A very nice experiment using notation: we define the notation for natural

[helm.git] / helm / software / matita / library / logic / equality.ma

diff --git a/helm/software/matita/library/logic/equality.ma b/helm/software/matita/library/logic/equality.ma
index 510f0c5c6fe3144b395840770c1f8dbe15084163..cc181dfbf4f21c1ad15679de180126bb1a67ca73 100644 (file)
--- a/helm/software/matita/library/logic/equality.ma
+++ b/helm/software/matita/library/logic/equality.ma
@@ -12,8 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/logic/equality/".
-
 include "higher_order_defs/relations.ma".
 
 inductive eq (A:Type) (x:A) : A \to Prop \def
@@ -60,6 +58,18 @@ theorem eq_elim_r:
 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.
@@ -71,8 +81,8 @@ 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"
@@ -81,6 +91,10 @@ default "equality"
  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.