
+*)
(* We clone these proofs from CReals1.v just because there IR is an axiom *)
Section morphism
*)
-alias id "R1" = "cic:/CoRN/reals/R_morphism/morphism/R1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/morphism/R1.var
+*)
-alias id "R2" = "cic:/CoRN/reals/R_morphism/morphism/R2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/morphism/R2.var
+*)
(* UNEXPORTED
Section morphism_details
*)
-alias id "phi" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/phi.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/morphism/morphism_details/phi.var
+*)
-alias id "p1" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/p1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/morphism/morphism_details/p1.var
+*)
-alias id "p2" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/p2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/morphism/morphism_details/p2.var
+*)
-alias id "f1" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/f1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/morphism/morphism_details/f1.var
+*)
-alias id "f2" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/f2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/morphism/morphism_details/f2.var
+*)
-alias id "g1" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/morphism/morphism_details/g1.var
+*)
-alias id "g2" = "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/morphism/morphism_details/g2.var
+*)
inline procedural "cic:/CoRN/reals/R_morphism/fun_pres_relation.con" as definition.
Section composition
*)
-alias id "R1" = "cic:/CoRN/reals/R_morphism/composition/R1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/composition/R1.var
+*)
-alias id "R2" = "cic:/CoRN/reals/R_morphism/composition/R2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/composition/R2.var
+*)
-alias id "R3" = "cic:/CoRN/reals/R_morphism/composition/R3.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/composition/R3.var
+*)
-alias id "f" = "cic:/CoRN/reals/R_morphism/composition/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/composition/f.var
+*)
-alias id "g" = "cic:/CoRN/reals/R_morphism/composition/g.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/composition/g.var
+*)
inline procedural "cic:/CoRN/reals/R_morphism/compose.con" as definition.
Section isomorphism
*)
-alias id "R1" = "cic:/CoRN/reals/R_morphism/isomorphism/R1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/isomorphism/R1.var
+*)
-alias id "R2" = "cic:/CoRN/reals/R_morphism/isomorphism/R2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/isomorphism/R2.var
+*)
(* UNEXPORTED
Section identity_map
*)
-alias id "R3" = "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/R3.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/isomorphism/identity_map/R3.var
+*)
-alias id "f" = "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/isomorphism/identity_map/f.var
+*)
inline procedural "cic:/CoRN/reals/R_morphism/map_is_id.con" as definition.
Section surjective_map
*)
-alias id "R1" = "cic:/CoRN/reals/R_morphism/surjective_map/R1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/surjective_map/R1.var
+*)
-alias id "R2" = "cic:/CoRN/reals/R_morphism/surjective_map/R2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/surjective_map/R2.var
+*)
-alias id "f" = "cic:/CoRN/reals/R_morphism/surjective_map/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/surjective_map/f.var
+*)
inline procedural "cic:/CoRN/reals/R_morphism/map_is_surjective.con" as definition.
Section simplification
*)
-alias id "R1" = "cic:/CoRN/reals/R_morphism/simplification/R1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/simplification/R1.var
+*)
-alias id "R2" = "cic:/CoRN/reals/R_morphism/simplification/R2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/simplification/R2.var
+*)
-alias id "f" = "cic:/CoRN/reals/R_morphism/simplification/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/simplification/f.var
+*)
-alias id "H1" = "cic:/CoRN/reals/R_morphism/simplification/H1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/simplification/H1.var
+*)
inline procedural "cic:/CoRN/reals/R_morphism/f_well_def.con" as lemma.
Section with_less
*)
-alias id "H2" = "cic:/CoRN/reals/R_morphism/simplification/with_less/H2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/simplification/with_less/H2.var
+*)
inline procedural "cic:/CoRN/reals/R_morphism/less_pres_f.con" as lemma.
Section with_plus
*)
-alias id "H3" = "cic:/CoRN/reals/R_morphism/simplification/with_plus/H3.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/simplification/with_plus/H3.var
+*)
inline procedural "cic:/CoRN/reals/R_morphism/f_pres_Zero.con" as lemma.
Section with_plus_less
*)
-alias id "H2" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H2.var
+*)
-alias id "H3" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H3.var".
+(* UNEXPORTED
+cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H3.var
+*)
inline procedural "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con" as lemma.
Section surjectivity_helps
*)
-alias id "f_surj" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/surjectivity_helps/f_surj.var".
+(* UNEXPORTED
+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" as lemma.
Section with_mult_plus_less
*)
-alias id "H4" = "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/with_mult_plus_less/H4.var".
+(* UNEXPORTED
+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" as lemma.
Section Continuity
*)
-alias id "f" = "cic:/CoRN/reals/RealFuncts/Continuity/f.var".
+(* UNEXPORTED
+cic:/CoRN/reals/RealFuncts/Continuity/f.var
+*)
-alias id "f2" = "cic:/CoRN/reals/RealFuncts/Continuity/f2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/RealFuncts/Continuity/f2.var
+*)
(*#*
Let [f] be a unary setoid operation on [IR] and
%\end{convention}%
*)
-alias id "x" = "cic:/CoRN/reals/Series/Definitions/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Definitions/x.var
+*)
inline procedural "cic:/CoRN/reals/Series/seq_part_sum.con" as definition.
Section More_Definitions
*)
-alias id "x" = "cic:/CoRN/reals/Series/More_Definitions/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/More_Definitions/x.var
+*)
(*#* We also define absolute convergence. *)
%\end{convention}%
*)
-alias id "c" = "cic:/CoRN/reals/Series/Power_Series/c.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Power_Series/c.var
+*)
-alias id "H0c" = "cic:/CoRN/reals/Series/Power_Series/H0c.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Power_Series/H0c.var
+*)
-alias id "Hc1" = "cic:/CoRN/reals/Series/Power_Series/Hc1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Power_Series/Hc1.var
+*)
inline procedural "cic:/CoRN/reals/Series/c_exp_Lim.con" as lemma.
%\end{convention}%
*)
-alias id "x" = "cic:/CoRN/reals/Series/Operations/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Operations/x.var
+*)
-alias id "y" = "cic:/CoRN/reals/Series/Operations/y.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Operations/y.var
+*)
-alias id "convX" = "cic:/CoRN/reals/Series/Operations/convX.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Operations/convX.var
+*)
-alias id "convY" = "cic:/CoRN/reals/Series/Operations/convY.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Operations/convY.var
+*)
inline procedural "cic:/CoRN/reals/Series/convergent_wd.con" as lemma.
(*#* Multiplication by a scalar [c] is also permitted. *)
-alias id "c" = "cic:/CoRN/reals/Series/Operations/c.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Operations/c.var
+*)
inline procedural "cic:/CoRN/reals/Series/conv_series_mult_scal.con" as lemma.
Section More_Operations
*)
-alias id "x" = "cic:/CoRN/reals/Series/More_Operations/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/More_Operations/x.var
+*)
-alias id "convX" = "cic:/CoRN/reals/Series/More_Operations/convX.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/More_Operations/convX.var
+*)
(*#* As a corollary, we get the series of the inverses. *)
Let [x,y : nat->IR] be equal after some natural number.
*)
-alias id "x" = "cic:/CoRN/reals/Series/Almost_Everywhere/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Almost_Everywhere/x.var
+*)
-alias id "y" = "cic:/CoRN/reals/Series/Almost_Everywhere/y.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Almost_Everywhere/y.var
+*)
inline procedural "cic:/CoRN/reals/Series/aew_eq.con" as definition.
-alias id "aew_equal" = "cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var
+*)
inline procedural "cic:/CoRN/reals/Series/aew_Cauchy.con" as lemma.
(*#* Suppose furthermore that [x,y] are Cauchy sequences. *)
-alias id "x" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/x.var
+*)
-alias id "y" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/y.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/y.var
+*)
-alias id "aew_equal" = "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var
+*)
inline procedural "cic:/CoRN/reals/Series/aew_Lim.con" as lemma.
%\end{convention}%
*)
-alias id "x" = "cic:/CoRN/reals/Series/Convergence_Criteria/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Convergence_Criteria/x.var
+*)
(*#* We include the comparison test for series, both in a strong and in a less
general (but simpler) form.
Section More_CC
*)
-alias id "x" = "cic:/CoRN/reals/Series/More_CC/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/More_CC/x.var
+*)
inline procedural "cic:/CoRN/reals/Series/ratio_test_conv.con" as lemma.
decreasing convergent to 0.
*)
-alias id "x" = "cic:/CoRN/reals/Series/Alternate_Series/x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Alternate_Series/x.var
+*)
-alias id "pos_x" = "cic:/CoRN/reals/Series/Alternate_Series/pos_x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Alternate_Series/pos_x.var
+*)
-alias id "Lim_x" = "cic:/CoRN/reals/Series/Alternate_Series/Lim_x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Alternate_Series/Lim_x.var
+*)
-alias id "mon_x" = "cic:/CoRN/reals/Series/Alternate_Series/mon_x.var".
+(* UNEXPORTED
+cic:/CoRN/reals/Series/Alternate_Series/mon_x.var
+*)
(* begin hide *)
Section Concrete_iso_between_Creals
*)
-alias id "R1" = "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R1.var".
+(* UNEXPORTED
+cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R1.var
+*)
-alias id "R2" = "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R2.var".
+(* UNEXPORTED
+cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R2.var
+*)
inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con" as lemma.
Section Automatizing_Continuity
*)
-alias id "a" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/a.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/a.var
+*)
-alias id "b" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/b.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/b.var
+*)
inline procedural "cic:/CoRN/tactics/DiffTactics2/cont_function.ind".
Section Automatizing_Derivatives
*)
-alias id "a" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/a.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/a.var
+*)
-alias id "b" = "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/b.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/b.var
+*)
inline procedural "cic:/CoRN/tactics/DiffTactics2/deriv_function.ind".
Section Field_Interpretation_Function
*)
-alias id "F" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/F.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/F.var
+*)
-alias id "val" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/val.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/val.var
+*)
-alias id "unop" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/unop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/unop.var
+*)
-alias id "binop" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/binop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/binop.var
+*)
-alias id "pfun" = "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/pfun.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/pfun.var
+*)
inline procedural "cic:/CoRN/tactics/FieldReflection/interpF.ind".
Section Field_NormCorrect
*)
-alias id "F" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/F.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/F.var
+*)
-alias id "val" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/val.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/val.var
+*)
-alias id "unop" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/unop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/unop.var
+*)
-alias id "binop" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/binop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/binop.var
+*)
-alias id "pfun" = "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/pfun.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/pfun.var
+*)
(* NOTATION
Notation II := (interpF F val unop binop pfun).
Section Group_Interpretation_Function
*)
-alias id "G" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/G.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/G.var
+*)
-alias id "val" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/val.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/val.var
+*)
-alias id "unop" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/unop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/unop.var
+*)
-alias id "binop" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/binop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/binop.var
+*)
-alias id "pfun" = "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/pfun.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/pfun.var
+*)
inline procedural "cic:/CoRN/tactics/GroupReflection/interpG.ind".
Section Group_NormCorrect
*)
-alias id "G" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/G.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/G.var
+*)
-alias id "val" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/val.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/val.var
+*)
-alias id "unop" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/unop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/unop.var
+*)
-alias id "binop" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/binop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/binop.var
+*)
-alias id "pfun" = "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/pfun.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/pfun.var
+*)
(* NOTATION
Notation II := (interpG G val unop binop pfun).
Section Ring_Interpretation_Function
*)
-alias id "R" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/R.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/R.var
+*)
-alias id "val" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/val.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/val.var
+*)
-alias id "unop" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/unop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/unop.var
+*)
-alias id "binop" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/binop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/binop.var
+*)
-alias id "pfun" = "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/pfun.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/pfun.var
+*)
inline procedural "cic:/CoRN/tactics/RingReflection/interpR.ind".
Section Ring_NormCorrect
*)
-alias id "R" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/R.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/R.var
+*)
-alias id "val" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/val.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/val.var
+*)
-alias id "unop" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/unop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/unop.var
+*)
-alias id "binop" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/binop.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/binop.var
+*)
-alias id "pfun" = "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/pfun.var".
+(* UNEXPORTED
+cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/pfun.var
+*)
(* NOTATION
Notation II := (interpR R val unop binop pfun).
Section ArcTan_Range
*)
-alias id "x" = "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/x.var".
+(* UNEXPORTED
+cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/x.var
+*)
(* begin hide *)
%\end{convention}%
*)
-alias id "J" = "cic:/CoRN/transc/PowerSeries/Power_Series/J.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/Power_Series/J.var
+*)
-alias id "x0" = "cic:/CoRN/transc/PowerSeries/Power_Series/x0.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/Power_Series/x0.var
+*)
-alias id "Hx0" = "cic:/CoRN/transc/PowerSeries/Power_Series/Hx0.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/Power_Series/Hx0.var
+*)
-alias id "a" = "cic:/CoRN/transc/PowerSeries/Power_Series/a.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/Power_Series/a.var
+*)
inline procedural "cic:/CoRN/transc/PowerSeries/FPowerSeries.con" as definition.
(* begin show *)
-alias id "Ha" = "cic:/CoRN/transc/PowerSeries/Power_Series/Ha.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/Power_Series/Ha.var
+*)
inline procedural "cic:/CoRN/transc/PowerSeries/Power_Series/r.con" "Power_Series__" as definition.
(* begin show *)
-alias id "Ha'" = "cic:/CoRN/transc/PowerSeries/Power_Series/Ha'.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/Power_Series/Ha'.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "x0" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/x0.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/x0.var
+*)
-alias id "a" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/a.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/a.var
+*)
(* begin hide *)
(* begin show *)
-alias id "Hf" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf.var
+*)
-alias id "Hf'" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf'.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf'.var
+*)
-alias id "Hg" = "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hg.var".
+(* UNEXPORTED
+cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hg.var
+*)
(* end show *)
%\end{convention}%
*)
-alias id "J" = "cic:/CoRN/transc/RealPowers/Power_Function/J.var".
+(* UNEXPORTED
+cic:/CoRN/transc/RealPowers/Power_Function/J.var
+*)
-alias id "F" = "cic:/CoRN/transc/RealPowers/Power_Function/F.var".
+(* UNEXPORTED
+cic:/CoRN/transc/RealPowers/Power_Function/F.var
+*)
-alias id "G" = "cic:/CoRN/transc/RealPowers/Power_Function/G.var".
+(* UNEXPORTED
+cic:/CoRN/transc/RealPowers/Power_Function/G.var
+*)
inline procedural "cic:/CoRN/transc/RealPowers/FPower.con" as definition.
Section Definitions
*)
-alias id "J" = "cic:/CoRN/transc/TaylorSeries/Definitions/J.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Definitions/J.var
+*)
-alias id "pJ" = "cic:/CoRN/transc/TaylorSeries/Definitions/pJ.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Definitions/pJ.var
+*)
-alias id "F" = "cic:/CoRN/transc/TaylorSeries/Definitions/F.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Definitions/F.var
+*)
-alias id "diffF" = "cic:/CoRN/transc/TaylorSeries/Definitions/diffF.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Definitions/diffF.var
+*)
-alias id "a" = "cic:/CoRN/transc/TaylorSeries/Definitions/a.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Definitions/a.var
+*)
-alias id "Ha" = "cic:/CoRN/transc/TaylorSeries/Definitions/Ha.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Definitions/Ha.var
+*)
inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con" as definition.
%\end{convention}%
*)
-alias id "f" = "cic:/CoRN/transc/TaylorSeries/Definitions/f.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Definitions/f.var
+*)
-alias id "derF" = "cic:/CoRN/transc/TaylorSeries/Definitions/derF.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Definitions/derF.var
+*)
inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series.con" as definition.
[F].
*)
-alias id "H" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H.var
+*)
-alias id "F" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/F.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/F.var
+*)
-alias id "a" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/a.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/a.var
+*)
-alias id "Ha" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Ha.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Ha.var
+*)
-alias id "f" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/f.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/f.var
+*)
-alias id "derF" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/derF.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/derF.var
+*)
inline procedural "cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con" as lemma.
(* begin show *)
-alias id "bndf" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/bndf.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/bndf.var
+*)
(* end show *)
(* begin show *)
-alias id "Hf" = "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Hf.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Hf.var
+*)
(* end show *)
Taylor series converge to themselves.
*)
-alias id "F" = "cic:/CoRN/transc/TaylorSeries/Other_Results/F.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/F.var
+*)
-alias id "G" = "cic:/CoRN/transc/TaylorSeries/Other_Results/G.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/G.var
+*)
-alias id "a" = "cic:/CoRN/transc/TaylorSeries/Other_Results/a.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/a.var
+*)
-alias id "f" = "cic:/CoRN/transc/TaylorSeries/Other_Results/f.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/f.var
+*)
-alias id "g" = "cic:/CoRN/transc/TaylorSeries/Other_Results/g.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/g.var
+*)
-alias id "derF" = "cic:/CoRN/transc/TaylorSeries/Other_Results/derF.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/derF.var
+*)
-alias id "derG" = "cic:/CoRN/transc/TaylorSeries/Other_Results/derG.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/derG.var
+*)
-alias id "bndf" = "cic:/CoRN/transc/TaylorSeries/Other_Results/bndf.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/bndf.var
+*)
-alias id "bndg" = "cic:/CoRN/transc/TaylorSeries/Other_Results/bndg.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/bndg.var
+*)
(* begin show *)
-alias id "Heq" = "cic:/CoRN/transc/TaylorSeries/Other_Results/Heq.var".
+(* UNEXPORTED
+cic:/CoRN/transc/TaylorSeries/Other_Results/Heq.var
+*)
(* end show *)
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