# Formalization Techniques for Asymptotic Reasoning in Classical Analysis

## DOI:

https://doi.org/10.6092/issn.1972-5787/8124## Keywords:

Formal Proofs, Coq, Classical Analysis, Bachmann-Landau Notations## Abstract

Formalizing analysis on a computer involves a lot of “epsilon-delta” reasoning, while informal reasoning may use some asymptotical hand-waving. Whether or not the arithmetic details are hidden using some abstraction like filters, a human user eventually has to break it down for the proof assistant anyway, and provide a witness for the existential variable “delta”. We describe formalization techniques that take advantage of existential variables to delay the input of witnesses until a stage where the proof assistant can actually infer them. We use these techniques to prove theorems about classical analysis and to provide equational Bachmann-Landau notations. This partially restores the simplicity of informal hand-waving without compromising the proof. As expected this also reduces the size of proof scripts and the time to write them, and it also makes proofs more stable.

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*Journal of Formalized Reasoning*,

*11*(1), 43–76. https://doi.org/10.6092/issn.1972-5787/8124

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Copyright (c) 2018 Reynald Affeldt, Cyril Cohen, Damien Rouhling

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