
theorem Th35:
  for T being _Tree for P being Path of T for a, b being Vertex of
  T for i, j being odd Nat st i <= j & j <= len P & P.i = a & P.j = b holds T
  .pathBetween(a,b) = P.cut(i, j)
proof
  let T be _Tree, P be Path of T, a, b be Vertex of T, i, j be odd Nat such
  that
A1: i <= j & j <= len P & P.i = a & P.j = b;
  reconsider i9 = i, j9 = j as odd Element of NAT by ORDINAL1:def 12;
  P.cut(i9, j9) is_Walk_from a, b by A1,GLIB_001:37;
  hence thesis by Def2;
end;
