
theorem Th27:
  for L be add-associative right_zeroed right_complementable non
  empty addLoopStr for p be sequence of L holds p-p = 0_.(L)
proof
  let L be add-associative right_zeroed right_complementable non empty
  addLoopStr;
  let p be sequence of L;
  now
    let n be Element of NAT;
    thus (p-p).n = p.n - p.n by NORMSP_1:def 3
      .= 0.L by RLVECT_1:15
      .= (0_.(L)).n by FUNCOP_1:7;
  end;
  hence thesis;
end;
