intuition.
simpl.
eapply ratMult_eqRat_compat; intuition.
eapply ratMult_eqRat_compat.
unfold indicator.
rewrite H0.
intuition.
eapply ratInverse_eqRat_compat.
intuition.
eapply getSupport_In_evalDist.
eapply filter_In.
eauto.
eapply sumList_0 in H3; eauto.
trivial.
Qed.
Definition intersect(A : Set)(eqd : eq_dec A)(ls1 ls2 : list A) :=
filter (fun x => if (in_dec eqd x ls1) then true else false) ls2.

(* Specifications: *)
Lemma in_intersect : forall (A : Set)(eqd : eq_dec A)(ls1 ls2 : list A) a,
In a (intersect eqd ls1 ls2) <->
In a ls1 /\ In a ls2.