#[local]
Hint Resolve incl_soustr_add_r: sets.

Theorem covers_is_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)).