Definition eqm a b := (a mod N = b mod N).Infix "==" := eqm (at level 70).

(* Specifications: *)
Lemma eqm_refl : forall a, a == a.
Lemma eqm_sym : forall a b, a == b -> b == a.
Lemma eqm_trans : forall a b c, a == b -> b == c -> a == c.