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Lean formalisations of major chunks of chapters 4 and 5 - #251
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pink-iguana wants to merge 48 commits into
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pink-iguana wants to merge 48 commits into
pink-iguana wants to merge 48 commits into
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…ring in exponent pairs file
…m power asymptotics
… Lemma 4.9 from the blueprint
…nds file; standardised private lemmas to theorems for consistency
…already mentioned in the individual files
…ventually remove them as Mathlib expands
…tion of exponent pairs, proving it equivalent to the previous definition, added the abbreviation IsDyadicSubinterval
…led out in the blueprint
… growth exponent by removing the structure which was not too useful
….3 explicit and match the conditions imposed there
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Blueprint changes:
Corrected the general van der Corput bound (Proposition 4.7) and its k=3 specialization
Restricted the optimized bound to 0<α≤1 (Corollary 4.8) otherwise it seems to be false as stated because of the \beta(\alpha)=\alpha-1 for \alpha > 1 in Lemma 4.4, also slightly revised/corrected its induction proof
Remove duplicated hypotheses from the exponent-pair definition (Definition 5.1)
Made the model exponent and derivative tolerance explicit in the non-asymptotic characterization of exponent pairs (Lemma 5.2) as it invokes eq (4.3) which has those assumptions anyway
Corrected the small-shift cutoff and shifted intervals in the proof of the A-process bound (Lemma 4.6), and adjusted the difference phase to keep its arguments in [1,2].
Added the missing α>1 case in the full-interval reduction (Lemma 4.9), corrected the reference justifying the α=1 case, and fixed the Fourier cutoff inequalities.
New formalization:
Formalised all of Section 4.2. Used external formalisations (available with Apache 2.0 license) for van der Corput-B process. Also formalised the introductory section of Chapter 5.
Statements without proofs:
Added the known bounds in Section 4.3 with sorry.