If in (2.25) the inf is redundunt, i.e., for every fixed m the subspace L is unique, then subspaces L with smaller m are evidently subsets of subspaces L with larger m. This implies that the right-hand side bound in (2.25) is minimized if the range of L is the smallest possible, i.e., m=1. But this gives just the same bound as (2.24) with m=1, so (2.25) in this case does not give anything new compared to (2.24).