theorem Th45:
  for V being add-associative right_zeroed right_complementable
  non empty addLoopStr, v,u being Element of V holds Sum<* v,u *> = v + u
proof
  let V be add-associative right_zeroed right_complementable non empty
  addLoopStr, v,u be Element of V;
  <* v,u *> = <* v *> ^ <* u *> by FINSEQ_1:def 9;
  hence Sum<* v,u *> = Sum<* v *> + Sum<* u *> by Th41
    .= v + Sum<* u *> by Lm6
    .= v + u by Lm6;
end;
