
theorem Th30:
  for G being _Graph, P being Path of G, n, m being odd Element of NAT
  st n < m & m <= len P & (n <> 1 or m <> len P) holds P.cut(n,m) is open
proof
  let G be _Graph, P be Path of G, n, m be odd Element of NAT;
  assume A1: n < m & m <= len P & (n <> 1 or m <> len P);
  then A2: P.cut(n,m).first() = P.n & P.cut(n,m).last()=P.m by GLIB_001:37;
  assume P.cut(n,m) is closed;
  then P.n = P.m by A2, GLIB_001:def 24;
  hence contradiction by A1, GLIB_001:def 28;
end;
