# Library Coq.Arith.Peano_dec

Require Import Decidable.
Require Eqdep_dec.
Require Import Le Lt.
Local Open 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).
Definition UIP_nat:= Eqdep_dec.UIP_dec eq_nat_dec.
Lemma le_unique: forall m n (h1 h2: m <= n), h1 = h2.