Section Sets_as_an_algebra.
Variable U : Type.
Hint Resolve incl_soustr_add_r: sets.

Lemma setcover_inv :
forall A x y:Ensemble U,
covers (Ensemble U) (Power_set_PO U A) y x ->
Strict_Included U x y /\
(forall z:Ensemble U, Included U x z -> Included U z y -> x = z \/ z = y).