Library Coq.Arith.Peano_dec
Require Import Decidable.
Open Local Scope nat_scope.
Implicit Types m n x y : nat.
Theorem O_or_S : forall n, {m : nat | S m = n} + {0 = n}.
Theorem eq_nat_dec : forall n m, {n = m} + {n <> m}.
Hint Resolve O_or_S eq_nat_dec: arith.
Theorem dec_eq_nat : forall n m, decidable (n = m).