feat: improve doc-strings for differential geometry elaborators

[grunweg]

Right now, the custom elaborators in the manifold library have doc-strings which explain what the elaborator
expands to --- but don't show what the expanded concept means. It would be much better to show that also.
Verso allows doing so easily: this PR implements this as a proof of concept for the elaborator for mvfderiv.

This is not ready to land yet:

• making importing doc-string across files work requires lean4#14120 (merged in mid-June)

• the verso command should move to a better place

• in the medium-term, there will be a Lean core command for this!

• Right now, the concatenated doc-string is formatted as pure text (not markdown): Lean core will implement this soon, but has not done so yet.

• this technique should be applied to all the custom elaborators

• the doc-strings of the elaborators may need to be rewritten, to start with the subject they're defining. (Once this happens, just concatenating the doc-strings produces reasonable results. This PR does this for mvfderiv only.)

Made with in-person help of David Thrane Christiansen at the MI retreat. Thanks a lot!

---

Actually, leanprover/lean4#14115 implements the same functionality properly.

• depends on: [Merged by Bors] - chore(Geometry/Manifold): make some doc-strings follow the style guide #39729

[github-actions]

PR summary b9e65c5893

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Geometry.Manifold.Notation	2172	2173	+1 (+0.05%)
Mathlib.Geometry.Manifold.MFDeriv.NormedSpace	2185	2186	+1 (+0.05%)

Import changes for all files

Files

Import difference

113 files Mathlib.Analysis.Calculus.Rademacher Mathlib.Analysis.Complex.UpperHalfPlane.Manifold Mathlib.Analysis.Complex.UpperHalfPlane.Measure Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff Mathlib.Analysis.Distribution.FourierMultiplier Mathlib.Analysis.Distribution.SchwartzSpace.Basic Mathlib.Analysis.Distribution.SchwartzSpace.Deriv Mathlib.Analysis.Distribution.SchwartzSpace.Fourier Mathlib.Analysis.Distribution.SchwartzSpace Mathlib.Analysis.Distribution.Sobolev Mathlib.Analysis.Distribution.Support Mathlib.Analysis.Distribution.TemperedDistribution Mathlib.Analysis.Fourier.Convolution Mathlib.Analysis.Fourier.LpSpace Mathlib.Analysis.Fourier.PoissonSummation Mathlib.Analysis.Normed.Lp.SmoothApprox Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation Mathlib.Geometry.Manifold.Algebra.LieGroup Mathlib.Geometry.Manifold.Algebra.Monoid Mathlib.Geometry.Manifold.Algebra.SMul Mathlib.Geometry.Manifold.Algebra.SmoothFunctions Mathlib.Geometry.Manifold.Algebra.Structures Mathlib.Geometry.Manifold.Bordism Mathlib.Geometry.Manifold.BumpFunction Mathlib.Geometry.Manifold.Complex Mathlib.Geometry.Manifold.ContMDiffMFDeriv Mathlib.Geometry.Manifold.ContMDiffMap Mathlib.Geometry.Manifold.DerivationBundle Mathlib.Geometry.Manifold.Diffeomorph Mathlib.Geometry.Manifold.GroupLieAlgebra Mathlib.Geometry.Manifold.Immersion Mathlib.Geometry.Manifold.Instances.Icc Mathlib.Geometry.Manifold.Instances.Real Mathlib.Geometry.Manifold.Instances.Sphere Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra Mathlib.Geometry.Manifold.IntegralCurve.Basic Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique Mathlib.Geometry.Manifold.IntegralCurve.Transform Mathlib.Geometry.Manifold.IntegralCurve.UniformTime Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary Mathlib.Geometry.Manifold.LocalDiffeomorph Mathlib.Geometry.Manifold.MFDeriv.Atlas Mathlib.Geometry.Manifold.MFDeriv.Basic Mathlib.Geometry.Manifold.MFDeriv.FDeriv Mathlib.Geometry.Manifold.MFDeriv.NormedSpace Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions Mathlib.Geometry.Manifold.MFDeriv.Tangent Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential Mathlib.Geometry.Manifold.Notation Mathlib.Geometry.Manifold.PartitionOfUnity Mathlib.Geometry.Manifold.PoincareConjecture Mathlib.Geometry.Manifold.Riemannian.Basic Mathlib.Geometry.Manifold.Riemannian.PathELength Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace Mathlib.Geometry.Manifold.Sheaf.Smooth Mathlib.Geometry.Manifold.SmoothApprox Mathlib.Geometry.Manifold.SmoothEmbedding Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Basic Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Metric Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Torsion Mathlib.Geometry.Manifold.VectorBundle.Hom Mathlib.Geometry.Manifold.VectorBundle.LocalFrame Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable Mathlib.Geometry.Manifold.VectorBundle.Pullback Mathlib.Geometry.Manifold.VectorBundle.Riemannian Mathlib.Geometry.Manifold.VectorBundle.SmoothSection Mathlib.Geometry.Manifold.VectorBundle.Tangent Mathlib.Geometry.Manifold.VectorBundle.Tensoriality Mathlib.Geometry.Manifold.VectorField.LieBracket Mathlib.Geometry.Manifold.VectorField.Pullback Mathlib.Geometry.Manifold.WhitneyEmbedding Mathlib.NumberTheory.EulerProduct.DirichletLSeries Mathlib.NumberTheory.Harmonic.ZetaAsymp Mathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.NumberTheory.LSeries.Dirichlet Mathlib.NumberTheory.LSeries.HurwitzZetaEven Mathlib.NumberTheory.LSeries.HurwitzZetaOdd Mathlib.NumberTheory.LSeries.HurwitzZetaValues Mathlib.NumberTheory.LSeries.HurwitzZeta Mathlib.NumberTheory.LSeries.Nonvanishing Mathlib.NumberTheory.LSeries.PrimesInAP Mathlib.NumberTheory.LSeries.RiemannZeta Mathlib.NumberTheory.LSeries.ZMod Mathlib.NumberTheory.LSeries.ZetaZeros Mathlib.NumberTheory.ModularForms.Basic Mathlib.NumberTheory.ModularForms.Bounds Mathlib.NumberTheory.ModularForms.CuspFormSubmodule Mathlib.NumberTheory.ModularForms.DedekindEta Mathlib.NumberTheory.ModularForms.Delta Mathlib.NumberTheory.ModularForms.Derivative Mathlib.NumberTheory.ModularForms.DimensionFormulas.LevelOne Mathlib.NumberTheory.ModularForms.Discriminant Mathlib.NumberTheory.ModularForms.EisensteinSeries.Basic Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.MDifferentiable Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds Mathlib.NumberTheory.ModularForms.JacobiTheta.Manifold Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable Mathlib.NumberTheory.ModularForms.LevelOne.Basic Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula Mathlib.NumberTheory.ModularForms.LevelOne.GradedRing Mathlib.NumberTheory.ModularForms.LevelOne Mathlib.NumberTheory.ModularForms.NormTrace Mathlib.NumberTheory.ModularForms.Petersson Mathlib.NumberTheory.ModularForms.QExpansion Mathlib.Topology.Compactification.OnePoint.Sphere

1

---

Declarations diff (regex)

No declarations were harmed in the making of this PR! 🐙

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 -- pending)

Computed after the build finishes.

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit b9e65c5893
Reference commit f8fd74f95c

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).

[grunweg]

Good news: with the recent core bump, the verso command works (within vscode, in the same file now) 🎉
Bad news: I get a bizarre error about vs code building a file fine, while lake build file not working.

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - chore(Geometry/Manifold): make some doc-strings follow the style guide #39729
  By Dependent Issues (🤖). Happy coding!

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.