Coq.Bool.Zerob

# Module Coq.Bool.Zerob

``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`.

`

Index