induction x0; intuition; simpl in *.
intuition; subst.
eapply Permutation_refl.
intuition; subst.
eapply Permutation_refl.
eapply in_map_iff in H0.
destruct H0.
intuition; subst.
eapply perm_trans.
2:{
eapply perm_swap.
}
eapply perm_skip.
eapply IHx0.
trivial.
Qed.

Theorem getAllPermutations_perms :
forall (A : Set)(ls1 ls2 : list A),
In ls2 (getAllPermutations ls1) ->
Permutation ls1 ls2.