Section TBLatticeTheory.
Context {disp : unit} {L : tbLatticeType disp}.
Implicit Types (I : finType) (T : eqType) (x y : L).
Local Notation "1" := top.
Hint Resolve le0x lex1 : core.

Lemma joins_disjoint I (d : L) (P : {pred I}) (F : I -> L) :
(forall i : I, P i -> d `&` F i = 0) -> d `&` \join_(i | P i) F i = 0.