proposition: Lemma Lub_Rbar_eqset (E1 E2 : R -> Prop) : (forall x, E1 x <-> E2 x) -> Lub_Rbar E1 = Lub_Rbar E2.
proof: Proof. move => H ; rewrite {2}/Lub_Rbar ; case: ex_lub_Rbar => l /= Hl. apply is_lub_Rbar_unique. move: Hl ; by apply is_lub_Rbar_eqset. Qed.
imports: Coq(Reals ssreflect) Rbar Rcomplements Markov