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 leU2r_le y t x z : x `&` t = 0 -> y `|` x <= t `|` z -> x <= z.