intuition.
inversion H; subst; clear H.
inversion H0; subst; clear H0.
f_equal.
eapply evalDet_steps_done_func; eauto.
exfalso.
eapply evalDet_steps_done_eof_func; eauto.
inversion H0; clear H0; subst.
exfalso.
eapply evalDet_steps_done_eof_func; eauto.
trivial.
Qed.
Definition evalDet_equiv(A : Set)(c1 c2 : Comp A) :=
(forall s y, evalDet c1 s y <-> evalDet c2 s y).

(* Specifications: *)
Lemma evalDet_equiv_symm : forall (A : Set)(c1 c2 : Comp A),
evalDet_equiv c1 c2 ->
evalDet_equiv c2 c1.