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(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(*i $Id$ i*)
(*s John Major's Equality as proposed by C. Mc Bride *)
Set Implicit Arguments.
Inductive JMeq [A:Set;x:A] : (B:Set)B->Prop :=
JMeq_refl : (JMeq x x).
Hints Resolve JMeq_refl.
Lemma JMeq_sym : (A,B:Set)(x:A)(y:B)(JMeq x y)->(JMeq y x).
NewDestruct 1; Trivial.
Save.
Hints Immediate JMeq_sym.
Lemma JMeq_trans : (A,B,C:Set)(x:A)(y:B)(z:C)
(JMeq x y)->(JMeq y z)->(JMeq x z).
NewDestruct 1; Trivial.
Save.
Axiom JMeq_eq : (A:Set)(x,y:A)(JMeq x y)->(x=y).
Lemma JMeq_eq_ind : (A:Set)(x,y:A)(P:A->Prop)(P x)->(JMeq x y)->(P y).
Intros A x y P H H'; Case JMeq_eq with 1:=H'; Trivial.
Save.
Lemma JMeq_eq_rec : (A:Set)(x,y:A)(P:A->Set)(P x)->(JMeq x y)->(P y).
Intros A x y P H H'; Case JMeq_eq with 1:=H'; Trivial.
Save.
Lemma JMeq_eq_ind_r : (A:Set)(x,y:A)(P:A->Prop)(P y)->(JMeq x y)->(P x).
Intros A x y P H H'; Case JMeq_eq with 1:=(JMeq_sym H'); Trivial.
Save.
Lemma JMeq_eq_rec_r : (A:Set)(x,y:A)(P:A->Set)(P y)->(JMeq x y)->(P x).
Intros A x y P H H'; Case JMeq_eq with 1:=(JMeq_sym H'); Trivial.
Save.
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