Definition interlaced_prebilattice_eq {X : hSet} (b1 : interlaced_prebilattice X) (b2 : interlaced_prebilattice X) (m : meet b1 ~ meet b2) (j : join b1 ~ join b2) (c : consensus b1 ~ consensus b2) (g : gullibility b1 ~ gullibility b2): b1 = b2. Proof. use total2_paths_f. - use (prebilattice_eq b1 b2 m j c g). - apply isaprop_is_interlaced. 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.