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 meets_total I (d : L) (P : {pred I}) (F : I -> L) :
(forall i : I, P i -> d `|` F i = 1) -> d `|` \meet_(i | P i) F i = 1.