theorem Th46:
  for V being add-associative right_zeroed right_complementable
  non empty addLoopStr, v,u,w being Element of V holds
  Sum<* v,u,w *> = v + u + w
proof
  let V be add-associative right_zeroed right_complementable non empty
  addLoopStr, v,u,w be Element of V;
  <* v,u,w *> = <* v,u *> ^ <* w *> by FINSEQ_1:43;
  hence Sum<* v,u,w *> = Sum<* v,u *> + Sum<* w *> by Th41
    .= Sum<* v,u *> + w by Lm6
    .= v + u + w by Th45;
end;
