proposition: Theorem round_pred_lt_0 : forall P : R -> R -> Prop, round_pred_monotone P -> P 0 0 -> forall x f, P x f -> f < 0 -> x < 0.
proof: Proof. intros P HP HP0 x f Hxf Hf. apply Rnot_le_lt. intros Hx. apply Rlt_not_le with (1 := Hf). now apply (HP 0 x). Qed.
imports: Coq(Reals) Raux Defs