
theorem Th15:
  for G being _Graph for W1, W2 being Walk of G holds W1
  is_a_prefix_of W1.append(W2)
proof
  let G be _Graph, W1, W2 be Walk of G;
  set W1a = W1.append(W2);
  per cases;
  suppose
    W1.last() = W2.first();
    then len W1 <= len W1a by GLIB_001:29;
    then
A1: dom W1 c= dom W1a by FINSEQ_3:30;
    for x being object st x in dom W1 holds W1.x = W1a.x by GLIB_001:32;
    hence thesis by A1,GRFUNC_1:2;
  end;
  suppose
    W1.last() <> W2.first();
    hence thesis by GLIB_001:def 10;
  end;
end;
