(** [sqrt_up] and addition *)

(* Specifications: *)
Lemma sqrt_up_add_le : forall a b, √°(a+b) <= √°a + √°b.
(** Convexity-like inequality for [sqrt_up]: [sqrt_up] of middle is above middle of square roots. We cannot say more, for instance take a=b=2, then 2+2 <= S 3 *)
Lemma add_sqrt_up_le : forall a b, 0<=a -> 0<=b -> √°a + √°b <= S √°(2*(a+b)).
End NZSqrtUpProp.