intuition.
eapply evalDet_steps_repeat_eof_inv_h.
eauto.
econstructor.
trivial.
Qed.

Lemma evalDet_repeat_steps_nil_inv_h : forall (A : Set) P (x y : comp_state A),
evalDet_repeat_steps P x y ->
forall (P : A -> bool) c a ls',
x = (cs_more c nil) ->
y = (cs_done a ls') ->
ls' = nil.