proposition: Lemma sqrt_le_compat : forall a b, 0 <= a -> 0 <= b -> a * a <= b * b -> a <= b.
proof: Proof. intros a b Pa Pb E. destruct (Z.eq_dec 0 (a + b)) as [F|F]. lia. cut (0 <= b - a); [ lia | ]. apply Zmult_le_reg_r with (a + b); notzero. ring_simplify. do 2 rewrite rewrite_power_2; lia. Qed.
imports: ZArith Lia Znumtheory