Module ClauseUniverseFinite : CLAUSE_UNIVERSE_FINITE.
Implicit Arguments Finite.
Implicit Arguments Union.
Implicit Arguments Intersection.
Implicit Arguments Im.
Implicit Arguments In.
Implicit Arguments Add.
Implicit Arguments Subtract.
Implicit Arguments Singleton.
Implicit Arguments injective.
Implicit Arguments Included.
Implicit Arguments Power_set.
Ltac inv H := inversion H; clear H; subst.

Lemma finite_pair:
forall U V (S : Ensemble U) (T: Ensemble V),
Finite S -> Finite T ->
Finite (fun xy => S (fst xy) /\ T (snd xy)).