Let (N; v) be a coalitional game with a coalitional structure B.
Let k and l be two players who are members of different coalitions in B.
Prove that if k and l are symmetric players, i.e., v(S ∪ {k}) = v(S ∪ {l}) for every coalition S that does not contain either of them, then for every imputation x in the core of the game with coalitional structure B, one has xk = xl.