feat(Combinatorics): Set-Valued Pigeonhole Principle

[cjrl]

This PR contributes two theorems to combinatorics:

• exists_lt_card_cover_of_card_biUnion_lt_card is a set-valued version of the pigeonhole principle.

• sum_card_eq_sum_card_cover_biUnion is a set theoretic corollary of a double counting result proved for bipartite graphs (Finset.sum_card_bipartiteAbove_eq_sum_card_bipartiteBelow). This was needed to prove the above pigeonhole principle.

The motivation for these results is our Latin Square PR #36698. These results were proved in less general terms in that PR, but are independent of Latin Square considerations and so we have generalized and moved them into more relevant files.

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[github-actions]

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[github-actions]

PR summary 322515540d

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Combinatorics.Pigeonhole	776	777	+1 (+0.13%)

Import changes for all files

Files

Import difference

13 files Mathlib.Combinatorics.Additive.AP.Three.Behrend Mathlib.Combinatorics.Pigeonhole Mathlib.Dynamics.Ergodic.Conservative Mathlib.NumberTheory.ClassNumber.AdmissibleAbs Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue Mathlib.NumberTheory.ClassNumber.AdmissibleCardPowDegree Mathlib.NumberTheory.ClassNumber.Finite Mathlib.NumberTheory.ClassNumber.FunctionField Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.NumberTheory.NumberField.Cyclotomic.PID Mathlib.NumberTheory.NumberField.DedekindZeta Mathlib.NumberTheory.NumberField.Ideal.Asymptotics

1

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Declarations diff

+ exists_mem_biUnion_inf'_card_lt
+ sum_card_eq_sum_biUnion_card

You can run this locally as follows

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

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

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

---

No changes to technical debt.

You can run this locally as

./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).

[cjrl]

+t-combinatorics

[cjrl]

-awaiting-author

[vlad902]

LGTM otherwise