helm/software/matita/nlibrary/logic/equality.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "logic/connectives.ma".
  16
  17 ninductive eq (A: Type) (a: A) : A → CProp ≝
  18  refl: eq A a a.
  19
  20 nlet rec eq_rect (A: Type) (x: A) (P: ∀y:A. eq A x y → CProp) (q: P x (refl A x))
  21  (y: A) (p: eq A x y) on p : P y p ≝
  22  match p with
  23   [ refl ⇒ q ].
  24
  25 interpretation "leibnitz's equality" 'eq t x y = (eq t x y).
  26
  27 interpretation "leibnitz's non-equality" 'neq t x y = (Not (eq t x y)).