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r-irber-irbe/proof-skills/skills/lean-math-analysis/SKILL.md

lean-math-analysis

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: real analysis, functional analysis, topology, and measure theory in Lean 4 / Mathlib: continuous functions. DO NOT USE FOR: stochastic / probabilistic convergence (@lean-math-stochastic). TRIGGERS: continuous, derivative, integral, metric space, normed space.

The file

We split this skill into the rules it gives an agent

3 rules. About 0 are common, 0 are distinctive, and 3 are very specific to this project.

  • ≈0

    Common · estimate

    Many files like this have a rule of this kind.

  • ≈0

    Distinctive · estimate

    This author's own choices. Worth a look.

  • 3

    Very specific

    Tied to their project's names, files or tools. Probably skip.

  • Common
  • Distinctive
  • Very specific
  1. Very specific:

    If the result is a concrete proof obligation, handoff to @lean-proof.

    line 43
  2. Very specific:

    STOP if the lemma you need is not in Mathlib at the current pin — escalate to @lean-research to verify, then @lean-proof to author a local …

    line 47
  3. Very specific:

    STOP if a classical-only result is invoked and the project has documented constructive constraints — escalate to @lean-review-council.

    line 51

≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.

Keep what fits and drop the rest. Your version, ready for your agents.
Files
SKILL.md

Lean 4 Real Analysis & Topology

Guide to formalizing analysis and topology in Lean 4 using Mathlib's filter-based approach.

Routing

  • USE FOR: real analysis, functional analysis, topology, and measure theory in Lean 4 / Mathlib — continuous functions, derivatives, integrals, metric / normed spaces, filter-based convergence, contraction mappings, convex analysis, spectral theory, and the real-valued bridges from a Nat-scaled model.
  • DO NOT USE FOR: stochastic / probabilistic convergence (delegate to @lean-math-stochastic); deterministic dynamical-system stability proofs (delegate to @lean-math-dynamical); pure optimization (delegate to @lean-math-optimization); typeclass-tower reasoning (delegate to

Workflow

  1. Map the problem to Mathlib's filter-based architecture (Part 1) — most analysis goals can be phrased as Tendsto … atTop or ContinuousAt.
  2. Locate the relevant Part below (continuity, derivatives, integrals, normed spaces, measure theory) and apply the pattern.
  3. If the result is a concrete proof obligation, handoff to @lean-proof; if it depends on a foundational instance, handoff to @lean-math-foundations.

Recovery & STOP

  • STOP if the lemma you need is not in Mathlib at the current pin — escalate to @lean-research to verify, then @lean-proof to author a local helper.
  • STOP if a classical-only result is invoked and the project has documented constructive constraints — escalate to @lean-review-council.

Handoffs

  • Predecessors: agent:gateway, skill:lean-proof (mid-proof convergence goal), skill:lean-research (when a survey turns up an analysis API).
  • Successors: skill:lean-proof (apply the analysis pattern), skill:lean-proof-review (audit the resulting proof), skill:lean-math-foundations (when the goal collapses to a typeclass-tower issue).

Detailed reference

Full encyclopedic reference, decision trees, and lookup tables live in references/lean-math-analysis-handbook.md .

See also

  • ../../references/lean-math-analysis-handbook.md -- Complete lean-math-analysis Handbook
  • ../lean-gateway/SKILL.md -- Top-level skill router

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