proposition: Lemma Rbar_is_glb_subset (E1 E2 : Rbar -> Prop) (l1 l2 : Rbar) : (forall x, E2 x -> E1 x) -> (Rbar_is_glb E1 l1) -> (Rbar_is_glb E2 l2) -> Rbar_le l1 l2.
proof: Proof. intros Hs (H1, _) (_, H2). apply H2 ; intros x Hx ; apply H1, Hs, Hx. Qed.
imports: Coq(Reals ssreflect) Rbar Rcomplements Markov