proof app:A-long-proofs@proof-191

open in the book · appendices/A-long-proofs.tex:15106

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proof : app:A-long-proofs@proof-191prooflemma A.306: The standard smooth bumpA.306definition 7.53: e7.53proposition 7.104: Chain rule in several variables7.104theorem 7.37: Cauchy mean value theorem and l'Hôpital's rule7.37lemma A.307: Partition of unity on a compact manifoldA.307

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proves The standard smooth bump declared appendices/A-long-proofs.tex:15106