
theorem Th38:
  for G being VGraph, v,x being set st v in the_Vertices_of G
  holds the_VLabel_of G.labelVertex(v,x) = the_VLabel_of G +* (v .--> x)
proof
  let G be VGraph, e,x be set;
  assume e in the_Vertices_of G;
  then
  the_VLabel_of G.labelVertex(e,x) = G.set(VLabelSelector, the_VLabel_of G
  +* (e .-->x)).VLabelSelector by Def22;
  hence thesis by GLIB_000:8;
end;
