Fixes 1948

[affeldt-aist]

Motivation for this change

fixes #1948

fixes #1945

closes #1950

Checklist

• added corresponding entries in CHANGELOG_UNRELEASED.md

• added corresponding documentation in the headers

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[affeldt-aist]

Since this PR is just about replacing a bunch of Local Lemma to Let, which is good.

It reveals in particular that the extension measure theorem was actually relying on a local lemma and a few type casts; I think that the proper way to do that with HB is to introduce an identifier.
This PR also implements this fix.