(* Where should this sit? *)
Arguments In {_} _ _.
Arguments Included {_} _ _.
Arguments Singleton {_} _.
Arguments Union {_} _ _.
Arguments Add {_} _ _.
Arguments Intersection {_} _ _.
Arguments Complement {_} _.
Arguments Setminus {_} _ _.
Arguments Subtract {_} _ _.
Arguments Disjoint {_} _ _.
Arguments Same_set {_} _ _.
Hint Resolve Included_Full.
Notation cored := own.cored.

Lemma cored_dup : forall P, P && cored |-- (P && cored) * (P && cored).