
theorem Th36:
  for G being EVGraph, e,x being set holds the_VLabel_of G =
  the_VLabel_of G.labelEdge(e,x)
proof
  let G be EVGraph, e,x be set;
  set G2 = G.labelEdge(e,x);
  now
    per cases;
    suppose
      e in the_Edges_of G;
      then G2 = G.set(ELabelSelector, the_ELabel_of G +* (e.-->x)) by Def21;
      hence thesis by GLIB_000:9;
    end;
    suppose
      not e in the_Edges_of G;
      hence thesis by Def21;
    end;
  end;
  hence thesis;
end;
