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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 *)
(************************************************************************)
(* Ancien bug signale par Laurent Thery sur la condition de garde *)
Require Import Bool.
Require Import ZArith.
Definition rNat := positive.
Inductive rBoolOp: Set :=
rAnd: rBoolOp
| rEq: rBoolOp .
Definition rlt: rNat -> rNat ->Prop := [a, b:rNat](compare a b EGAL)=INFERIEUR.
Definition rltDec: (m, n:rNat){(rlt m n)}+{(rlt n m) \/ m=n}.
Intros n m; Generalize (compare_convert_INFERIEUR n m);
Generalize (compare_convert_SUPERIEUR n m);
Generalize (compare_convert_EGAL n m); Case (compare n m EGAL).
Intros H' H'0 H'1; Right; Right; Auto.
Intros H' H'0 H'1; Left; Unfold rlt.
Apply convert_compare_INFERIEUR; Auto.
Intros H' H'0 H'1; Right; Left; Unfold rlt.
Apply convert_compare_INFERIEUR; Auto.
Apply H'0; Auto.
Defined.
Definition rmax: rNat -> rNat ->rNat.
Intros n m; Case (rltDec n m); Intros Rlt0.
Exact m.
Exact n.
Defined.
Inductive rExpr: Set :=
rV: rNat ->rExpr
| rN: rExpr ->rExpr
| rNode: rBoolOp -> rExpr -> rExpr ->rExpr .
Fixpoint maxVar[e:rExpr]: rNat :=
Cases e of
(rV n) => n
| (rN p) => (maxVar p)
| (rNode n p q) => (rmax (maxVar p) (maxVar q))
end.
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