
theorem
  ex F be Function of BOOLEAN*,NAT
  st
  for x be Element of BOOLEAN*
  ex x0 be Tuple of len x, BOOLEAN
  st x=x0 &
  F.x = Absval x0
  proof
    defpred P[Element of BOOLEAN*,object] means
    ex x0 be Tuple of len $1, BOOLEAN
    st $1=x0 &
    $2 = Absval x0;
    A1: for x being Element of BOOLEAN* ex y being Element of NAT st P[x,y]
    proof
      let x be Element of BOOLEAN*;
      x is Element of (len x) -tuples_on BOOLEAN by FINSEQ_2:92;
      then
      reconsider x0=x as Tuple of len x, BOOLEAN;
      reconsider n =Absval x0 as Element of NAT;
      take n;
      thus ex x0 be Tuple of len x, BOOLEAN st x=x0 & n= Absval x0;
    end;
    consider f being Function of BOOLEAN*,NAT such that
    A2:for x being Element of BOOLEAN* holds P[x,f.x]
    from FUNCT_2:sch 3(A1);
    take f;
    thus thesis by A2;
  end;
