(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/I.con" "Maps_into_Compacts__Part_Funct__".
+inline procedural "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/I.con" "Maps_into_Compacts__Part_Funct__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/maps_into_compacts.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_into_compacts.con" as definition.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/maps_lemma'.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_lemma'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/maps_lemma.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_lemma.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_less.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_less.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_inc.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_lemma_inc.con" as lemma.
(* UNEXPORTED
End Part_Funct
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/included_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/included_comp.con" as lemma.
(* UNEXPORTED
End Mapping
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Composition/Interval_Continuity/I.con" "Interval_Continuity__".
+inline procedural "cic:/CoRN/ftc/Composition/Interval_Continuity/I.con" "Interval_Continuity__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/Continuous_I_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Continuous_I_comp.con" as lemma.
(* UNEXPORTED
End Interval_Continuity
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hab.con" "Derivative__".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hab.con" "Derivative__" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hcd.con" "Derivative__".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative/Hcd.con" "Derivative__" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/Derivative/I.con" "Derivative__".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative/I.con" "Derivative__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/included_comp'.con".
+inline procedural "cic:/CoRN/ftc/Composition/included_comp'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/maps'.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps'.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/Derivative_I_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative_I_comp.con" as lemma.
(*#*
The next lemma will be useful when we move on to differentiability.
*)
-inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con".
+inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con" as lemma.
(* UNEXPORTED
End Derivative
(* begin hide *)
-inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hab.con" "Differentiability__".
+inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hab.con" "Differentiability__" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hcd.con" "Differentiability__".
+inline procedural "cic:/CoRN/ftc/Composition/Differentiability/Hcd.con" "Differentiability__" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/Differentiability/I.con" "Differentiability__".
+inline procedural "cic:/CoRN/ftc/Composition/Differentiability/I.con" "Differentiability__" as definition.
(* end hide *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Diffble_I_comp.con" as lemma.
(* UNEXPORTED
End Differentiability
alias id "pJ" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/pJ.var".
-inline procedural "cic:/CoRN/ftc/Composition/maps_compacts_into.con".
+inline procedural "cic:/CoRN/ftc/Composition/maps_compacts_into.con" as definition.
(*#*
Now everything comes naturally:
*)
-inline procedural "cic:/CoRN/ftc/Composition/comp_inc_lemma.con".
+inline procedural "cic:/CoRN/ftc/Composition/comp_inc_lemma.con" as lemma.
alias id "F" = "cic:/CoRN/ftc/Composition/Generalized_Intervals/F.var".
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/Continuous_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Continuous_comp.con" as lemma.
(* begin show *)
(* end show *)
-inline procedural "cic:/CoRN/ftc/Composition/Derivative_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Derivative_comp.con" as lemma.
(* UNEXPORTED
End Generalized_Intervals
Finally, some criteria to prove that a function with a specific domain maps compacts into compacts:
*)
-inline procedural "cic:/CoRN/ftc/Composition/positive_fun.con".
+inline procedural "cic:/CoRN/ftc/Composition/positive_fun.con" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/negative_fun.con".
+inline procedural "cic:/CoRN/ftc/Composition/negative_fun.con" as definition.
-inline procedural "cic:/CoRN/ftc/Composition/positive_imp_maps_compacts_into.con".
+inline procedural "cic:/CoRN/ftc/Composition/positive_imp_maps_compacts_into.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/negative_imp_maps_compacts_into.con".
+inline procedural "cic:/CoRN/ftc/Composition/negative_imp_maps_compacts_into.con" as lemma.
-inline procedural "cic:/CoRN/ftc/Composition/Continuous_imp_maps_compacts_into.con".
+inline procedural "cic:/CoRN/ftc/Composition/Continuous_imp_maps_compacts_into.con" as lemma.
(*#*
As a corollary, we get the generalization of differentiability property.
*)
-inline procedural "cic:/CoRN/ftc/Composition/Diffble_comp.con".
+inline procedural "cic:/CoRN/ftc/Composition/Diffble_comp.con" as lemma.
(* UNEXPORTED
End Corollaries