
theorem Th1:
  for R being non degenerated add-associative right_zeroed
  right_complementable non empty doubleLoopStr holds 0.R <> -1.R
proof
  let R be non degenerated add-associative right_zeroed right_complementable
  non empty doubleLoopStr;
  assume 0.R = -1.R;
  then 0.R = -(-1.R) by RLVECT_1:12
    .= 1.R by RLVECT_1:17;
  hence contradiction;
end;
