proposition: Theorem round_pred_ge_0 : forall P : R -> R -> Prop, round_pred_monotone P -> P 0 0 -> forall x f, P x f -> 0 <= x -> 0 <= f.
proof: Proof. intros P HP HP0 x f Hxf Hx. now apply (HP 0 x). Qed.
imports: Coq(Reals) Raux Defs