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 Th2:
  (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
  set G = DTConMSA 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 Lm3;
end;
