intuition.
apply evalDet_steps_eof_inv in H.
destruct H.
destruct H.
intuition.
eapply evalDet_steps_trans.
eapply evalDet_steps_bind_more.
eauto.
econstructor.
simpl.
rewrite H1.
eauto.
econstructor.
Qed.
Inductive comp_state_eq(A : Set) : comp_state A -> comp_state A -> Prop :=
| cse_done :
forall a s,
comp_state_eq (cs_done a s) (cs_done a s)
| cse_eof :
comp_state_eq (@cs_eof A) (@cs_eof A)
| cse_more :
forall c1 c2 s,
Comp_eq c1 c2 ->
comp_state_eq (cs_more c1 s) (cs_more c2 s).

(* Specifications: *)
Theorem comp_state_eq_refl : forall (A : Set)(c : comp_state A),
comp_state_eq c c.