reserve Y for non empty set;

theorem ::Distributive
  for a,b,c,d being Function of Y,BOOLEAN holds a '&' (b 'or' c
  'or' d) = (a '&' b) 'or' (a '&' c) 'or' (a '&' d)
proof
  let a,b,c,d be Function of Y,BOOLEAN;
  a '&' (b 'or' c 'or' d) =(a '&' (b 'or' c)) 'or' (a '&' d) by BVFUNC_1:12
    .=(a '&' b) 'or' (a '&' c) 'or' (a '&' d) by BVFUNC_1:12;
  hence thesis;
end;
