blob: 78802516199de4cb23ff812ddc172ea7c75371f0 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(*i $Id$ i*)
Require Arith.
Require Bool.
V7only [Import nat_scope.].
Open Local Scope nat_scope.
Definition zerob : nat->bool
:= [n:nat]Cases n of O => true | (S _) => false end.
Lemma zerob_true_intro : (n:nat)(n=O)->(zerob n)=true.
NewDestruct n; [Trivial with bool | Inversion 1].
Qed.
Hints Resolve zerob_true_intro : bool.
Lemma zerob_true_elim : (n:nat)(zerob n)=true->(n=O).
NewDestruct n; [Trivial with bool | Inversion 1].
Qed.
Lemma zerob_false_intro : (n:nat)~(n=O)->(zerob n)=false.
NewDestruct n; [NewDestruct 1; Auto with bool | Trivial with bool].
Qed.
Hints Resolve zerob_false_intro : bool.
Lemma zerob_false_elim : (n:nat)(zerob n)=false -> ~(n=O).
NewDestruct n; [Intro H; Inversion H | Auto with bool].
Qed.
|
