proposition: Lemma inverse_image_family_union_image {X Y : Type} (f : X -> Y) (F : Family Y) : inverse_image f (FamilyUnion F) = FamilyUnion (Im F (inverse_image f)).
proof: Proof. apply Extensionality_Ensembles. split; red; intros; inversion H; inversion H0; subst; repeat econstructor; eassumption + now destruct H1. Qed.
imports: FunctionProperties Ensembles EnsemblesImplicit EnsemblesSpec IndexedFamilies