feat: Finite.linearOrder, choosing *some* linear order on a finite type#27020
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grunweg wants to merge 2 commits intoleanprover-community:masterfrom
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feat: Finite.linearOrder, choosing *some* linear order on a finite type#27020grunweg wants to merge 2 commits intoleanprover-community:masterfrom
grunweg wants to merge 2 commits intoleanprover-community:masterfrom
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This is useful if you want *just some* linear order (but will give wrong results if you expect anything particular about this order). [Zulip discussion](https://leanprover.zulipchat.com/#narrow/channel/217875-Is-there-code-for-X.3F/topic/LocallyFiniteOrderBot.20instance.20for.20Fintype/with/528420842)
PR summary 628f824785Import changes for modified filesNo significant changes to the import graph Import changes for all files
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./scripts/declarations_diff.sh long <optional_commit>The doc-module for No changes to technical debt.You can run this locally as
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eric-wieser
reviewed
Jul 12, 2025
eric-wieser
reviewed
Jul 12, 2025
| is preferred over choosing *any* linear order. -/ | ||
| protected noncomputable def Finite.linearOrder {α : Type*} [Finite α] : LinearOrder α := | ||
| haveI := Fintype.ofFinite α | ||
| LinearOrder.lift' _ (Fintype.equivFin α).injective |
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I guess arguably we should rename Fintype.equivFin to Finite.equivFin, since the former is very non-constructive anyway.
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This hasn't anything to do with finiteness, right? Any type can be endowed with a linear order (and even a well order). This is already known in mathlib, here is a short illustration
def foo (α : Type*) : LinearOrder α := by
choose r wo using exists_wellOrder α
exact rSo I'm not sure the PR is worth it...
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Thanks for pointing this out; I hadn't realised. I agree that this PR should be closed.
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This is useful if you want just some linear order (but will give wrong results if you expect anything particular about this order). Zulip discussion
This PR was mostly inspired by help of Aaron, Yael and Eric - thank you!
Part of the path towards geodesics and the Levi-Civita connection.