#[local]
Hint Resolve Subtract_intro : sets.

(* Specifications: *)
Lemma Subtract_inv :
forall (A:Ensemble U) (x y:U), In U (Subtract U A x) y -> In U A y /\ x <> y.
Lemma Included_Strict_Included :
forall X Y:Ensemble U, Included U X Y -> Strict_Included U X Y \/ X = Y.
Lemma Strict_Included_inv :
forall X Y:Ensemble U,
Strict_Included U X Y -> Included U X Y /\ Inhabited U (Setminus U Y X).
Lemma not_SIncl_empty :
forall X:Ensemble U, ~ Strict_Included U X (Empty_set U).
Lemma Complement_Complement :
forall A:Ensemble U, Complement U (Complement U A) = A.