[Merged by Bors] - refactor(Analysis,Geometry): assume n ≠ 0, not 1 ≤ n

[urkud]

This way it's a positivity goal.

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[github-actions]

PR summary e9a7156e27

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

-+-+ mdifferentiable'
-+-+ mdifferentiableOn

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).

[grunweg]

Thanks for proposing this! Most changes are neutral, some are a bit nicer and other slightly more cumbersome to write. I agree that being able to use positivity is useful --- but I think this PR's convention should be documented somewhere. A new library note, perhaps?

Let me get another opinion, as this change is sufficiently far-reaching: CC @fpvandoorn @sgouezel @PatrickMassot
maintainer delegate?

[grunweg]

Should this lemma also be changed? (There's another such instance somewhere below.)

[urkud]

The lemma HasFTaylorSeriesUpTo.cont works for any (m : Nat) (hm : m ≤ n). When specialized to m = 1, it naturally requires a proof of 1 ≤ n.

[github-actions]

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

[urkud]

Thanks for proposing this! Most changes are neutral, some are a bit nicer and other slightly more cumbersome to write. I agree that being able to use positivity is useful --- but I think this PR's convention should be documented somewhere. A new library note, perhaps?

Let me get another opinion, as this change is sufficiently far-reaching: CC @fpvandoorn @sgouezel @PatrickMassot maintainer delegate?

I think that it goes along the general convention of assuming a seemingly weaker result.

[ocfnash]

Thanks, I think this is a clear improvement.

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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