proposition: Proposition map_from_basis_monotone (x₁ x₂ : X) (p : x₁ ⊑ x₂) : map_from_basis x₁ ⊑ map_from_basis x₂.
proof: Proof. unfold map_from_basis. use dcpo_lub_is_least ; cbn. intro i. use less_than_dcpo_lub. - refine (pr1 i ,, _). exact (trans_way_below_le (pr2 i) p). - cbn. apply refl_dcpo. 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