induction 1;
intuition.
unfold compFold.
fold compFold.
comp_skip.
eapply IHPermutation; intuition.
eapply H1.
simpl.
right.
eapply H4.
eapply H5.
trivial.
eapply H1.
simpl.
left.
eauto.
eauto.
trivial.
unfold compFold.
fold compFold.
eapply (trans _  (evalDist (init'0 <-$ (init' <-$ c init y; c init' x); compFold eqd c init'0 l) x0)).
inline_first.
intuition.
eapply trans.
comp_skip.
eapply eqRat_refl.
inline_first.
intuition.
eapply trans.
eapply IHPermutation1; intuition.
eapply H1; intuition.
eapply Permutation_in; eauto.
eapply IHPermutation2; intuition.
eapply H1; intuition.
eapply Permutation_in.
eapply Permutation_sym.
eauto.
trivial.
eapply H2; eauto.
eapply Permutation_in.
eapply Permutation_sym.
eauto.
trivial.
Qed.

Lemma list_pred_app_both :
forall (A B : Set)(P : A -> B -> Prop)(lsa1 lsa2 : list A)(lsb1 lsb2 : list B),
list_pred P lsa1 lsb1 ->
list_pred P lsa2 lsb2 ->
list_pred P (lsa1 ++ lsa2) (lsb1 ++ lsb2).