theorem
  for t being Element of fT holds height(fT|t) <= height fT
proof
  let t be Element of fT;
  consider p such that
A1: p in fT|t and
A2: len p = height(fT|t) by Def12;
 t^p in fT by A1,Def6;
then A3: len(t^p) <= height fT by Def12;
   len(t^p) = len t + len p & len p <= len p + len t by FINSEQ_1:22,NAT_1:11;
  hence thesis by A2,A3,XXREAL_0:2;
end;
