
theorem
  for G being VGraph, v being Vertex of G, x being set holds v in G
  .labelVertex(v,x).labeledV()
proof
  let G be VGraph, v be Vertex of G, x be set;
  G.labelVertex(v,x).labeledV() = G.labeledV() \/ {v} & v in {v} by Th52,
TARSKI:def 1;
  hence thesis by XBOOLE_0:def 3;
end;
