reserve Y for non empty set;

theorem ::Distributive
  for a,b,c,d being Function of Y,BOOLEAN holds a 'or' (b '&' c
  '&' d) = (a 'or' b) '&' (a 'or' c) '&' (a 'or' d)
proof
  let a,b,c,d be Function of Y,BOOLEAN;
  a 'or' (b '&' c '&' d) =(a 'or' (b '&' c)) '&' (a 'or' d) by BVFUNC_1:11
    .=((a 'or' b) '&' (a 'or' c)) '&' (a 'or' d) by BVFUNC_1:11;
  hence thesis;
end;
