reserve n,m,k for Nat,
  x,y for set,
  r for Real;
reserve C,D for non empty finite set,
  a for FinSequence of bool D;

theorem Th7:
  for a be terms've_same_card_as_number FinSequence of bool D st n
  in dom a holds a.n <> {}
proof
  let A be terms've_same_card_as_number FinSequence of bool D;
  assume n in dom A;
  then
A1: 1<=n & n<=len A by FINSEQ_3:25;
  assume A.n = {};
  hence contradiction by A1,Def1,CARD_1:27;
end;
