intuition.
eapply evalDet_steps_done_inv_h; eauto.
Qed.

Lemma evalDet_steps_eof_inv_h : forall (A : Set)(x y : comp_state A),
evalDet_steps x y ->
forall (c : Comp A) s,
x = (cs_more c s) ->
y = (@cs_eof A) ->
exists c'' s'', evalDet_steps (cs_more c s) (cs_more c'' s'') /\ evalDet_step c'' s'' = (@cs_eof A).