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

Theorem covers_Add :
forall A a a':Ensemble U,
Included U a A ->
Included U a' A ->
covers (Ensemble U) (Power_set_PO U A) a' a ->
exists x : _, a' = Add U a x /\ In U A x /\ ~ In U a x.