
theorem Th2: :: 4.9
  for L being Huntington join-commutative join-associative non
  empty ComplLLattStr, a being Element of L holds a + a` = a` + a``
proof
  let L be Huntington join-commutative join-associative non empty
  ComplLLattStr, a be Element of L;
  set y = a`, z = y``;
  a = ((a` + y``)` + (a` + y`)`) & a` = ((a`` + a```)` + (a`` + a``)`) by Def6;
  then a + a` = (y + z)` + (y + y`)` + (y` + y`)` + (y` + z)` by LATTICES:def 5
    .= (y` + y`)` + (y + y`)` + (y + z)` + (y` + z)` by LATTICES:def 5
    .= (y` + y)` + (y` + y`)` + ((y + z)` + (y` + z)`) by LATTICES:def 5
    .= y + ((y + z)` + (y` + z)`) by Def6
    .= y + y` by Def6;
  hence thesis;
end;
