
theorem Th9:
  for L being add-associative right_zeroed right_complementable
  non empty addLoopStr holds -0_.(L) = 0_.(L)
proof
  let L be add-associative right_zeroed right_complementable non empty
  addLoopStr;
  set e = 0_.(L), f = - 0_.(L);
A1: for x being Nat st x < len e holds e.x = f.x by POLYNOM4:3;
  len f = len e by POLYNOM4:8;
  hence thesis by A1,ALGSEQ_1:12;
end;
