intros x ni1 ni2 in_x.
apply in_or_app.
right; assumption.
Qed.

Lemma in_ni_x_ni_rev :
forall (x x' : nested_imp) (ni1 ni2 : nested_imps),
In x (ni1 ++ x' :: ni2) -> In x (ni1 ++ ni2) \/ x = x'.