feat(Data/List): list splitting definitions and lemmas

[rudynicolop]

This PR continues the work from #24395.

Original PR: #24395

[rudynicolop]

Comments from Original PR #24395

This section contains 2 comment(s) from the original PR, excluding bot comments.

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@rudynicolop (2025-10-09 22:07 UTC):
Thanks for the feedback @BoltonBailey, my apologies for putting this on hold for so long.

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@rudynicolop (2025-10-09 22:56 UTC):
Ah, I guess I can no longer push to this branch? should I re-open this PR from my fork of Mathlib? Thanks!

[github-actions]

PR summary df375c234e

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Data.List.Perm.Lattice	318	319	+1 (+0.31%)

Import changes for all files

Files	Import difference
Mathlib.Data.List.Perm.Lattice	1

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Declarations diff

+ Disjoint_self
+ Nodup.splits_nodup
+ Nodup.splits₃_left_nodup
+ Nodup.splits₃_right_nodup
+ Perm.splits₃_left_right_perm
+ mem_splits_iff
+ mem_splits₃_left_iff
+ mem_splits₃_right_iff
+ nil_self_mem_splits
+ self_nil_mem_splits
+ splits
+ splits_cons
+ splits_nil
+ splits₃_left
+ splits₃_right

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).