reserve x,y for set,
  n for Nat;

theorem Th3:
  for f be non empty FinSequence of NAT, X be disjoint_with_NAT set
  holds (Terminals (DTConUA(f,X))) = X
proof
  let f be non empty FinSequence of NAT, X be disjoint_with_NAT set;
  set A = DTConUA(f,X);
  thus Terminals A c= X by Th2;
  let x be object;
  assume
A1: x in X;
A2: NonTerminals A = dom f by Th2;
A3: not x in NonTerminals A by A2,A1,Def1,XBOOLE_0:3;
  the carrier of A = (Terminals A) \/ (NonTerminals A) & x in (dom f) \/ X
  by A1,LANG1:1,XBOOLE_0:def 3;
  hence thesis by A3,XBOOLE_0:def 3;
end;
