Local Notation int := I.t.

(* Specifications: *)
Lemma eqb_eq n p : (n =? p) = true <-> n == p.
Lemma eqb_neq n p : (n =? p) = false <-> ~(n == p).
Lemma ltb_lt n p : (n <? p) = true <-> n < p.
Lemma ltb_nlt n p : (n <? p) = false <-> ~(n < p).
Lemma leb_le n p : (n <=? p) = true <-> n <= p.
Lemma leb_nle n p : (n <=? p) = false <-> ~(n <= p).