theorem Th44:
  T deg<= 0 = Union FreeGen T
  proof
A0: T deg<= 0 = the set of all x-term by Th11;
    thus T deg<= 0 c= Union FreeGen T
    proof
      let x be object; assume x in T deg<= 0;
      then consider s being SortSymbol of S, y being Element of X.s such that
A1:   x = y-term by A0;
      x in FreeGen(s,X) by A1,MSAFREE:def 15;
      then x in (FreeGen T).s & s in the carrier of S = dom FreeGen T
      by PARTFUN1:def 2,MSAFREE:def 16;
      hence thesis by CARD_5:2;
    end;
    let a being object; assume a in Union FreeGen T;
    then consider b such that
A2: b in dom FreeGen T & a in (FreeGen T).b by CARD_5:2;
    reconsider b as SortSymbol of S by A2;
    a in FreeGen(b,X) by A2,MSAFREE:def 16;
    then consider y being set such that
A3: y in X.b & a = root-tree [y,b] by MSAFREE:def 15;
    reconsider y as Element of X.b by A3;
    a = y-term by A3;
    hence a in T deg<= 0 by A0;
  end;
