
theorem
  for F being non empty finite set, A being non-empty FinSequence of
  bool F, i being Element of NAT, B being Singlification of A, i st i in dom A
  holds B.i <> {}
proof
  let F be non empty finite set, A be non-empty FinSequence of bool F, i be
  Element of NAT, B be Singlification of A, i;
  assume
A1: i in dom A;
  then A.i <> {} by Th2;
  hence thesis by A1,Def7,CARD_1:27;
end;
