[Merged by Bors] - feat(Algebra): add abstract prod_apply and FunLike.coe_prod

[mcdoll]

Follow-up of #37779, where abstract IsApply classes were introduced. Now, we can prove a generic sum_apply lemma
and in following PRs this will replace specific ones in function spaces.

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[github-actions]

PR summary 6575e8668e

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.BigOperators.Pi	548	549	+1 (+0.18%)
Mathlib.Data.Matrix.PEquiv	790	791	+1 (+0.13%)
Mathlib.LinearAlgebra.Matrix.Polynomial	1291	1292	+1 (+0.08%)
Mathlib.LinearAlgebra.QuadraticForm.Dual	1621	1622	+1 (+0.06%)
Mathlib.Analysis.Calculus.FDeriv.Add	1743	1744	+1 (+0.06%)

Import changes for all files

Files	Import difference
../mathlib-ci/scripts/pr_summary/import_trans_difference.sh all
There are 3837 files with changed transitive imports taking up over 176703 characters: this is too many to display!
You can run this locally from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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Declarations diff

+ FunLike.coe_prod
+ prod_apply

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.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 6575e8668e
Reference commit 041f76daf0

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).

[mcdoll]

I am slightly confused about CI - I would have expected more to break..

[Vierkantor]

Looks good to me, thanks!

bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Lint style
• ci (staging) / Build
• ci (staging) / Post-Build Step
• ci (staging) / Post-CI job