Fact joinKI y x : meet x (join x y) = x.
Definition Mixin := LatticeMixin meetC joinC meetA joinA joinKI meetKU leEmeet meetUl.
End TotalLattice.
End TotalLattice.
Module TotalTheory.
Section TotalTheory.
Context {display : unit}.
Local Notation orderType := (orderType display).
Context {T : orderType}.
Implicit Types (x y : T).

Lemma joins_setU (I : finType) (A B : {set I}) (F : I -> L) :
\join_(i in (A :|: B)) F i = \join_(i in A) F i `|` \join_(i in B) F i.