feat(Mathlib.Data.Ordering.Dickson): Dickson orders

[AntoineChambert-Loir]

This PR continues the work from #16704.

Original PR: #16704

[AntoineChambert-Loir]

Comments from Original PR #16704

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

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@joneugster (2026-09-19 13:40 UTC):
Mathlib has moved to PRs from forks. This PR is still from a branch of the main repository and will soon be closed! Please migrate the content to a fork and reopen a PR from there if you wish to do so. See Zulip topic for more instructions. Thank you for contributing to mathlib!

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@mathlib-bors (2026-09-19 16:46 UTC):
This pull request is now in draft mode. No active bors state needed cleanup.

While this PR remains draft, bors will ignore commands on this PR. Mark it ready for review before using commands like bors r+ or bors try.

[github-actions]

PR summary 893e7867a0

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Data.Ordering.Dickson (new file)	969

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Declarations diff (regex)

+ Equiv.isDickson_of_monotone
+ Fin.isDickson_nat
+ Finsupp.isDickson
+ Finsupp.isDickson_equiv
+ Finsupp.isDickson_nat
+ Nat.isDickson
+ Preorder.isDickson
+ Set.isBasis
+ WellFoundedLT.isDickson
+ exists_lt_and_le_of_isDickson
+ isDickson.wf
+ isDickson_iff_exists_monotone
+ isDickson_of_minimal_ne_and_finite
+ isDickson_prod
+ isDickson_tfae
+ minimal_ne_and_finite_of
+ wellFounded_iff_not_exists

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

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

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean -- pending)

Computed after the build finishes.

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No changes to strong technical debt.
No changes to weak technical debt.

Current commit 893e7867a0
Reference commit 158047ba1d

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.py 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).