theorem Th57:
  for S,s,X,x,C st C = x-term holds
  transl C = id((the Sorts of Free(S,X)).s)
  proof
    let S,s,X,x,C;
    assume Z0: C = x-term;
    let t be Element of (the Sorts of Free(S,X)).s;
A2: the_sort_of t = s by SORT;
    hence (transl C).t = C-sub(t) by TRANS
    .= (id((the Sorts of Free(S,X)).s)).t by Z0,A2,Th41;
  end;
