theorem
  for i holds T deg<= i c= Free(S,X) deg<= i
  proof
    defpred P[Nat] means T deg<= $1 c= Free(S,X) deg<= $1;
    T deg<= 0 = Union FreeGen T & Free(S,X) deg<= 0 = Union FreeGen Free(S,X)
    by Th44;
    then
A0: P[0];
A1: now let i; assume P[i];
      thus P[i+1]
      proof
        let x be object; assume x in T deg<= (i+1);
        then consider r such that
A3:     x = r & deg r <= i+1;
        reconsider t = r as Element of Free(S,X) by MSAFREE4:39;
        deg t = deg r;
        hence thesis by A3;
      end;
    end;
    thus for i holds P[i] from NAT_1:sch 2(A0,A1);
  end;
