
theorem Th12: :: 4.5
  for L being join-commutative join-associative Huntington non
  empty ComplLLattStr, a being Element of L holds a + a = a
proof
  let L be join-commutative join-associative Huntington non empty
  ComplLLattStr, a be Element of L;
A1: (a + a)` = (a`` + a`)` + (a + a)` by Th11
    .= (a`` + a`)` + (a`` + a)` by Th3
    .= a` by Def6;
  thus a + a = (a + a)`` by Th3
    .= a by A1,Th3;
end;
