proposition: Lemma add_DN_correct : forall p x y, valid_lb x = true -> valid_lb y = true -> (valid_lb (add_DN p x y) = true /\ le_lower (toX (add_DN p x y)) (Xadd (toX x) (toX y))).
proof: Proof. intros p x y _ _; split; [easy|]. now apply (rnd_binop_DN_correct _ _ (@Fadd_correct _)). Qed.
imports: Coq(ZArith Reals Psatz) Flocq(Zaux Raux) Xreal Basic Generic Generic_proof Sig