[Merged by Bors] - feat(Analysis): asymptotics of inversion at atBot and 𝓝[<] 0

[vasnesterov]

Prove some lemmas about the inversion function's asymptotics at atBot and 𝓝[<] 0 filters, analogous to the existing API for atTop and 𝓝[>] 0

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[github-actions]

PR summary 6c02dc9c4e

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

+ Filter.Tendsto.const_div_atBot
+ Filter.Tendsto.div_atBot
+ Filter.Tendsto.inv_tendsto_atBot
+ Filter.Tendsto.inv_tendsto_nhdsLT_zero
+ inv_Iio₀
+ inv_Ioo_0_right
+ inv_atBot₀
+ inv_nhdsLT_zero
+ tendsto_inv_atBot_zero
+ tendsto_inv_atBot_zero'
+ tendsto_inv_zero_atBot

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).

[b-mehta]

In #18912 I also added these, sometimes with shorter proofs and with division versions too. If you'd like, you can copy those and include them here too.

[vasnesterov]

In #18912 I also added these, sometimes with shorter proofs and with division versions too. If you'd like, you can copy those and include them here too.

Thank you! Perhaps you should merge this branch into yours and mark your PR as dependent on this PR? It might prevent reviewers from doing duplicate work. The only thing my PR includes that yours doesn't is Filter.Tendsto.inv_tendsto_zero_left/right.

[j-loreaux]

LGTM. Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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