Proposition cha_not_not_disj_not {H : complete_heyting_algebra} (x y : H) : ¬ ¬ (¬x ∨ ¬y) = ¬(x ∧ y). Proof. use cha_le_antisymm. - rewrite <- (cha_not_not_not (x ∧ y)). use cha_not_not_monotone. apply cha_disj_not. - rewrite <- cha_conj_not. rewrite <- (cha_not_not_not (x ∧ y)). rewrite <- cha_not_not_conj. apply cha_le_refl. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.OrderTheory.Lattice.Bounded. Require Import UniMath.OrderTheory.Lattice.Heyting. Require Import UniMath.OrderTheory.Lattice.CompleteHeyting.