#[global]
Instance lt_strorder : StrictOrder lt.#[global]
Instance lt_compat : Proper (Logic.eq==>Logic.eq==>iff) lt.

(* Specifications: *)
Lemma lt_total p q : p < q \/ p = q \/ q < p.
Lemma le_refl p : p <= p.
Lemma le_lt_trans n m p : n <= m -> m < p -> n < p.
Lemma lt_le_trans n m p : n < m -> m <= p -> n < p.
Lemma le_trans n m p : n <= m -> m <= p -> n <= p.
Lemma le_succ_l n m : succ n <= m <-> n < m.
Lemma le_antisym p q : p <= q -> q <= p -> p = q.