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 lexUr z x y : x `&` z = 0 -> (x <= z `|` y) = (x <= y).