proposition: Lemma Continuous_I_imp_glb : {x : IR | fun_glb_IR F I x}.
proof: Proof. unfold fun_glb_IR in |- *. apply totally_bounded_has_glb. apply Continuous_I_imp_tb_image. Qed.
imports: CoRN.reals.NRootIR CoRN.ftc.FunctSums CoRN.tactics.CornTac