reserve V for non empty RLSStruct;
reserve x,y,y1 for set;
reserve v for VECTOR of V;
reserve a,b for Real;

theorem Th30:
  for V being add-associative right_zeroed right_complementable
  non empty addLoopStr, v,w being Element of V holds - (v + w) = (- w) - v
proof
  let V be add-associative right_zeroed right_complementable non empty
  addLoopStr;
  let v,w be Element of V;
  thus - (v + w) = 0.V - (v + w)
    .= (0.V - w) - v by Th27
    .= (- w) - v;
end;
