
theorem Th11:
  for K, L being non empty LattStr st the LattStr of K = the
  LattStr of L & K is join-associative holds L is join-associative
proof
  let K, L be non empty LattStr;
  assume that
A1: the LattStr of K = the LattStr of L and
A2: K is join-associative;
  L is join-associative
  proof
    let x, y, z be Element of L;
    reconsider x9 = x, y9 = y, z9 = z as Element of K by A1;
    (x9 |_| y9) |_| z9 = x9 |_| (y9 |_| z9) by A2;
    hence thesis by A1;
  end;
  hence thesis;
end;
