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 Th3:
  for a be terms've_same_card_as_number length_equal_card_of_set
  FinSequence of bool D holds a.(len a) = D
proof
  let A be terms've_same_card_as_number length_equal_card_of_set FinSequence
  of bool D;
A1: len A = card D by Th1;
  then 1 <= len A by NAT_1:14;
  then A.(len A) is finite set by Lm2;
  hence thesis by A1,Lm3;
end;
