
theorem
  for G being real-weighted WGraph, W1, W2 being Walk of G st W1.last()
  = W2.first() holds W1.append(W2).cost() = W1.cost() + W2.cost()
proof
  let G be real-weighted WGraph, W1, W2 be Walk of G;
  set W3 = W1.append(W2);
  assume W1.last() = W2.first();
  then W3.weightSeq() = W1.weightSeq() ^ W2.weightSeq() by Th16;
  hence thesis by RVSUM_1:75;
end;
