[Merged by Bors] - refactor(Order/Basic): move Pi & Prop orders to a new file

[SnirBroshi]

Move the LE instances of Pi & Prop from Order/Basic.lean to a new Order/Defs/Prop.lean.
This lets Logic/Relation.lean import them so that it can use ≤ between relations.

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Extracted from #30526

About the copyright of the new file:

• leanprover/lean3@9c28552 (Johannes Hölzl, 2016) introduced LE on both Prop and functions (called weak_order_Prop and weak_order_fun respectively)
• leanprover-community/mathlib3@ce09c18 (Johannes Hölzl, 2017) generalized from functions to dependent functions (the instance is now called preorder_fun)
• leanprover-community/mathlib3@40f673e (Yury Kudryashov, 2020) added Pi.le_def
• leanprover-community/mathlib3@93bc7e0 (Yury Kudryashov, 2021) added le_Prop_eq

[github-actions]

PR summary 7ab71b05d7

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
../mathlib-ci/scripts/pr_summary/import_trans_difference.sh all
There are 7441 files with changed transitive imports taking up over 331369 characters: this is too many to display!
You can run this locally from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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Declarations diff (regex)

No declarations were harmed in the making of this PR! 🐙

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)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 7ab71b0).

• +0 new declarations
• −0 removed declarations

No declaration differences.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 7ab71b05d7
Reference commit 9c27dca6e4

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.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).

[eric-wieser]

Also reverts #34391

I think the reason for this PR still applies; we shouldn't ungeneralize the lemmas about the general definitions in core. This might mean having separate Sort and Type sections, or it might mean making an RFC to ungeneralize them upstream.

[eric-wieser]

because Pi.hasLe doesn't support sorts, see this thread.

Please add the explanation in the commit message above the fold; GitHub discuseions are hard to find in large PRs

[SnirBroshi]

Moved that sentence above the fold.

GitHub discussions are hard to find in large PRs

(link)
(edit: see also small Zulip remark)

[eric-wieser]

Oh, I thought you had a reason to justify why it didn't support sorts

[joneugster]

Thank you for the PR! This looks reasonable to me.

About the specialisation back from Sort to Type: My personal opinion in this instance is that this kind of generalisation is nice if it works out-of-the-box, but it might not be worth to deal with any complications just for the sake of generalisation. It seems to me that #34391 also has been created in this spirit, i.e. it has been generalised because it works without any issues, not because there was any real use case.

With that, I recommend

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by joneugster.

[eric-wieser]

I'd like to hear from @b-mehta here before reverting his PR

[eric-wieser]

(the long PR title is perhaps good evidence that this PR is doing two unrelated things that would happen in separate PRs)

[b-mehta]

I don't think the universe ungeneralisation is a good idea, and it's not clear to me that it's motivated. It looks like exactly one lemma doesn't work with the generalised universes, but that doesn't motivate making a whole series of true lemmas unusable. Can't we just change map_mono to take {α β : Type*} instead?

[SnirBroshi]

exactly one lemma

See #30526, it's the entire file, I changed just map_mono here as a proof-of-concept since it has a TODO comment.
But regardless, I prefer to postpone this discussion to #30526 if the move itself is good to go, so I reverted the changes to Logic/Relation.lean.

[b-mehta]

LGTM, will wait for CI then merge

[SnirBroshi]

(btw my comment above reads a bit snarky to me but I'm not sure how to phrase it better, no snarky-ness intended)

Letting LE accept Sort will solve the universe issues, do you think core will be okay with such a change?

[eric-wieser]

Letting LE accept Sort will solve the universe issues, do you think core will be okay with such a change?

I think the first half of this question is a good one for Zulip; in particular, this is needed for allow f ≤ g when f g : \forall x ≤ 3, Nat.

It sounds like the motivation is also that there are other core defs which already are generalized to Sort

[b-mehta]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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