(**************************************************)
(* 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 joinC (x y : lift A) : join x y = join y x.