proposition: Lemma int_to_nat_mult_nonneg_r x y : 0 ≤ y → int_to_nat Z N (x * y) = int_to_nat Z N x * int_to_nat Z N y.
proof: Proof. rewrite (commutativity x), (commutativity (int_to_nat Z N x)). now apply int_to_nat_mult_nonneg_l. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.naturals MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.nat_int MathClasses.theory.integers MathClasses.theory.rings MathClasses.orders.rings