Lemma interlaced_leqk_leqt_leqtconsensus {X:hSet}: ∏ (b : interlaced_prebilattice X) (x y : X) , (∑ r : X, kle b x r × tle b r y) -> tle b x (consensus b y x). Proof. intro b'. use (interlaced_leqt_leqk_leqkmeet (make_interlaced_prebilattice (dual_prebilattice_is_interlaced b'))). Defined.
Require Import UniMath.OrderTheory.Prebilattice.Prebilattice. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Subtypes. Require Import UniMath.Algebra.BinaryOperations.