Require
Arith.
Require
Bool.
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].
Save
.
Hints
Resolve zerob_true_intro : bool.
Lemma
zerob_true_elim : (n:nat)(zerob n)=true->(n=O).
NewDestruct n; [Trivial with bool | Inversion 1].
Save
.
Lemma
zerob_false_intro : (n:nat)~(n=O)->(zerob n)=false.
NewDestruct n; [NewDestruct 1; Auto with bool | Trivial with bool].
Save
.
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].
Save
.