The Coq Proof Assistant

# Library Coq.Bool.Zerob

Require Import Arith.
Require Import Bool.
Local Open Scope nat_scope.
Definition zerob (n:nat) : bool :=
match n with
| O => true
| S _ => false
end.
Lemma zerob_true_intro : forall n:nat, n = 0 -> zerob n = true.
Hint Resolve zerob_true_intro: bool.
Lemma zerob_true_elim : forall n:nat, zerob n = true -> n = 0.
Lemma zerob_false_intro : forall n:nat, n <> 0 -> zerob n = false.
Hint Resolve zerob_false_intro: bool.
Lemma zerob_false_elim : forall n:nat, zerob n = false -> n <> 0.