X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Flogic%2Fequality.ma;h=f4f12ec6c103a8290765517c95b151985e04cbab;hb=2dc6ec0db2156431948014a6498c9901f8759e39;hp=1f68503df37cdb4cb6d31003da083a42fb51052b;hpb=38aca08eb6a2385504947c96a1cfcd19f71ec0e4;p=helm.git

diff --git a/helm/software/matita/library/logic/equality.ma b/helm/software/matita/library/logic/equality.ma
index 1f68503df..f4f12ec6c 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||                                                             *)
@@ -12,20 +12,14 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/logic/equality/".
-
 include "higher_order_defs/relations.ma".
 
 inductive eq (A:Type) (x:A) : A \to Prop \def
     refl_eq : eq A x x.
 
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "leibnitz's equality"
-   'eq x y = (cic:/matita/logic/equality/eq.ind#xpointer(1/1) _ x y).
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "leibnitz's non-equality"
-  'neq x y = (cic:/matita/logic/connectives/Not.con
-    (cic:/matita/logic/equality/eq.ind#xpointer(1/1) _ x y)).
+interpretation "leibnitz's equality" 'eq t x y = (eq t x y).
+
+interpretation "leibnitz's non-equality" 'neq t x y = (Not (eq t x y)).
 
 theorem eq_rect':
  \forall A. \forall x:A. \forall P: \forall y:A. x=y \to Type.
@@ -54,12 +48,31 @@ qed.
 variant trans_eq : \forall A:Type.\forall x,y,z:A. x=y  \to y=z \to x=z
 \def transitive_eq.
 
+theorem symmetric_not_eq: \forall A:Type. symmetric A (λx,y.x ≠ y).
+unfold symmetric.simplify.intros.unfold.intro.apply H.apply sym_eq.assumption.
+qed.
+
+variant sym_neq: ∀A:Type.∀x,y.x ≠ y →y ≠ x
+≝ symmetric_not_eq.
+
 theorem eq_elim_r:
  \forall A:Type.\forall x:A. \forall P: A \to Prop.
    P x \to \forall y:A. y=x \to P y.
 intros. elim (sym_eq ? ? ? H1).assumption.
 qed.
 
+theorem eq_elim_r':
+ \forall A:Type.\forall x:A. \forall P: A \to Set.
+   P x \to \forall y:A. y=x \to P y.
+intros. elim (sym_eq ? ? ? H).assumption.
+qed.
+
+theorem eq_elim_r'':
+ \forall A:Type.\forall x:A. \forall P: A \to Type.
+   P x \to \forall y:A. y=x \to P y.
+intros. elim (sym_eq ? ? ? H).assumption.
+qed.
+
 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.apply refl_eq.
@@ -70,19 +83,28 @@ theorem eq_f': \forall  A,B:Type.\forall f:A\to B.
 intros.elim H.apply refl_eq.
 qed.
 
-(* 
-coercion cic:/matita/logic/equality/sym_eq.con.
-coercion cic:/matita/logic/equality/eq_f.con.
-*)
+(*  *)
+coercion sym_eq.
+coercion eq_f.
+(* *)
 
 default "equality"
  cic:/matita/logic/equality/eq.ind
- cic:/matita/logic/equality/symmetric_eq.con
+ cic:/matita/logic/equality/sym_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_rec.con
+ cic:/matita/logic/equality/eq_elim_r'.con
+ cic:/matita/logic/equality/eq_rect.con
+ cic:/matita/logic/equality/eq_elim_r''.con
  cic:/matita/logic/equality/eq_f.con
+(* *)
+ cic:/matita/logic/equality/eq_OF_eq.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.