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

lean-math-discrete

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: graph theory, applied lattice theory, combinatorics, DAGs, posets, provenance chains, dependency orders. DO NOT USE FOR: the abstract algebraic typeclass tower (@lean-math-foundations). TRIGGERS: graph, DAG, lattice, poset, combinatorics, provenance.

The file

We split this skill into the rules it gives an agent

2 rules. About 0 are common, 0 are distinctive, and 2 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.

  • 2

    Very specific

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

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

    STOP if cardinality blows up or a Fintype instance cannot be synthesised — handoff to @lean-math-foundations for the instance plumbing.

    line 42
  2. Very specific:

    STOP if the lattice instance you need does not exist at the current Mathlib pin — escalate to @lean-research, then author the instance …

    line 46

≈ “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 Discrete Mathematics & Graph Theory

Guide to formalizing graphs, lattices, combinatorics, and discrete structures in Lean 4.

Routing

  • USE FOR: graph theory, applied lattice theory, combinatorics, DAGs, posets, provenance chains, dependency orders, lattice operations (severity / quality-gate / trust-vector / information-flow lattices), combinatorial bounds, and finite structures in Lean 4. Owns all applied lattice instances.
  • DO NOT USE FOR: the abstract algebraic typeclass tower (delegate to @lean-math-foundations); continuous structures (delegate to @lean-math-analysis); writing one specific proof (delegate to @lean-proof).

Workflow

  1. Identify the discrete structure (graph, lattice, poset, finite set, combinatorial relation).
  2. Map to the matching Mathlib.Combinatorics.* / Mathlib.Order.* API and read the relevant Part below.
  3. Apply the pattern; handoff to @lean-proof for the concrete proof and to @lean-math-foundations if a DecidableEq / Fintype instance is missing.

Recovery & STOP

  • STOP if cardinality blows up or a Fintype instance cannot be synthesised — handoff to @lean-math-foundations for the instance plumbing.
  • STOP if the lattice instance you need does not exist at the current Mathlib pin — escalate to @lean-research, then author the instance under @lean-proof.

Handoffs

  • Predecessors: agent:gateway, skill:lean-proof (mid-proof graph or lattice goal), skill:lean-research (combinatorial result survey).
  • Successors: skill:lean-proof (apply the discrete pattern), skill:lean-proof-review (audit the instance), skill:lean-math-foundations (typeclass / decidability plumbing).

Detailed reference

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

See also

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

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