
theorem Th16:
  for F being finite set, A being FinSequence of bool F,
      i being Element of NAT st i in dom A & A is Hall holds
    card (A.i) >= 1
proof
  let F be finite set, A be FinSequence of bool F, i be Element of NAT;
  assume that
A1: i in dom A and
A2: A is Hall;
  set J = {i};
  J c= dom A by A1,ZFMISC_1:31; then
A3: card J <= card (union (A,J)) by A2;
  assume
A4: card (A.i) < 1;
  union (A,J) = A.i by A1,Th5;
  hence thesis by A4,A3,CARD_2:42;
end;
