[Merged by Bors] - feat(Data/Seq): coinductive predicates for sequences#28874
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vasnesterov wants to merge 49 commits intoleanprover-community:masterfrom
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[Merged by Bors] - feat(Data/Seq): coinductive predicates for sequences#28874vasnesterov wants to merge 49 commits intoleanprover-community:masterfrom
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This looks pretty reasonable to me. Granted, I haven't checked the code in #28291 where this is used yet though.
@plp127 @eric-wieser any final comments?
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* Prove `eq_of_bisim'` and `eq_of_bisim_strong` coinductive principles for equality. * Develop API for a predicate `∀ x ∈ s, p x` where `s : Seq α`, including coinductive principle `all_coind`. * Introduce the `Pairwise` predicate along with API and coinductive principles `Pairwise.coind` and `Pairwise.coind_trans`. * Introduce `ENat`-valued length of a sequence, `length'`, along with minimal API. * Move theorems about `length` from `Defs.lean` to `Basic.lean`. * Prove a coinductive principle for a predicate `a.length' ≤ b.length'`. All of these "coinductive principles" are stated in the form as similar as possible to inductive principles. Co-authored-by: Vasily Nesterov <vas.nesterov63@gmail.com>
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…unity#28874) * Prove `eq_of_bisim'` and `eq_of_bisim_strong` coinductive principles for equality. * Develop API for a predicate `∀ x ∈ s, p x` where `s : Seq α`, including coinductive principle `all_coind`. * Introduce the `Pairwise` predicate along with API and coinductive principles `Pairwise.coind` and `Pairwise.coind_trans`. * Introduce `ENat`-valued length of a sequence, `length'`, along with minimal API. * Move theorems about `length` from `Defs.lean` to `Basic.lean`. * Prove a coinductive principle for a predicate `a.length' ≤ b.length'`. All of these "coinductive principles" are stated in the form as similar as possible to inductive principles. Co-authored-by: Vasily Nesterov <vas.nesterov63@gmail.com>
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…unity#28874) * Prove `eq_of_bisim'` and `eq_of_bisim_strong` coinductive principles for equality. * Develop API for a predicate `∀ x ∈ s, p x` where `s : Seq α`, including coinductive principle `all_coind`. * Introduce the `Pairwise` predicate along with API and coinductive principles `Pairwise.coind` and `Pairwise.coind_trans`. * Introduce `ENat`-valued length of a sequence, `length'`, along with minimal API. * Move theorems about `length` from `Defs.lean` to `Basic.lean`. * Prove a coinductive principle for a predicate `a.length' ≤ b.length'`. All of these "coinductive principles" are stated in the form as similar as possible to inductive principles. Co-authored-by: Vasily Nesterov <vas.nesterov63@gmail.com>
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eq_of_bisim'andeq_of_bisim_strongcoinductive principles for equality.∀ x ∈ s, p xwheres : Seq α, including coinductive principleall_coind.Pairwisepredicate along with API and coinductive principlesPairwise.coindandPairwise.coind_trans.ENat-valued length of a sequence,length', along with minimal API.lengthfromDefs.leantoBasic.lean.a.length' ≤ b.length'.All of these "coinductive principles" are stated in the form as similar as possible to inductive principles.
updateandsetoperations forSeq#26120This PR is necessary for a new tactic (#28291), which computes the asymptotics of real functions.
This PR continues the work from #20241.
Original PR: #20241