theorem
  for V being Abelian add-associative right_zeroed right_complementable
  non empty addLoopStr, v,u,w being Element of V holds
  Sum<* u,v,w *> = Sum<* v,w *> + u
proof
  let V be Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr, v,u,w be Element of V;
  thus Sum<* u,v,w *> = u + v + w by Th46
    .= u + (v + w) by Def3
    .= Sum<* v,w *> + u by Th45;
end;
