induction 1; intuition; simpl in *.
destruct (P x).
eapply perm_skip.
trivial.
trivial.
destruct (P x).
destruct (P y).
eapply perm_swap.
eapply Permutation_refl.
destruct (P y).
eapply Permutation_refl.
eapply Permutation_refl.
eapply perm_trans;
eauto.
Qed.

Lemma evalDet_step_more_support_preserved : forall (A : Set)(c c' : Comp A) s,
evalDet_step c s = (cs_more c' s) ->
Permutation (getSupport c) (getSupport c').