X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Flogic%2Fequality.ma;h=715423143e7185debaf41b69046ba5e1ccde202b;hb=7fd4f2f66fb8fe010bbd2bfe1f6b542c2da6c83f;hp=d940b97c0eec3fcc80694496fdc9a1c9022ed2b8;hpb=9a7ec6adbfd12e5305800a033d1b471afe316abd;p=helm.git

diff --git a/helm/software/matita/nlibrary/logic/equality.ma b/helm/software/matita/nlibrary/logic/equality.ma
index d940b97c0..715423143 100644
--- a/helm/software/matita/nlibrary/logic/equality.ma
+++ b/helm/software/matita/nlibrary/logic/equality.ma
@@ -13,10 +13,29 @@
 (**************************************************************************)
 
 include "logic/connectives.ma".
+include "properties/relations.ma".
 
-ninductive eq (A: Type) (a: A) : A → Prop ≝
+ninductive eq (A: Type[0]) (a: A) : A → CProp[0] ≝
  refl: eq A a a.
- 
+
+nlemma eq_rect_CProp0_r':
+ ∀A.∀a,x.∀p:eq ? x a.∀P: ∀x:A. eq ? x a → CProp[0]. P a (refl A a) → P x p.
+ #A; #a; #x; #p; ncases p; #P; #H; nassumption.
+nqed.
+
+nlemma eq_rect_CProp0_r:
+ ∀A.∀a.∀P: ∀x:A. eq ? x a → CProp[0]. P a (refl A a) → ∀x.∀p:eq ? x a.P x p.
+ #A; #a; #P; #p; #x0; #p0; napply (eq_rect_CProp0_r' ??? p0); nassumption.
+nqed.
+
 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)).
\ No newline at end of file
+interpretation "leibnitz's non-equality" 'neq t x y = (Not (eq t x y)).
+
+ndefinition EQ: ∀A:Type[0]. equivalence_relation A.
+ #A; napply mk_equivalence_relation
+  [ napply eq
+  | napply refl
+  | #x; #y; #H; nrewrite < H; napply refl
+  | #x; #y; #z; #Hyx; #Hxz; nrewrite < Hxz; nassumption]
+nqed.