(** we can use [multiplicity] to define [InA] and [NoDupA]. *)
Fact if_eqA_then : forall a a' (B:Type)(b b':B),
eqA a a' -> (if eqA_dec a a' then b else b') = b.

Lemma permut_app_inv2 :
forall l l1 l2, permutation (l ++ l1) (l ++ l2) -> permutation l1 l2.