Lemma interlaced_leqt_leqk_leqtconsensus {X : hSet} : ∏ (b : interlaced_prebilattice X) (x y : X) , (∑ r : X, tle b x r × kle b r y) -> tle b x (consensus b y x). Proof. intros b' ? ? [? [p1 p2]]. set (pp := interlaced_leqt_leqk_leqkmeet _ _ _ (_,,p1,,p2)). rewrite (iscomm_meet) in pp. use (interlaced_leqk_leqt_leqtconsensus _ _ _ (_,, pp,, Lmin_le_r (tlattice 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.