proposition: Lemma sub_UP_correct : forall p x y, valid_ub x = true -> valid_lb y = true -> (valid_ub (sub_UP p x y) = true /\ le_upper (Xsub (toX x) (toX y)) (toX (sub_UP p x y))).
proof: Proof. intros p x y _ _; split; [easy|]. now apply (rnd_binop_UP_correct _ _ (@Fsub_correct _)). Qed.
imports: Coq(ZArith Reals Psatz) Flocq(Zaux Raux) Xreal Basic Generic Generic_proof Sig