
theorem LM210:
  ex F be Function of BOOLEAN*,NAT
  st
  for x be Element of BOOLEAN*
  holds F.x = ExAbsval(x)
  proof
    defpred P[Element of BOOLEAN*,object] means $2 = ExAbsval($1);
    A1: for x being Element of BOOLEAN*
    ex y being Element of NAT st P[x,y]
    proof
      let x be Element of BOOLEAN*;
      set y = ExAbsval(x);
      reconsider y as Element of NAT by ORDINAL1:def 12;
      take y;
      thus thesis;
    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;
