
theorem
  for G being _Graph, W being Walk of G, m, n being Nat st W.cut(m,n) is
  non trivial holds W is non trivial
proof
  let G be _Graph, W be Walk of G, m, n be Nat such that
A1: W.cut(m,n) is non trivial and
A2: W is trivial;
  reconsider W as trivial Walk of G by A2;
  reconsider m9 = m, n9 = n as Element of NAT by ORDINAL1:def 12;
  W.cut(m9,n9) is trivial;
  hence thesis by A1;
end;
