X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FCoRN-Decl%2Fftc%2FPartFunEquality.ma;h=9771d16f2b7abeba20d66dc2222281f40a8fd29e;hb=bf0cc84dcef9ae3d2145e79754bb39feb3985574;hp=c3b8f1c56b47a699698e8265edef6d718a6f1b90;hpb=80110e17ef1d38d71473e9471ce15beddde663bb;p=helm.git diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma index c3b8f1c56..9771d16f2 100644 --- a/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma +++ b/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma @@ -27,7 +27,7 @@ include "reals/Intervals.ma". include "tactics/DiffTactics1.ma". (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* *Equality of Partial Functions @@ -71,11 +71,11 @@ than in an existentially quantified one. *) (* UNEXPORTED -End Definitions. +End Definitions *) (* UNEXPORTED -Section Equality_Results. +Section Equality_Results *) (*#* **Properties of Inclusion @@ -87,21 +87,21 @@ by [P] and [Q], respectively, the domains of [F] and [G]. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/I.var". +alias id "I" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/I.var". -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/F.var". -inline "cic:/CoRN/ftc/PartFunEquality/G.var". +alias id "G" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/G.var". (* begin hide *) -inline "cic:/CoRN/ftc/PartFunEquality/P.con". +inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/P.con" "Equality_Results__". -inline "cic:/CoRN/ftc/PartFunEquality/Q.con". +inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/Q.con" "Equality_Results__". (* end hide *) -inline "cic:/CoRN/ftc/PartFunEquality/R.var". +alias id "R" = "cic:/CoRN/ftc/PartFunEquality/Equality_Results/R.var". (*#* We start with two lemmas which make it much easier to prove and use @@ -115,7 +115,7 @@ inline "cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con". inline "cic:/CoRN/ftc/PartFunEquality/included_IR.con". (* UNEXPORTED -End Equality_Results. +End Equality_Results *) (* UNEXPORTED @@ -123,7 +123,7 @@ Hint Resolve included_IR : included. *) (* UNEXPORTED -Section Some_More. +Section Some_More *) (*#* @@ -133,15 +133,15 @@ If two function coincide on a given subset then they coincide in any smaller sub inline "cic:/CoRN/ftc/PartFunEquality/included_Feq.con". (* UNEXPORTED -End Some_More. +End Some_More *) (* UNEXPORTED -Section Away_from_Zero. +Section Away_from_Zero *) (* UNEXPORTED -Section Definitions. +Section Definitions *) (*#* **Away from Zero @@ -156,13 +156,13 @@ the domain of [F]. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/I.var". +alias id "I" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/I.var". -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/F.var". (* begin hide *) -inline "cic:/CoRN/ftc/PartFunEquality/P.con". +inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/P.con" "Away_from_Zero__Definitions__". (* end hide *) @@ -174,7 +174,7 @@ If [F] is bounded away from zero in [I] then [F] is necessarily apart from zero (* begin show *) -inline "cic:/CoRN/ftc/PartFunEquality/Hf.var". +alias id "Hf" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/Hf.var". (* end show *) @@ -185,7 +185,7 @@ inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con". inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con". (* UNEXPORTED -End Definitions. +End Definitions *) (*#* @@ -195,11 +195,11 @@ Boundedness away from zero is preserved through restriction of the set. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/F.var". -inline "cic:/CoRN/ftc/PartFunEquality/P.var". +alias id "P" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/P.var". -inline "cic:/CoRN/ftc/PartFunEquality/Q.var". +alias id "Q" = "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Q.var". inline "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con". @@ -222,7 +222,7 @@ inline "cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con". inline "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con". (* UNEXPORTED -End Away_from_Zero. +End Away_from_Zero *) (* UNEXPORTED @@ -249,7 +249,7 @@ Ltac FEQ := apply eq_imp_Feq; (* end hide *) (* UNEXPORTED -Section More_on_Equality. +Section More_on_Equality *) (*#* **Properties of Equality @@ -261,17 +261,17 @@ partial functions. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/I.var". +alias id "I" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/I.var". (* UNEXPORTED -Section Feq_Equivalence. +Section Feq_Equivalence *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +alias id "F" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/F.var". -inline "cic:/CoRN/ftc/PartFunEquality/G.var". +alias id "G" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/G.var". -inline "cic:/CoRN/ftc/PartFunEquality/H.var". +alias id "H" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/H.var". inline "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con". @@ -280,24 +280,24 @@ inline "cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con". inline "cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con". (* UNEXPORTED -End Feq_Equivalence. +End Feq_Equivalence *) (* UNEXPORTED -Section Operations. +Section Operations *) (*#* Also it is preserved through application of functional constructors and restriction. *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +alias id "F" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F.var". -inline "cic:/CoRN/ftc/PartFunEquality/F'.var". +alias id "F'" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F'.var". -inline "cic:/CoRN/ftc/PartFunEquality/G.var". +alias id "G" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G.var". -inline "cic:/CoRN/ftc/PartFunEquality/G'.var". +alias id "G'" = "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G'.var". inline "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con". @@ -332,15 +332,15 @@ The image of a set is extensional. inline "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con". (* UNEXPORTED -End Operations. +End Operations *) (* UNEXPORTED -End More_on_Equality. +End More_on_Equality *) (* UNEXPORTED -Section Nth_Power. +Section Nth_Power *) (*#* **Nth Power @@ -355,34 +355,34 @@ equality relation. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/F.var". (* begin hide *) -inline "cic:/CoRN/ftc/PartFunEquality/P.con". +inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/P.con" "Nth_Power__". (* end hide *) -inline "cic:/CoRN/ftc/PartFunEquality/Q.var". +alias id "Q" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Q.var". -inline "cic:/CoRN/ftc/PartFunEquality/H.var". +alias id "H" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H.var". -inline "cic:/CoRN/ftc/PartFunEquality/Hf.var". +alias id "Hf" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Hf.var". inline "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con". -inline "cic:/CoRN/ftc/PartFunEquality/n.var". +alias id "n" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/n.var". -inline "cic:/CoRN/ftc/PartFunEquality/H'.var". +alias id "H'" = "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H'.var". inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con". (* UNEXPORTED -End Nth_Power. +End Nth_Power *) (* UNEXPORTED -Section Strong_Nth_Power. +Section Strong_Nth_Power *) (*#* @@ -391,27 +391,27 @@ is included in the domain of [F]. %\end{convention}% *) -inline "cic:/CoRN/ftc/PartFunEquality/a.var". +alias id "a" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/a.var". -inline "cic:/CoRN/ftc/PartFunEquality/b.var". +alias id "b" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/b.var". -inline "cic:/CoRN/ftc/PartFunEquality/Hab.var". +alias id "Hab" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/Hab.var". (* begin hide *) -inline "cic:/CoRN/ftc/PartFunEquality/I.con". +inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/I.con" "Strong_Nth_Power__". (* end hide *) -inline "cic:/CoRN/ftc/PartFunEquality/F.var". +alias id "F" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/F.var". -inline "cic:/CoRN/ftc/PartFunEquality/incF.var". +alias id "incF" = "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/incF.var". inline "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con". inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con". (* UNEXPORTED -End Strong_Nth_Power. +End Strong_Nth_Power *)