proof-theory
Problem-solving strategies for proof theory in mathematical logic
它会碰到什么
扫了多少1 个文本文件，2 KB
它会碰到什么不碰外部（只输出文字）
命中总数0 处
命中统计严重 0 · 高 0 · 中 0 · 低 0
这一栏是扫描器报的事实，不是结论。命中多不等于有毒（安全工具、规则库、示例脚本本来就会包含危险写法），命中少也不等于干净。它和你手上的凭据、文件、网络有什么关系，需要你自己看。
技能内容
Proof Theory
When to Use
Use this skill when working on proof-theory problems in mathematical logic.
Decision Tree
- 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
- 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"
- Cut Elimination
- Gentzen's Hauptsatz: cuts can be eliminated
- Subformula property: only subformulas appear
- Useful for proof normalization
- Completeness/Soundness Check
- Soundness: if provable then valid
- Completeness: if valid then provable
z3_solve.py prove "soundness_theorem"
- 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.
想直接用这个技能？
本站把开放许可（MIT / Apache 等）的技能按仓库打包整理到网盘，点一下转存到你自己的网盘，不用一个个从 GitHub 拉。许可未声明的技能只给原始仓库链接，不打包。
它属于哪个仓库
星标★ 3,941
本站分层T1
该仓技能数158
原文件路径
.claude/skills/math/mathematical-logic/proof-theory/SKILL.md