(** [sqrt_up] is a monotone function (but not a strict one) *)

(** [sqrt_up] and multiplication. *)
(** Due to rounding error, we don't have the usual [√(a*b) = √a*√b] but only lower and upper bounds. *)
Lemma sqrt_up_mul_above : forall a b, 0<=a -> 0<=b -> √°(a*b) <= √°a * √°b.