proposition: Lemma mult_mod_associative : forall x y z, x * (y * z) = x * y * z.
proof: Proof. intros x y z. unfold mod_op, mult_op, mult_mod. rewrite N.mul_mod_idemp_r;auto with chains. rewrite N.mul_mod_idemp_l;auto with chains. now rewrite N.mul_assoc. Qed.
imports: Monoid_def RelationClasses Morphisms ZArith PArith Arith NArith Ring63