Lemma evalDist_getSupport_perm : forall (A B : Set)(c1 : Comp A)(c2 : Comp B) (f : A -> B)(f_inv : B -> A), (forall b, In b (getSupport c2) -> (f (f_inv b)) = b) -> (forall a, In a (getSupport c1) -> (f_inv (f a)) = a) -> (forall a, In a (getSupport c1) -> eqRat (evalDist c1 a) (evalDist c2 (f a))) -> (forall a, In a (getSupport c2) -> eqRat (evalDist c2 a) (evalDist c1 (f_inv a))) -> Permutation (map f (getSupport c1)) (getSupport c2).