theorem Th54:
  for V being Abelian add-associative right_zeroed right_complementable
  non empty addLoopStr, v,w being Element of V holds
  Sum<* v,w *> = Sum<* w,v*>
proof
  let V be Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr, v,w be Element of V;
  thus Sum<* v,w *> = v + w by Th45
    .= Sum<* w,v *> by Th45;
end;
