npx skills add majiayu000/claude-skill-registry --skill proof-theory-namesreallyblank-clorch-39665a56 --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Proof Theory ## When to Use Use this skill when working on proof-theory problems in mathematical logic. ## Decision Tree 1. **Proof Strategy Selection** - Direct proof: assume premises, derive conclusion - Proof by contradiction: assume negation, derive false - Proof by cases: split on disjunction - Induction: base case + inductive step 2. **Structural Induction** - Define well-founded ordering on structures - Base: prove for minimal elements - Step: assume for smaller, prove for current - `z3_solve.py prove "induction_principle"` 3. **Cut Elimination** - Gentzen's Hauptsatz: cuts can be eliminated - Subformula property: only subformulas appear - Useful for proof normalization 4. **Completeness/Soundness Check** - Soundness: if provable then valid - Completeness: if valid then provable - `z3_solve.py prove "soundness_theorem"` 5. **Proof Verification** - Check each step follows from rules - Verify dependencies are satisfied - `math_scratchpad.py verify "proof_steps"` ## Tool Commands ### Z3_Induction_Base ```bash uv run python -m runtime.harness scripts/z3_solve.py prove "P(0)" ``` ### Z3_Induction_Step ```bash uv run python -m runtime.harness scripts/z3_solve.py prove "ForAll([n
- When to Use
- Decision Tree
- Tool Commands
- Z3InductionBase
- Z3InductionStep
- Z3Soundness
- MathVerify
- Cognitive Tools Reference
uv run python -m runtime.harness scripts/z3_solve.py prove "P(0)" uv run python -m runtime.harness scripts/z3_solve.py prove "ForAll([n], Implies(P(n), P(n+1)))" uv run python -m runtime.harness scripts/z3_solve.py prove "Implies(derivable(phi), valid(phi))" uv run python -m runtime.harness scripts/math_scratchpad.py verify "proof_structure"
What does the proof-theory skill do?
Problem-solving strategies for proof theory in mathematical logic
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill proof-theory-namesreallyblank-clorch-39665a56 --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.