Proposition trans_abstract_basis {B : abstract_basis} {b₁ b₂ b₃ : B} (p : b₁ ≺ b₂) (q : b₂ ≺ b₃) : b₁ ≺ b₃. Proof. exact (pr12 B b₁ b₂ b₃ p q). 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.