Instance eqm_setoid : Equivalence eqm.Instance Zplus_eqm : Proper (eqm ==> eqm ==> eqm) Z.add.Instance Zminus_eqm : Proper (eqm ==> eqm ==> eqm) Z.sub.Instance Zmult_eqm : Proper (eqm ==> eqm ==> eqm) Z.mul.Instance Zopp_eqm : Proper (eqm ==> eqm) Z.opp.

Lemma Z_mod_zero_opp : forall a b:Z, b > 0 -> a mod b = 0 -> (-a) mod b = 0.