Proof of `Measurability of Bernstein numbers and of pushforwards` (7th statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Measurability into $𝒢_k X$ is tested on distances to fixed subspaces, which are computed as limits of countable suprema over a dense subset of $X$ .

Lax Lean Archive