Lemma k_opp_prebilattice_is_interlaced {X : hSet} (b : interlaced_prebilattice X) : is_interlaced (k_opp_prebilattice b). Proof. destruct (t_opp_prebilattice_is_interlaced (make_interlaced_prebilattice (dual_prebilattice_is_interlaced b))) as [? [? [? ?]]]. do 3 (try split); assumption. 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.