X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Flibrary%2Flogic%2Fequality.ma;h=2dc6cb435ee610d899c234c5760e3a187b3816cf;hb=41af0583fbc8183183d389303951dca94f2965b0;hp=b87dc6c95656dcf5de3c3ceb00e9ed105067c6b8;hpb=7f2444c2670cadafddd8785b687ef312158376b0;p=helm.git

diff --git a/matita/library/logic/equality.ma b/matita/library/logic/equality.ma
index b87dc6c95..2dc6cb435 100644
--- a/matita/library/logic/equality.ma
+++ b/matita/library/logic/equality.ma
@@ -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:
@@ -60,18 +60,30 @@ theorem eq_elim_r:
 intros. elim (sym_eq ? ? ? H1).assumption.
 qed.
 
-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/eq_ind.con
- cic:/matita/logic/equality/eq_elim_r.con. 
- 
 theorem eq_f: \forall  A,B:Type.\forall f:A\to B.
 \forall x,y:A. x=y \to f x = f y.
-intros.elim H.reflexivity.
+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/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_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.
 x1=x2 \to y1=y2 \to f x1 y1 = f x2 y2.