proposition: Lemma int_to_nat_nonneg_plus x y : 0 ≤ x → 0 ≤ y → int_to_nat Z N (x + y) = int_to_nat Z N x + int_to_nat Z N y.
proof: Proof. intros. apply (injective f). rewrite preserves_plus, !int_to_nat_of_nonneg; intuition. now apply nonneg_plus_compat. 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