theorem Th5:
  for u being Term of S,X st t = u holds the_sort_of t = the_sort_of u
  proof let u be Term of S,X;
    assume t = u;
    then t in FreeSort(X, the_sort_of u) by MSATERM:def 5;
    then t in (the Sorts of FreeMSA X).the_sort_of u by MSAFREE:def 11;
    then t in (the Sorts of Free(S,X)).the_sort_of u by MSAFREE3:31;
    hence thesis by SORT;
  end;
