feat(DoubleCounting): parity of odd-degree vertices in bipartite incidence

[SproutSeeds]

Summary

Adds a parity theorem for bipartite incidence in Mathlib.Combinatorics.Enumerative.DoubleCounting:

• odd_card_filter_odd_bipartiteAbove_iff_odd_card_filter_odd_bipartiteBelow

This is intended as the first small supporting step for #25231.

Local checks

• ~/.elan/bin/lake build Mathlib/Combinatorics/Enumerative/DoubleCounting.lean
• ~/.elan/bin/lake exe lint-style Mathlib/Combinatorics/Enumerative/DoubleCounting.lean
• ~/.elan/bin/lake exe runLinter --trace Mathlib.Combinatorics.Enumerative.DoubleCounting
• bash /Users/codymitchell/Documents/code/sunflower-coda/repo/scripts/mathlib-issue-local-gate.sh --repo /Users/codymitchell/Documents/code/mathlib4 --issue 25231 --build-target Mathlib/Combinatorics/Enumerative/DoubleCounting.lean --lint-module Mathlib.Combinatorics.Enumerative.DoubleCounting --skip-mk-all

[github-actions]

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[github-actions]

PR summary 922238718f

Import changes exceeding 2%

%	File
+18.22%	Mathlib.Combinatorics.Enumerative.DoubleCounting

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Combinatorics.Enumerative.DoubleCounting	642	759	+117 (+18.22%)

Import changes for all files

Files	Import difference
4 files Mathlib.Combinatorics.Additive.Corner.Roth Mathlib.Combinatorics.Extremal.RuzsaSzemeredi Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity Mathlib.Combinatorics.SimpleGraph.Triangle.Removal	1
5 files Mathlib.Combinatorics.Additive.ApproximateSubgroup Mathlib.Combinatorics.SimpleGraph.Acyclic Mathlib.Combinatorics.SimpleGraph.Bipartite Mathlib.Combinatorics.SimpleGraph.ConcreteColorings Mathlib.Combinatorics.SimpleGraph.Girth	2
Mathlib.Combinatorics.SimpleGraph.Triangle.Basic Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite	3
Mathlib.Combinatorics.SetFamily.LYM	79
Mathlib.Combinatorics.Additive.SmallTripling	91
Mathlib.Combinatorics.Additive.DoublingConst Mathlib.Combinatorics.Additive.PluenneckeRuzsa	94
Mathlib.Combinatorics.Enumerative.DoubleCounting	117

---

Declarations diff

+ odd_card_filter_odd_bipartiteAbove_iff_odd_card_filter_odd_bipartiteBelow

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).