intuition.
rewrite (sumList_filter_partition (eqb true)).
eapply ratAdd_eqRat_compat.
destruct (eq_Rat_dec (Pr[c]) 0).
rewrite e.
eapply sumList_0.
intuition.
apply filter_In in H.
intuition.
rewrite eqb_leibniz in H1.
subst.
trivial.
eapply sumList_exactly_one.
eapply filter_NoDup.
eapply getSupport_NoDup.
eapply filter_In.
intuition.
eapply getSupport_In_evalDist.
intuition.
eapply eqb_leibniz.
trivial.
intuition.
eapply filter_In in H.
intuition.
rewrite eqb_leibniz in H2.
subst.
intuition.
destruct (eq_Rat_dec (evalDist c false) 0).
rewrite e.
eapply sumList_0.
intuition.
eapply filter_In in H.
intuition.
destruct a.
rewrite eqb_refl in H1.
simpl in *.
discriminate.
trivial.
eapply sumList_exactly_one.
eapply filter_NoDup.
eapply getSupport_NoDup.
eapply filter_In.
intuition.
eapply getSupport_In_evalDist.
intuition.
case_eq (eqb true false); intuition.
rewrite eqb_leibniz in H.
discriminate.
intuition.
eapply filter_In in H.
intuition.
destruct b.
rewrite eqb_refl in H2.
simpl in *.
discriminate.
intuition.
Qed.

Lemma evalDist_sum_le_1 : forall (A : Set)(c : Comp A),
sumList (getSupport c) (evalDist c) <= 1.