Proposition is_ideal_principal_ideal (b : B) : is_ideal (λ a, a ≺ b). Proof. repeat split. - exact (nullary_interpolation_abstract_basis b). - intros a₁ a₂ p q. exact (binary_interpolation_abstract_basis p q). - intros a₁ a₂ p q. exact (trans_abstract_basis q p). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottContinuous. Require Import UniMath.OrderTheory.DCPOs.Core.WayBelow. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous. Require Import UniMath.OrderTheory.DCPOs.Basis.Algebraic. Require Import UniMath.OrderTheory.DCPOs.Basis.Basis. Require Import UniMath.OrderTheory.DCPOs.Basis.CompactBasis. Require Import UniMath.OrderTheory.DCPOs.Elements.Maximal. Require Import UniMath.OrderTheory.DCPOs.Examples.Products. Require Import UniMath.OrderTheory.DCPOs.Examples.SubDCPO. Require Import UniMath.OrderTheory.DCPOs.Examples.Propositions.