Hint Rewrite @liftx_id : norm2.

Lemma liftx3_liftx2:
forall {A1 A2 A3 B} f (x: A1),
@liftx (Tarrow A1 (Tarrow A2 (Tarrow A3 (LiftEnviron B)))) f (@liftx (LiftEnviron A1) x) =
@liftx (Tarrow A2 (Tarrow A3 (LiftEnviron B))) (f x).