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[Merged by Bors] - feat(Order/WellFoundedSet): minimal element of a nonempty set exists if < is well founded on the set#39777

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[Merged by Bors] - feat(Order/WellFoundedSet): minimal element of a nonempty set exists if < is well founded on the set#39777
Hagb wants to merge 4 commits into
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WuProver:WellFoundedOn-minimal

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@Hagb Hagb commented May 24, 2026

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There exists a inimal element in a nonempty set if < is well founded on the set.


It was a lemmas for #39781, which has been closed since there would be a better proof.

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Hagb added 2 commits May 24, 2026 23:15
…stricted on the subtype is `WellFounded`

It is a lemma for

```lean
theorem wellFoundedLT_of_monotone_prod
    {α β γ : Type*} [LinearOrder α] [LinearOrder β] [WellFoundedLT α] [WellFoundedLT β]
    [PartialOrder γ] {f : α × β ≃ γ} (mono : Monotone f) : WellFoundedLT γ
```
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github-actions Bot commented May 24, 2026

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PR summary 6d08d809d6

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ WellFoundedOn.exists_minimal

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.


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

@github-actions github-actions Bot added the t-order Order theory label May 24, 2026
@mathlib-dependent-issues mathlib-dependent-issues Bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label May 24, 2026
@Hagb Hagb changed the title feat(Order/WellFoundedSet): minimal elements of a set exists if WellFoundedOn the set feat(Order/WellFoundedSet): minimal element of a set exists if WellFoundedOn the set May 24, 2026
@Hagb Hagb changed the title feat(Order/WellFoundedSet): minimal element of a set exists if WellFoundedOn the set feat(Order/WellFoundedSet): minimal element of a nonempty set exists if WellFoundedOn the set May 24, 2026
@Hagb Hagb changed the title feat(Order/WellFoundedSet): minimal element of a nonempty set exists if WellFoundedOn the set feat(Order/WellFoundedSet): minimal element of a nonempty set exists if < is well founded on the set May 24, 2026
@Hagb
Hagb marked this pull request as ready for review May 24, 2026 17:55
Comment thread Mathlib/Order/WellFoundedSet.lean Outdated
Hagb and others added 2 commits May 25, 2026 13:38
Co-authored-by: Snir Broshi <26556598+SnirBroshi@users.noreply.github.com>
…ation restricted on the subtype is `WellFounded`"

This reverts commit 21ca935.
@mathlib-dependent-issues mathlib-dependent-issues Bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label May 25, 2026

@b-mehta b-mehta left a comment

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Thanks!

bors merge

@mathlib-triage mathlib-triage Bot added the ready-to-merge This PR has been sent to bors. label May 25, 2026
mathlib-bors Bot pushed a commit that referenced this pull request May 25, 2026
… if `<` is well founded on the set (#39777)

There exists a inimal element in a nonempty set if `<` is well founded on the set.
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Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors Bot changed the title feat(Order/WellFoundedSet): minimal element of a nonempty set exists if < is well founded on the set [Merged by Bors] - feat(Order/WellFoundedSet): minimal element of a nonempty set exists if < is well founded on the set May 25, 2026
@mathlib-bors mathlib-bors Bot closed this May 25, 2026
b-mehta pushed a commit to b-mehta/mathlib4 that referenced this pull request Jun 2, 2026
… if `<` is well founded on the set (leanprover-community#39777)

There exists a inimal element in a nonempty set if `<` is well founded on the set.
Bergschaf pushed a commit to Bergschaf/mathlib4 that referenced this pull request Jun 3, 2026
… if `<` is well founded on the set (leanprover-community#39777)

There exists a inimal element in a nonempty set if `<` is well founded on the set.
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3 participants