reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set;
reserve Y for non empty set,
  a,b,c,d,e,f,g for Function of Y,BOOLEAN;
reserve Y for non empty set;

theorem
  for a,b,c,d being Function of Y,BOOLEAN holds (a 'or' b) '&' (c
  'or' d) = (a '&' c) 'or' (a '&' d) 'or' (b '&' c) 'or' (b '&' d)
proof
  let a,b,c,d be Function of Y,BOOLEAN;
  (a 'or' b) '&' (c 'or' d) =((a 'or' b) '&' c) 'or' ((a 'or' b) '&' d) by
BVFUNC_1:12
    .=(a '&' c) 'or' (b '&' c) 'or' ((a 'or' b) '&' d) by BVFUNC_1:12
    .=(a '&' c) 'or' (b '&' c) 'or' ((a '&' d) 'or' (b '&' d)) by BVFUNC_1:12
    .=(a '&' c) 'or' (b '&' c) 'or' (a '&' d) 'or' (b '&' d) by BVFUNC_1:8
    .=(a '&' c) 'or' (a '&' d) 'or' (b '&' c) 'or' (b '&' d) by BVFUNC_1:8;
  hence thesis;
end;
