- setters for data structures now support "commuting conversion"-like

[helm.git] / helm / software / matita / contribs / CoRN-Decl / ftc / PartFunEquality.ma

diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma
index 0ca5ba98a84281b6556bb80279dee6a375c6ce11..9771d16f2b7abeba20d66dc2222281f40a8fd29e 100644 (file)
--- a/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma
+++ b/helm/software/matita/contribs/CoRN-Decl/ftc/PartFunEquality.ma
@@ -16,20 +16,18 @@
 
 set "baseuri" "cic:/matita/CoRN-Decl/ftc/PartFunEquality".
 
+include "CoRN.ma".
+
 (* $Id: PartFunEquality.v,v 1.8 2004/04/23 10:00:59 lcf Exp $ *)
 
 (*#* printing Feq %\ensuremath{\approx}% #≈# *)
 
-(* INCLUDE
-Intervals
-*)
+include "reals/Intervals.ma".
 
-(* INCLUDE
-DiffTactics1
-*)
+include "tactics/DiffTactics1.ma".
 
 (* UNEXPORTED
-Section Definitions.
+Section Definitions
 *)
 
 (*#* *Equality of Partial Functions
@@ -42,7 +40,7 @@ given predicate rather than to the predicate itself.  The following
 definition makes this possible.
 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/subset.con.
+inline "cic:/CoRN/ftc/PartFunEquality/subset.con".
 
 (*#*
 The core of our work will revolve around the following fundamental
@@ -54,7 +52,7 @@ it is easier to consider a generic case%.}%.  This file is concerned
 with proving the main properties of this equality relation.
 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq.con".
 
 (*#*
 Notice that, because the quantification over the proofs is universal,
@@ -73,11 +71,11 @@ than in an existentially quantified one.
 *)
 
 (* UNEXPORTED
-End Definitions.
+End Definitions
 *)
 
 (* UNEXPORTED
-Section Equality_Results.
+Section Equality_Results
 *)
 
 (*#* **Properties of Inclusion
@@ -89,35 +87,35 @@ 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
 this definition:
 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/eq_imp_Feq.con.
+inline "cic:/CoRN/ftc/PartFunEquality/eq_imp_Feq.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_imp_eq.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/included_IR.con.
+inline "cic:/CoRN/ftc/PartFunEquality/included_IR.con".
 
 (* UNEXPORTED
-End Equality_Results.
+End Equality_Results
 *)
 
 (* UNEXPORTED
@@ -125,25 +123,25 @@ Hint Resolve included_IR : included.
 *)
 
 (* UNEXPORTED
-Section Some_More.
+Section Some_More
 *)
 
 (*#*
 If two function coincide on a given subset then they coincide in any smaller subset.
 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/included_Feq.con.
+inline "cic:/CoRN/ftc/PartFunEquality/included_Feq.con".
 
 (* UNEXPORTED
-End Some_More.
+End Some_More
 *)
 
 (* UNEXPORTED
-Section Away_from_Zero.
+Section Away_from_Zero
 *)
 
 (* UNEXPORTED
-Section Definitions.
+Section Definitions
 *)
 
 (*#* **Away from Zero
@@ -158,17 +156,17 @@ 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 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/bnd_away_zero.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero.con".
 
 (*#*
 If [F] is bounded away from zero in [I] then [F] is necessarily apart from zero in [I]; also this means that [I] is included in the domain of [{1/}F].
@@ -176,18 +174,18 @@ 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 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/bnd_imp_ap_zero.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_ap_zero.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_recip.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con".
 
 (* UNEXPORTED
-End Definitions.
+End Definitions
 *)
 
 (*#*
@@ -197,34 +195,34 @@ 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.
+inline "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/FRestr_bnd.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd.con".
 
 (*#*
 A function is said to be bounded away from zero everywhere if it is bounded away from zero in every compact subinterval of its domain; a similar definition is made for arbitrary sets, which will be necessary for future work.
 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_everywhere.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_everywhere.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_in_P.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_away_zero_in_P.con".
 
 (*#*
 An immediate consequence:
 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con.
+inline "cic:/CoRN/ftc/PartFunEquality/bnd_in_P_imp_ap_zero.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con".
 
 (* UNEXPORTED
-End Away_from_Zero.
+End Away_from_Zero
 *)
 
 (* UNEXPORTED
@@ -251,7 +249,7 @@ Ltac FEQ := apply eq_imp_Feq;
 (* end hide *)
 
 (* UNEXPORTED
-Section More_on_Equality.
+Section More_on_Equality
 *)
 
 (*#* **Properties of Equality
@@ -263,61 +261,61 @@ 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.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_symmetric.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con".
 
 (* UNEXPORTED
-End Feq_Equivalence.
+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.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_inv.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_inv.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_minus.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_minus.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_mult.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_mult.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_nth.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_nth.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_recip.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_recip.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_recip'.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_recip'.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_div.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_div.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/Feq_div'.con.
+inline "cic:/CoRN/ftc/PartFunEquality/Feq_div'.con".
 
 (*#*
 Notice that in the case of division we only need to require boundedness away from zero for one of the functions (as they are equal); thus the two last lemmas are stated in two different ways, as according to the context one or the other condition may be easier to prove.
@@ -325,24 +323,24 @@ Notice that in the case of division we only need to require boundedness away fro
 The restriction of a function is well defined.
 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/FRestr_wd.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FRestr_wd.con".
 
 (*#*
 The image of a set is extensional.
 *)
 
-inline cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con.
+inline "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con".
 
 (* UNEXPORTED
-End Operations.
+End Operations
 *)
 
 (* UNEXPORTED
-End More_on_Equality.
+End More_on_Equality
 *)
 
 (* UNEXPORTED
-Section Nth_Power.
+Section Nth_Power
 *)
 
 (*#* **Nth Power
@@ -357,34 +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/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.
+inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con".
 
 (* UNEXPORTED
-End Nth_Power.
+End Nth_Power
 *)
 
 (* UNEXPORTED
-Section Strong_Nth_Power.
+Section Strong_Nth_Power
 *)
 
 (*#*
@@ -393,27 +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_zero'.con".
 
-inline cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con.
+inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con".
 
 (* UNEXPORTED
-End Strong_Nth_Power.
+End Strong_Nth_Power
 *)