theorem
  for n being Element of NAT st n in dom W.edgeSeq() holds W.edgeSeq().n
  in the_Edges_of G
proof
  let n be Element of NAT;
  assume n in dom W.edgeSeq();
  then W.edgeSeq().n in rng W.edgeSeq() by FUNCT_1:def 3;
  hence thesis;
end;
