Section TBDistrLatticeTheory.
Context {disp : unit} {L : tbDistrLatticeType disp}.
Implicit Types (I : finType) (T : eqType) (x y : L).
Local Notation "1" := top.
Canonical join_addoid := Monoid.AddLaw (@meetUl _ L) (@meetUr _ _).
Canonical meet_addoid := Monoid.AddLaw (@joinIl _ L) (@joinIr _ _).

Lemma eq_sub x y z : (x `\` y == z) = (z <= x <= y `|` z) && (z `&` y == 0).