
theorem
  for G being non empty DTConstrStr holds Terminals G misses NonTerminals G
proof
  let G be non empty DTConstrStr;
A1: Terminals G = { t where t is Symbol of G :
  not ex tnt being FinSequence st t ==> tnt } by LANG1:def 2;
A2: NonTerminals G = { t where t is Symbol of G :
  ex tnt being FinSequence st t ==> tnt } by LANG1:def 3;
  assume not thesis;
  then consider x being object such that
A3: x in Terminals G and
A4: x in NonTerminals G by XBOOLE_0:3;
A5: ex t being Symbol of G st x = t & not ex tnt being FinSequence st t ==>
  tnt by A1,A3;
  ex t being Symbol of G st x = t & ex tnt being FinSequence st t ==> tnt
  by A2,A4;
  hence contradiction by A5;
end;
