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feat(order/well_founded): well_founded_lt.has_min, etc. #18751

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@vihdzp vihdzp commented Apr 6, 2023

We add some boilerplate code for porting well_founded.has_min to the typeclasses is_well_founded, well_founded_lt, and well_founded_gt.

Besides the usual convenience from using instances, there's two advantages of doing this:

  • the lemmas for well_founded_gt no longer have their names backwards (min instead of max)
  • we're able to directly state well_founded_lt.min_le and well_founded_gt.le_max in linear orders

Speaking of boilerplate, I'm not even sure we should keep well_founded.min and the like. In a proof, it's always better to use

obtain ⟨s, hs, hlt⟩ := well_founded.has_min s hns

and outside of it, I can't see much use for having a generic minimal element, unless you're already working in a linear order, in which case you can use Inf instead.

Zulip discussion: https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/well_founded.2Emin/near/347492784

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@vihdzp vihdzp added the awaiting-review The author would like community review of the PR label Apr 6, 2023
@mathlib-dependent-issues-bot mathlib-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Apr 6, 2023
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@vihdzp vihdzp marked this pull request as draft April 9, 2023 15:58
@kim-em kim-em added the too-late This PR was ready too late for inclusion in mathlib3 label Jul 16, 2023
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