[Merged by Bors] - feat: add ContMDiff.congr

[grunweg]

I wanted this lemma both while working on an early version of #28056 and while working on #23040: time to add it.
Besides, it fills a natural API gap.

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[github-actions]

PR summary ba1699697a

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ ContMDiff.congr
+ contMDiff_congr

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/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).

[peabrainiac]

You could golf this by one line by proving ContMDiff.congr using contMDiff_congr - but either way, looks good to me. I'm a bit surprised that we're phrasing equality of functions as ∀ y, f₁ y = f y instead of f₁ = f here, but Continuous.congr also does it, so it makes sense to stay consistent.

[grunweg]

You're right about the golf, good catch!
About the function equality: in general, there is a difference for dependent functions (e.g., sections of a vector bundle): saying f = g makes it not apply to dependent functions. In this case, that's probably no problem (as ContMDiff requires non-dependent functions anyway, and e.g. using TotalSpace.mk(') to turn a section into a function into the total space).

At the same time, staying consistent is good: if we wanted to change this, that should be a separate PR changing all such lemmas.

[grunweg]

Let's hope rebasing fixes the CI error!

[sgouezel]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• CI Success