[Merged by Bors] - feat(Topology): Add PairReduction.lean

[DavidLedvinka]

Add file PairReduction.lean which proves the theorem pair_reduction which is needed for the proof of the general Kolmogorov-Chentsov theorem in the Brownian Motion project.

Co-authored-by: @RemyDegenne

• depends on: [Merged by Bors] - feat: limits of ENNReal exponentiation #27239

[github-actions]

PR summary 5592362428

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Topology.EMetricSpace.PairReduction (new file)	1827

---

Declarations diff

+ EMetric.pair_reduction
+ antitone_logSizeBallSeq_add_one_subset
+ card_finset_logSizeBallSeq_add_one_lt
+ card_finset_logSizeBallSeq_card_eq_zero
+ card_finset_logSizeBallSeq_le
+ card_le_logSizeRadius_le_pow_logSizeRadius
+ card_pairSetSeq_le_logSizeRadius_mul
+ card_pairSet_le
+ disjoint_smallBall_logSizeBallSeq
+ edist_le_of_mem_pairSet
+ exists_radius_le
+ finset_logSizeBallSeq_add_one
+ finset_logSizeBallSeq_add_one_ssubset
+ finset_logSizeBallSeq_add_one_subset
+ finset_logSizeBallSeq_subset_logSizeBallSeq_init
+ finset_logSizeBallSeq_zero
+ iSup_edist_pairSet
+ logSizeBallSeq
+ logSizeBallStruct
+ logSizeBallStruct.ball
+ logSizeBallStruct.smallBall
+ logSizeRadius
+ logSizeRadius_le_card_smallBall
+ one_le_logSizeRadius
+ one_le_radius_logSizeBallSeq
+ pairSet
+ pairSetSeq
+ pairSet_empty_eq_empty
+ pairSet_subset
+ point_logSizeBallSeq_add_one
+ point_logSizeBallSeq_zero
+ point_mem_finset_logSizeBallSeq
+ point_mem_logSizeBallSeq_init
+ point_notMem_finset_logSizeBallSeq_add_one
+ pow_logSizeRadius_le_card_le_logSizeRadius
+ radius_logSizeBallSeq_add_one
+ radius_logSizeBallSeq_le
+ radius_logSizeBallSeq_zero
+ that

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.

---

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).

[EtienneC30]

Thanks! Many of my comments are suggestions for slightly shorter proofs. Please write the maths in comments between backticks and remove open Classical in all across the file.

[DavidLedvinka]

-awaiting-author

[DavidLedvinka]

-awaiting-author

[sgouezel]

bors d+
Thanks!

[mathlib-bors]

✌️ DavidLedvinka can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[DavidLedvinka]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

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