
theorem Th24:
  for L be add-associative non empty addLoopStr for p,q,r be
  sequence of L holds p+q+r = p+(q+r)
proof
  let L be add-associative non empty addLoopStr;
  let p,q,r be sequence of L;
  now
    let n be Element of NAT;
    thus (p+q+r).n = (p+q).n + r.n by NORMSP_1:def 2
      .= p.n + q.n + r.n by NORMSP_1:def 2
      .= p.n + (q.n + r.n) by RLVECT_1:def 3
      .= p.n + (q+r).n by NORMSP_1:def 2
      .= (p+(q+r)).n by NORMSP_1:def 2;
  end;
  hence thesis;
end;
