intuition.
unfold evalDist.
eapply eqRat_refl.
Qed.

Lemma evalDist_in_f : forall (A B : Set)(c1 : Comp A)(c2 : Comp B)(f : A -> B),
(forall a, eqRat (evalDist c1 a) (evalDist c2 (f a))) ->
(forall a, In a (getSupport c1) <-> In (f a) (getSupport c2)).