proposition: Theorem square_lt_simpl_nonpos : forall n m, m <= 0 -> n * n < m * m -> m < n.
proof: Proof. intros n m H1 H2. destruct (le_gt_cases n 0); [|order]. destruct (lt_ge_cases m n) as [LE|GT]; trivial. apply square_le_mono_nonpos in GT; order. Qed.
imports: ZAddOrder