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 Th1:
  for a be FinSequence of bool D holds a is
  length_equal_card_of_set iff len a = card D
proof
  let A be FinSequence of bool D;
  thus A is length_equal_card_of_set implies len A = card D
  by ZFMISC_1:81;
  assume
A1: len A = card D;
  take D;
  thus thesis by A1,ZFMISC_1:81;
end;
