intuition.
destruct H.
destruct H.
intuition.
econstructor.
econstructor.
intuition.
simpl.
eapply rel_map_eq.
eapply H0.
eauto.
intuition.
eauto.
intuition.
Qed.

Lemma evalDet_lowDistApprox_ls_done_inv : forall (A : Set)(eqd : eq_dec A)(c : Comp A) s a1 a2 n r,
evalDet c s (ca_done a1) ->
lowDistApprox_ls c a2 n s r ->
r == if (eqd a2 a1) then 1 else 0.