
theorem
  for G being VGraph, v,x being set st v in the_Vertices_of G holds G
  .labeledV() c= G.labelVertex(v,x).labeledV()
proof
  let G be VGraph, e,x be set;
  assume e in the_Vertices_of G;
  then G.labelVertex(e,x).labeledV() = G.labeledV() \/ {e} by Th52;
  hence thesis by XBOOLE_1:7;
end;
