reserve a,b,c,d for set;

theorem
  AND3(AND2(a,d),AND2(b,d),AND2(c,d)) is non empty iff AND2(AND3(a,b,c),
  d) is non empty
proof
  a is non empty & b is non empty & c is non empty & d is non empty iff
  AND3(a,b,c) is non empty & d is non empty;
  hence thesis;
end;
