intuition.
unfold left_total.
intuition.
edestruct (sumList_rel_left_total).
intuition.
2:{
econstructor.
econstructor.
eauto.
}
simpl.
edestruct lowDistApprox_left_total.
eapply bind_eq_dec; eauto.
eauto.
edestruct lowDistApprox_left_total.
eapply comp_eq_dec; eauto.
eapply H.
exists (x0 * x).
intuition.
eapply ratMult_eqRat_compat.
eapply lowDistApprox_func; eauto.
eapply lowDistApprox_func.
eapply H0.
eauto.
eauto.
eauto.
Qed.

Lemma lowDistApprox_bind_div2_left_total : forall (A B : Set)(c1 : Comp B)(c2 : B -> Comp A) a,
well_formed_comp c1 ->
(forall b, In b (getSupport c1) -> well_formed_comp (c2 b)) ->
left_total (fun n => lowDistApprox_bind c1 c2 a (div2 n)).