
theorem Th3:
  for L being non empty LattStr holds L is meet-Associative
  join-Associative meet-Absorbing join-absorbing implies L is meet-absorbing
proof
  let L be non empty LattStr;
  assume
A1: L is meet-Associative join-Associative meet-Absorbing join-absorbing;
  then
A2: L is meet-commutative join-commutative by Th2;
  for x,y being Element of L holds (x "/\" y) "\/" y = y
  proof
    let a,b be Element of L;
    b = b "\/" (b "/\" a) by A1
      .= b "\/" (a "/\" b) by A2
      .= (a "/\" b) "\/" b by A2;
    hence thesis;
  end;
  hence thesis;
end;
