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add Rintegral_gt0 and Rintegral_gt0_itvcc - #2086

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t6s:Rintegral_gt0_20260820
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add Rintegral_gt0 and Rintegral_gt0_itvcc#2086
t6s wants to merge 3 commits into
math-comp:masterfrom
t6s:Rintegral_gt0_20260820

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@t6s t6s commented Aug 19, 2026

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Motivation for this change

Context: https://rocq-prover.zulipchat.com/#narrow/channel/237666-math-comp-analysis/topic/natmul_inj.2C.20Rintegral_gt_0

This PR adds a lemma stating that the integral of a non-negative, continuous function that is nonzero at least at one point is positive.

Two variants are proved, one for open sets, another for closed intervals.

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 changed the title add Rintegral_gt0_itvcc add Rintegral_gt0 and Rintegral_gt0_itvcc Aug 19, 2026
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