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
  for t being c-Term of A,V holds (ex s being SortSymbol of S, x being
set st x in (the Sorts of A).s & t.{} = [x,s]) or (ex s being SortSymbol of S,
  v being Element of V.s st t.{} = [v,s]) or t.{} in [:the carrier' of S,{the
  carrier of S}:]
proof
  let t be c-Term of A,V;
  set G = DTConMSA ((the Sorts of A) (\/) V);
A1: the carrier of G = (Terminals G) \/ (NonTerminals G) by LANG1:1;
  reconsider e = {} as Node of t by TREES_1:22;
  NonTerminals G = [:the carrier' of S,{the carrier of S}:] by MSAFREE:6;
  then
  t.e in Terminals G or t.e in [:the carrier' of S,{the carrier of S}:] by A1,
XBOOLE_0:def 3;
  hence thesis by Lm4;
end;
