include "logic/connectives.ma".
-ninductive eq (A: Type) (a: A) : A → Prop ≝
+ninductive eq (A: Type) (a: A) : A → CProp ≝
refl: eq A a a.
+
+nlet rec eq_rect (A: Type) (x: A) (P: ∀y:A. eq A x y → CProp) (q: P x (refl A x))
+ (y: A) (p: eq A x y) on p : P y p ≝
+ match p with
+ [ refl ⇒ q ].
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)).
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+interpretation "leibnitz's non-equality" 'neq t x y = (Not (eq t x y)).