X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Flogic%2Fequality.ma;h=12c79763132bd4049492b493cde00e09b106fbbe;hb=0fadcf36d82e4ed816a50db09dfd1559a8507e6c;hp=0561fb993cb90045a502a12dcf28a14680f46fdb;hpb=7b4d519aefac94afb371a7e4da94779b40bf8608;p=helm.git

diff --git a/helm/software/matita/library/logic/equality.ma b/helm/software/matita/library/logic/equality.ma
index 0561fb993..12c797631 100644
--- a/helm/software/matita/library/logic/equality.ma
+++ b/helm/software/matita/library/logic/equality.ma
@@ -1,5 +1,5 @@
 (**************************************************************************)
-(*       ___	                                                            *)
+(*       ___	                                                          *)
 (*      ||M||                                                             *)
 (*      ||A||       A project by Andrea Asperti                           *)
 (*      ||T||                                                             *)
@@ -36,22 +36,22 @@ theorem eq_ind':
     [refl_eq \Rightarrow H]).
 qed.
  
-theorem reflexive_eq : \forall A:Type. reflexive A (eq A).
-simplify.intros.apply refl_eq.
-qed.
+variant reflexive_eq : \forall A:Type. reflexive A (eq A)
+\def refl_eq.
+(* simplify.intros.apply refl_eq. *)
     
 theorem symmetric_eq: \forall A:Type. symmetric A (eq A).
 unfold symmetric.intros.elim H. apply refl_eq.
 qed.
 
-theorem sym_eq : \forall A:Type.\forall x,y:A. x=y  \to y=x
+variant sym_eq : \forall A:Type.\forall x,y:A. x=y  \to y=x
 \def symmetric_eq.
 
 theorem transitive_eq : \forall A:Type. transitive A (eq A).
 unfold transitive.intros.elim H1.assumption.
 qed.
 
-theorem trans_eq : \forall A:Type.\forall x,y,z:A. x=y  \to y=z \to x=z
+variant trans_eq : \forall A:Type.\forall x,y,z:A. x=y  \to y=z \to x=z
 \def transitive_eq.
 
 theorem eq_elim_r:
@@ -65,17 +65,24 @@ theorem eq_f: \forall  A,B:Type.\forall f:A\to B.
 intros.elim H.apply refl_eq.
 qed.
 
+theorem eq_f': \forall  A,B:Type.\forall f:A\to B.
+\forall x,y:A. x=y \to f y = f x.
+intros.elim H.apply refl_eq.
+qed.
+
+(* 
 coercion cic:/matita/logic/equality/sym_eq.con.
 coercion cic:/matita/logic/equality/eq_f.con.
+*)
 
 default "equality"
  cic:/matita/logic/equality/eq.ind
- cic:/matita/logic/equality/sym_eq.con
- cic:/matita/logic/equality/trans_eq.con
+ cic:/matita/logic/equality/symmetric_eq.con
+ cic:/matita/logic/equality/transitive_eq.con
  cic:/matita/logic/equality/eq_ind.con
  cic:/matita/logic/equality/eq_elim_r.con
  cic:/matita/logic/equality/eq_f.con
- cic:/matita/logic/equality/eq_OF_eq.con. (* \x.sym (eq_f x) *)
+ cic:/matita/logic/equality/eq_f'.con. (* \x.sym (eq_f x) *)
  
 theorem eq_f2: \forall  A,B,C:Type.\forall f:A\to B \to C.
 \forall x1,x2:A. \forall y1,y2:B.