(**************************************************)
(* Lifting turns an unlifted structure into a PCM *)
(**************************************************)

Inductive lift A := down | up of A.(**************************************************)
(* Lifting turns an unlifted structure into a PCM *)
(**************************************************)

Inductive lift A := down | up of A.(**************************************************)
(* Lifting turns an unlifted structure into a PCM *)
(**************************************************)

Inductive lift A := down | up of A.

Lemma joinA (x y z : lift A) : join x (join y z) = join (join x y) z.