induction 1; intuition; subst.
discriminate.
inversion H1; clear H1; subst.
inversion H0; clear H0; subst.
eapply evalDet_step_done_evalDist; eauto.
assert (s = nil).
eapply evalDet_step_more_nil_inv.
eauto.
subst.
rewrite <- IHevalDet_steps; eauto.
erewrite evalDet_step_nil_dist_preserved; eauto.
intuition.
eapply evalDet_step_well_formed_comp_preserved;
eauto.
Qed.

Lemma evalDet_steps_done_evalDist : forall (A : Set)(eqd : eq_dec A)(c : Comp A) a a' s,
well_formed_comp c ->
evalDet_steps (cs_more c nil) (cs_done a s) ->
evalDist c a' == if (eqd a a') then 1 else 0.