theorem Th119:
  for i being object holds i in (FreeGen T).s iff ex x st i = x-term
  proof let i be object;
A3: (FreeGen T).s = FreeGen(s,X) & i is set by TARSKI:1,MSAFREE:def 16;
    hereby assume i in (FreeGen T).s;
      then consider x being set such that
A2:   x in X.s & i = root-tree[x,s] by A3,MSAFREE:def 15;
      reconsider x as Element of X.s by A2;
      take x; thus i = x-term by A2;
    end;
    thus thesis by A3,MSAFREE:def 15;
  end;
