
theorem Th13:
  for K, L being non empty LattStr st the LattStr of K = the
  LattStr of L & K is join-absorbing holds L is join-absorbing
proof
  let K, L be non empty LattStr;
  assume that
A1: the LattStr of K = the LattStr of L and
A2: K is join-absorbing;
  L is join-absorbing
  proof
    let x, y be Element of L;
    reconsider x9 = x, y9 = y as Element of K by A1;
    x9 "/\" (x9 "\/" y9) = x9 by A2;
    hence thesis by A1;
  end;
  hence thesis;
end;
