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Diffstat (limited to 'theories7/Arith/Peano_dec.v')
-rwxr-xr-x | theories7/Arith/Peano_dec.v | 36 |
1 files changed, 0 insertions, 36 deletions
diff --git a/theories7/Arith/Peano_dec.v b/theories7/Arith/Peano_dec.v deleted file mode 100755 index 6646545a..00000000 --- a/theories7/Arith/Peano_dec.v +++ /dev/null @@ -1,36 +0,0 @@ -(************************************************************************) -(* 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: Peano_dec.v,v 1.1.2.1 2004/07/16 19:31:25 herbelin Exp $ i*) - -Require Decidable. - -V7only [Import nat_scope.]. -Open Local Scope nat_scope. - -Implicit Variables Type m,n,x,y:nat. - -Theorem O_or_S : (n:nat)({m:nat|(S m)=n})+{O=n}. -Proof. -NewInduction n. -Auto. -Left; Exists n; Auto. -Defined. - -Theorem eq_nat_dec : (n,m:nat){n=m}+{~(n=m)}. -Proof. -NewInduction n; NewInduction m; Auto. -Elim (IHn m); Auto. -Defined. - -Hints Resolve O_or_S eq_nat_dec : arith. - -Theorem dec_eq_nat:(x,y:nat)(decidable (x=y)). -Intros x y; Unfold decidable; Elim (eq_nat_dec x y); Auto with arith. -Defined. - |