induction c; intuition; simpl in *.
inversion H; clear H; subst.
destruct (e a0 a'); subst.
destruct (eqd a' a').
intuition.
congruence.
destruct (eqd a0 a'); subst.
congruence.
intuition.
destruct (evalDet_step c nil); discriminate.
destruct n; discriminate.
congruence.
Qed.

Lemma evalDet_step_nil_dist_preserved : forall (A : Set)(c : Comp A),
well_formed_comp c ->
forall c' a,
evalDet_step c nil = cs_more c' nil ->
evalDist c a == evalDist c' a.