
theorem
  for x being Element of BOOLEAN holds buf1.<*x*> = x & buf1.<*x*> =
  and2.<*x,x*> & buf1.<*0*> = 0 & buf1.<*1*> = 1
proof
  let x be Element of BOOLEAN;
  thus buf1.<*x*> = x by Def2;
  thus buf1.<*x*> = x '&' x by Def2
    .= and2.<*x,x*> by FACIRC_1:def 6;
  thus buf1.<*0*> = FALSE by Def2
    .= 0;
  thus buf1.<*1*> = TRUE by Def2
    .= 1;
end;
