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(** *** Facts about [In] *)
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(** Characterization of [In] *)

Lemma app_inj_pivot x1 x2 y1 y2 (a : A): x1 ++ a :: x2 = y1 ++ a :: y2 ->
((In a x1 /\ In a y2) \/ (In a x2 /\ In a y1)) \/ (x1 = y1 /\ x2 = y2).