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 Th8:
  for s being SortSymbol of S, v being Element of V.s holds
  root-tree [v,s] is c-Term of A, V
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;
  then reconsider
  vs = [v,s] as Terminal of DTConMSA ((the Sorts of A) (\/) V) by MSAFREE:7;
  root-tree vs in TS DTConMSA ((the Sorts of A) (\/) V);
  hence thesis;
end;
