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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: Classical_Prop.v,v 1.1.2.1 2004/07/16 19:31:29 herbelin Exp $ i*)
-
-(** Classical Propositional Logic *)
-
-Require ProofIrrelevance.
-
-Hints Unfold not : core.
-
-Axiom classic: (P:Prop)(P \/ ~(P)).
-
-Lemma NNPP : (p:Prop)~(~(p))->p.
-Proof.
-Unfold not; Intros; Elim (classic p); Auto.
-Intro NP; Elim (H NP).
-Qed.
-
-Lemma not_imply_elim : (P,Q:Prop)~(P->Q)->P.
-Proof.
-Intros; Apply NNPP; Red.
-Intro; Apply H; Intro; Absurd P; Trivial.
-Qed.
-
-Lemma not_imply_elim2 : (P,Q:Prop)~(P->Q) -> ~Q.
-Proof.
-Intros; Elim (classic Q); Auto.
-Qed.
-
-Lemma imply_to_or : (P,Q:Prop)(P->Q) -> ~P \/ Q.
-Proof.
-Intros; Elim (classic P); Auto.
-Qed.
-
-Lemma imply_to_and : (P,Q:Prop)~(P->Q) -> P /\ ~Q.
-Proof.
-Intros; Split.
-Apply not_imply_elim with Q;  Trivial.
-Apply not_imply_elim2 with P; Trivial.
-Qed.
-
-Lemma or_to_imply : (P,Q:Prop)(~P \/ Q) -> P->Q.
-Proof.
-Induction 1; Auto.
-Intros H1 H2; Elim (H1 H2).
-Qed.
-
-Lemma not_and_or : (P,Q:Prop)~(P/\Q)-> ~P \/ ~Q.
-Proof.
-Intros; Elim (classic P); Auto.
-Qed.
-
-Lemma or_not_and : (P,Q:Prop)(~P \/ ~Q) -> ~(P/\Q).
-Proof.
-Induction 1; Red; Induction 2; Auto.
-Qed.
-
-Lemma not_or_and : (P,Q:Prop)~(P\/Q)-> ~P /\ ~Q.
-Proof.
-Intros; Elim (classic P); Auto.
-Qed.
-
-Lemma and_not_or : (P,Q:Prop)(~P /\ ~Q) -> ~(P\/Q).
-Proof.
-Induction 1; Red; Induction 3; Trivial.
-Qed.
-
-Lemma imply_and_or: (P,Q:Prop)(P->Q) -> P \/ Q -> Q.
-Proof.
-Induction 2; Trivial.
-Qed.
-
-Lemma imply_and_or2: (P,Q,R:Prop)(P->Q) -> P \/ R -> Q \/ R.
-Proof.
-Induction 2; Auto.
-Qed.
-
-Lemma proof_irrelevance: (P:Prop)(p1,p2:P)p1==p2.
-Proof (proof_irrelevance_cci classic).