
theorem Th34:
  for R being connected non empty Poset,
  a being Element of Fin the carrier of R
  holds a\{PosetMax a} is Element of Fin the carrier of R
proof
  let R be connected non empty Poset, a be Element of Fin the carrier of R;
  set CR = the carrier of R;
A1: a c= CR by FINSUB_1:def 5;
  reconsider a9=a as finite set;
  set z = a9\{PosetMax a};
  z c= CR by A1;
  hence thesis by FINSUB_1:def 5;
end;
