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add compatibility lemmas for Stdlib Rcos and Rsin - #2083

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t6s wants to merge 5 commits into
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t6s:RcosE_20260817
Open

add compatibility lemmas for Stdlib Rcos and Rsin #2083
t6s wants to merge 5 commits into
math-comp:masterfrom
t6s:RcosE_20260817

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@t6s

@t6s t6s commented Aug 16, 2026

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Motivation for this change

Context:
https://rocq-prover.zulipchat.com/#narrow/channel/237666-math-comp-analysis/topic/relating.20trigo.2Ecos.20to.20Rtrigo_def.2Ecos.2C.20etc.2E

This PR adds compatibility lemmas for a few trigonometry functions defined in Stdlib Reals,
namely Rcos and Rsin. A lemma for π is also added.

Checklist
  • added corresponding entries in CHANGELOG_UNRELEASED.md
  • added corresponding documentation in the headers

Reference: How to document

Merge policy

As a rule of thumb:

  • PRs with several commits that make sense individually and that
    all compile are preferentially merged into master.
  • PRs with disorganized commits are very likely to be squash-rebased.
Reminder to reviewers

@t6s

t6s commented Aug 16, 2026

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The proof turned out to be not as simple as for the exp case, due to a subtle difference in the defining series for Rcos and cos:
the former is
1 - (x^2/2!) + (x^4/4!) ...
while the latter is
1 + 0 - (x^2/2!) + 0 + (x^4/4!) + 0 ...

That said, the proof script for RcosE seems a bit too long, and there could be a better proof strategy.

@t6s t6s changed the title Rcos e 20260817 add compatibility lemmas for Stdlib Rcos and Rsin Aug 16, 2026
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