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.