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 (n : nat) : n = 0 -> zerob n = true.
#[global]
Hint Resolve zerob_true_intro: bool.
Lemma zerob_true_elim (n : nat) : zerob n = true -> n = 0.
Lemma zerob_false_intro (n : nat) : n <> 0 -> zerob n = false.
#[global]
Hint Resolve zerob_false_intro: bool.
Lemma zerob_false_elim (n : nat) : zerob n = false -> n <> 0.