(**************************************************)
(* 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 validL x y : valid (join x y) -> valid x.