intuition.
eapply evalDet_repeat_steps_nil_inv_h; eauto.
Qed.

(* Specifications: *)
Lemma evalDet_repeat_steps_app_nil_h : forall (A : Set) P (x y : comp_state A),
evalDet_repeat_steps P x y ->
forall c ls1 ls2 b a,
x = (cs_more c ls1) ->
y = (cs_eof A) ->
evalDet_repeat_steps P (cs_more c (ls1 ++ b :: nil)) (cs_done a ls2)->
(forall s s' b a,
evalDet_steps (cs_more c s) (cs_eof A) ->
evalDet_steps (cs_more c (s ++ b :: nil)) (cs_done a s') ->
s' = nil) ->
ls2 = nil.