set "baseuri" "cic:/matita/logic/equality/".
include "higher_order_defs/relations.ma".
+include "logic/connectives.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)).
theorem reflexive_eq : \forall A:Type. reflexive A (eq A).
simplify.intros.apply refl_eq.