fact: Definition direct_product_as_CMonoid := (Build_CMonoid (direct_product_as_CSemiGroup M1 M2) (pairT (@cm_unit M1)(@cm_unit M2)) direct_product_is_CMonoid).
imports: Coq.Arith.Euclid CoRN.model.Zmod.Cmod CoRN.algebra.CSemiGroups CoRN.tactics.csetoid_rewrite CoRN.model.structures.Nsec CoRN.util.SetoidPermutation Coq.Setoids.Setoid Coq.Classes.Morphisms