Instance list_PCM (P : Ghost) : Ghost := { valid a := True; Join_G := list_join }.

Lemma list_join_filler : forall {P : Ghost} l1 l2 l3 n, list_join l1 l2 l3 ->
(n <= length l3 - length l1)%nat -> list_join (l1 ++ repeat None n) l2 l3.