induction 1; intuition; simpl in *; subst.
discriminate.
inversion H1; clear H1; subst.
inversion H0; clear H0; subst.
eapply evalDet_step_nil_inv; eauto.
symmetry in H.
specialize (evalDet_step_more_nil_inv _ H); intuition.
subst.
eapply IHevalDet_steps.
eauto.
eauto.
eapply Permutation_in.
eapply evalDet_step_more_support_preserved.
eauto.
trivial.
Qed.

(* Specifications: *)
Lemma evalDet_steps_nil_eq : forall (A : Set)(c : Comp A)(a1 a2 : A) s2,
evalDet_steps (cs_more c nil) (cs_done a2 s2) ->
In a1 (getSupport c) ->
a1 = a2.