proposition: Theorem Zquot_sgn: forall a b, 0 <= Z.sgn (a÷b) * Z.sgn a * Z.sgn b.
proof: Proof. destruct a as [ |a|a]; destruct b as [ |b|b]; simpl; auto with zarith; unfold Z.quot; simpl; destruct N.pos_div_eucl; simpl; destruct n; simpl; auto with zarith. Qed.
imports: Nnat ZArith_base Lia ZArithRing Zdiv Morphisms