Proof of `Volume growth is comparable to products of Bernstein numbers` (1st statement)
What this proof establishes
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
The products are comparable to the volume growth (Lemma 8 of Lee 2024, after González-Tokman and Quas 2015), which is submultiplicative.