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

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