End Permut_map.
Section Permut_permut.
Variable A : Type.
Variable eqA : relation A.
Hypothesis eqA_dec : forall x y:A, {eqA x y} + {~ eqA x y}.
Hypothesis eqA_equiv : Equivalence eqA.

Lemma permut_eqA : forall l l', Forall2 eqA l l' -> permutation _ eqA_dec l l'.