
theorem
  for G being _Graph, S, x being set st x in G.AdjacentSet(S) holds not x in S
proof
  let G be _Graph, S,x be set;
  assume x in G.AdjacentSet(S);
  then ex t being Vertex of G st t=x &( not t in S)& ex v being Vertex of G
  st v in S & t,v are_adjacent;
  hence thesis;
end;
