feat(NumberTheory/Bernoulli): add bernoulli'_five and bernoulli'_six

[qdiazblanco]

Add bernoulli'_five and bernoulli'_six as simp lemmas, continuing the
existing sequence of explicit values bernoulli'_zero through
bernoulli'_four. In particular this records bernoulli' 5 = 0 and
bernoulli' 6 = 1 / 42.

These results are upstreamed from the FLT project
(ImperialCollegeLondon/FLT#1069, by William Coram
and Samuel Yin, written with the assistance of Claude and
cleaned up by Codex and then by Pepa Montero). I have done some further changes to fit Mathlib conventions.

---

[github-actions]

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[github-actions]

PR summary 6366d52008

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ bernoulli'_five
+ bernoulli'_six

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 6366d52).

• +2 new declarations
• −0 removed declarations

+bernoulli'_five
+bernoulli'_six

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 6366d52008
Reference commit ed0d70fdcd

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[YaelDillies]

Do we really want to add more computations of small Bernoulli numbers? Instead we should make it easier to compute them whenever needed. See https://leanprover.zulipchat.com/#narrow/channel/116395-maths/topic/Fast.20computation.20of.20Bernoulli.20numbers/with/590406943 for some ideas.

maintainer merge?

[github-actions]

🚀 Pull request has been placed on the maintainer queue by YaelDillies.

[b-mehta]

I am working on a metaprogram to compute these (which outperforms the methods in that thread), keep an eye out for a PR about this, or feel free to DM me if you need something sooner.