proposition: Proposition approximating_basis_lub (B : dcpo_basis) (x : X) : ⨆ (directed_set_from_basis B x) = x.
proof: Proof. use antisymm_dcpo. - use dcpo_lub_is_least. intro i. apply way_below_to_le. exact (pr2 i). - use (is_least_upperbound_is_least (is_least_upperbound_basis B x)). apply is_least_upperbound_is_upperbound. exact (is_least_upperbound_dcpo_lub (directed_set_from_basis B x)). Qed.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.ScottContinuous UniMath.OrderTheory.DCPOs.Core.WayBelow UniMath.OrderTheory.DCPOs.Basis.Continuous