Proof Theory
- 1 installs
- 3.9k repo stars
- Updated January 26, 2026
- parcadei/continuous-claude-v3
Guides Claude through proof-theory problems by selecting proof strategies and applying structural induction.
About
A decision-tree skill for proof theory, choosing direct, contradiction, cases, or induction strategies. A developer uses it when they want Claude to structure a mathematical proof.
- Proof-strategy selection
- Structural induction base case plus inductive step
Proof Theory by the numbers
- 1 all-time installs (skills.sh)
- Ranked #1,803 of 2,064 Data Science & ML skills by installs in the Skillselion catalog
- Data as of Aug 5, 2026 (Skillselion catalog sync)
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| Installs | 1 |
|---|---|
| repo stars | ★ 3.9k |
| Last updated | January 26, 2026 |
| Repository | parcadei/continuous-claude-v3 ↗ |
What it does
Guides Claude through proof-theory problems by selecting proof strategies and applying structural induction.
Files
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
uv run python -m runtime.harness scripts/cc_math/z3_solve.py prove "P(0)"Z3_Induction_Step
uv run python -m runtime.harness scripts/cc_math/z3_solve.py prove "ForAll([n], Implies(P(n), P(n+1)))"Z3_Soundness
uv run python -m runtime.harness scripts/cc_math/z3_solve.py prove "Implies(derivable(phi), valid(phi))"Math_Verify
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py verify "proof_structure"Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
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