
theorem Th8:
  for L being join-commutative join-associative join-idempotent
Huntington non empty ComplLLattStr, a being Element of L
 holds Bot L = (a + a`)`
proof
  let L be join-commutative join-associative join-idempotent Huntington non
  empty ComplLLattStr, a be Element of L;
  for b being Element of L holds (a + a`)` *' b = (a + a`)`
  proof
    let b be Element of L;
    (a + a`)` *' b = ((b + b`)`` + b`)` by Th4
      .= ((b + b`) + b`)` by Th3
      .= (b + (b` + b`))` by LATTICES:def 5
      .= (b + b`)` by Def7
      .= (a` + a)` by Th4;
    hence thesis;
  end;
  hence thesis by Def9;
end;
