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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(*i $Id: JMeq.v,v 1.1.2.1 2004/07/16 19:31:29 herbelin Exp $ i*)
+
+(** 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).
+Reset JMeq_ind.
+
+Hints Resolve JMeq_refl.
+
+Lemma sym_JMeq : (A,B:Set)(x:A)(y:B)(JMeq x y)->(JMeq y x).
+NewDestruct 1; Trivial.
+Qed.
+
+Hints Immediate sym_JMeq.
+
+Lemma trans_JMeq : (A,B,C:Set)(x:A)(y:B)(z:C)
+	(JMeq x y)->(JMeq y z)->(JMeq x z).
+NewDestruct 1; Trivial.
+Qed.
+
+Axiom JMeq_eq : (A:Set)(x,y:A)(JMeq x y)->(x=y).
+
+Lemma JMeq_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.
+Qed.
+
+Lemma JMeq_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.
+Qed.
+
+Lemma JMeq_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:=(sym_JMeq H'); Trivial.
+Qed.
+
+Lemma JMeq_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:=(sym_JMeq H'); Trivial.
+Qed.
+
+(** [JMeq] is equivalent to [(eq_dep Set [X]X)] *)
+
+Require Eqdep.
+
+Lemma JMeq_eq_dep : (A,B:Set)(x:A)(y:B)(JMeq x y)->(eq_dep Set [X]X A x B y).
+Proof.
+NewDestruct 1.
+Apply eq_dep_intro.
+Qed.
+
+Lemma eq_dep_JMeq : (A,B:Set)(x:A)(y:B)(eq_dep Set [X]X A x B y)->(JMeq x y).
+Proof.
+NewDestruct 1.
+Apply JMeq_refl. 
+Qed.