Lemma rel_same_SW2NE_join_gullibility {X : hSet} (b : interlaced_prebilattice X) (x y : X) : rel_same_SW2NE b (join b x y) (gullibility b x y) . Proof. exact (rel_same_SE2NW_meet_gullibility (make_interlaced_prebilattice (t_opp_prebilattice_is_interlaced b)) x y). Defined.
Require Import UniMath.OrderTheory.Prebilattice.Prebilattice. Require Import UniMath.OrderTheory.Prebilattice.Interlaced. Require Import UniMath.OrderTheory.Prebilattice.PrebilatticeDisplayedCat. Require Import UniMath.MoreFoundations.Equivalences. Require Import UniMath.Foundations.Sets. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.OrderTheory.Lattice.Bounded. Require Import UniMath.CategoryTheory.Core.Prelude.