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Diffstat (limited to 'theories7/Arith/Bool_nat.v')
| -rw-r--r-- | theories7/Arith/Bool_nat.v | 43 |
1 files changed, 0 insertions, 43 deletions
diff --git a/theories7/Arith/Bool_nat.v b/theories7/Arith/Bool_nat.v deleted file mode 100644 index c36f8f15..00000000 --- a/theories7/Arith/Bool_nat.v +++ /dev/null @@ -1,43 +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 *) -(************************************************************************) - -(* $Id: Bool_nat.v,v 1.1.2.1 2004/07/16 19:31:23 herbelin Exp $ *) - -Require Export Compare_dec. -Require Export Peano_dec. -Require Sumbool. - -V7only [Import nat_scope.]. -Open Local Scope nat_scope. - -Implicit Variables Type m,n,x,y:nat. - -(** The decidability of equality and order relations over - type [nat] give some boolean functions with the adequate specification. *) - -Definition notzerop := [n:nat] (sumbool_not ? ? (zerop n)). -Definition lt_ge_dec : (x,y:nat){(lt x y)}+{(ge x y)} := - [n,m:nat] (sumbool_not ? ? (le_lt_dec m n)). - -Definition nat_lt_ge_bool := - [x,y:nat](bool_of_sumbool (lt_ge_dec x y)). -Definition nat_ge_lt_bool := - [x,y:nat](bool_of_sumbool (sumbool_not ? ? (lt_ge_dec x y))). - -Definition nat_le_gt_bool := - [x,y:nat](bool_of_sumbool (le_gt_dec x y)). -Definition nat_gt_le_bool := - [x,y:nat](bool_of_sumbool (sumbool_not ? ? (le_gt_dec x y))). - -Definition nat_eq_bool := - [x,y:nat](bool_of_sumbool (eq_nat_dec x y)). -Definition nat_noteq_bool := - [x,y:nat](bool_of_sumbool (sumbool_not ? ? (eq_nat_dec x y))). - -Definition zerop_bool := [x:nat](bool_of_sumbool (zerop x)). -Definition notzerop_bool := [x:nat](bool_of_sumbool (notzerop x)). |