
theorem Th26: :: Only for _Tree as it is not true for cyclic paths
  for T being _Tree for P being Path of T for i, j being odd Nat
  st i < j & j <= len P holds P.i <> P.j
proof
  let T be _Tree, P be Path of T, i, j be odd Nat such that
A1: i < j and
A2: j <= len P and
A3: P.i = P.j;
  reconsider i, j as odd Element of NAT by ORDINAL1:def 12;
A4: i < j by A1;
  then
A5: i = 1 by A2,A3,GLIB_001:def 28;
  then
A6: P is non trivial by A1,A2,GLIB_001:126;
  P.first() = P.last() by A2,A3,A4,A5,GLIB_001:def 28;
  hence contradiction by A6,GLIB_001:def 24;
end;
