theorem
  for t being c-Term of A,V for s being SortSymbol of S, v being Element
  of V.s st t = root-tree [v,s] holds the_sort_of t = s
proof
  let t be c-Term of A,V;
  let s be SortSymbol of S, x be Element of V.s;
  x in (the Sorts of A).s \/ V.s by XBOOLE_0:def 3;
  then x in ((the Sorts of A) (\/) V).s by PBOOLE:def 4;
  hence thesis by Th14;
end;
