mathlib4
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feat: SuccOrder and recursion principle on well-ordered type
Order/SuccPred/Basic.lean: add SuccOrder.ofLinearWellFoundedLT, which puts a SuccOrder on an arbitrary well-ordered type. Also add the dual, PredOrder version. Add missing pred lemmas corresponding to existing succ lemmas.
Order/SuccPred/Limit.lean: add SuccOrder.limitRecOn generalizing Ordinal.limitRecOn to allow definition by transfinite recursion on an arbitrary well-ordered type. (It turns out a partial well-founded order is enough.)
SetTheory/Ordinal/Arithmetic.lean: refactor Ordinal.limitRecOn to use SuccOrder.limitRecOn.
SetTheory/Cardinal/Ordinal.lean: add a lemma saying that the initial ordinal of an infinite cardinal is a NoMaxOrder.
SetTheory/Ordinal/Basic.lean: add mk_Iio_ord_out_α, a restatement of card_typein_out_lt.
cc @digama0, the author of ordinal.limit_rec_on.
bors d+
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Thanks for the review and delegation!
As this PR is labelled auto-merge-after-CI, we are now sending it to bors:
bors merge
Pull request successfully merged into master.
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