Proposition cha_glb_conj {H : complete_heyting_algebra} {I : UU} (f : I → H) (x : H) : (/\_{ i : I } f i ∧ x) ≤ /\_{ i : I } (f i ∧ x). Proof. use cha_le_glb. intro i. use cha_and_monotone_l. use cha_glb_le. - exact i. - 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.