
theorem Th35:
  for L being join-commutative join-associative Huntington non
  empty ComplLLattStr holds Bot L = Bottom CLatt L
proof
  let L be join-commutative join-associative Huntington non empty
  ComplLLattStr;
  reconsider C = Bot L as Element of CLatt L by Def11;
  for a being Element of CLatt L holds C "/\" a = C & a "/\" C = C
  proof
    let a be Element of CLatt L;
    reconsider a9 = a as Element of L by Def11;
    thus C "/\" a = Bot L *' a9 by Def11
      .= C by Def9;
    hence thesis;
  end;
  hence thesis by LATTICES:def 16;
end;
