Lemma dual_lattice_is_distributive (l : distributive_lattice) : is_distributive (dual_lattice l) . Proof. assert (isldistr (Lmin l) (Lmax l) ) as d. { intros ? b c . rewrite ((distributive_lattice_is_distributive l) (Lmax _ _ _) c b). rewrite (iscomm_Lmin _ (Lmax _ _ _) _). rewrite (Lmin_absorb) . rewrite distrlattice_Lmax_rdistr. rewrite <- (isassoc_Lmax _ c). rewrite (Lmax_absorb). reflexivity. } intros ? ? ?. use d . Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.Algebra.Monoids. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.OrderTheory.Lattice.Bounded. Require Import UniMath.OrderTheory.Lattice.Complement.