reserve S for non void non empty ManySortedSign,
  V for non-empty ManySortedSet of the carrier of S;
reserve A for MSAlgebra over S,
  t for Term of S,V;

theorem Th19:
  for s being SortSymbol of S, v being Element of V.s holds
  the_sort_of (v-term A) = s
proof
  let s be SortSymbol of S, v be Element of V.s;
  ((the Sorts of A) (\/) V).s = (the Sorts of A).s \/ V.s by PBOOLE:def 4;
  then v in ((the Sorts of A) (\/) V).s by XBOOLE_0:def 3;
  hence thesis by Th14;
end;
