
theorem
  for n, k being Element of NAT holds not PFCrt (n,k) in PFBrt (n+1,k)
proof
  let n, k be Element of NAT;
  assume PFCrt (n,k) in PFBrt (n+1,k);
  then
  ( ex m being non zero Element of NAT st m <= n+1 & PFCrt (n,k) = PFArt
  (m,k) ) or PFCrt (n,k) = PFCrt (n+1,k) by Def4;
  hence thesis by Th17,Th18;
end;
