vibeeval/proof-theory
skills/math/mathematical-logic/proof-theory/SKILL.md
Problem-solving strategies for proof theory in mathematical logic
$ install --global
skillsauthnpx skillsauth add vibeeval/vibecosystem proof-theoryInstall this skill globally with one command. Works with Claude Code, Cursor, and Windsurf.
Security Scan Results
3 of 9 scanners reported clean
Some scanners were skipped, did not run, or reported a non-clean status. Review each row below.
3
Scanners Passed
9
Scanners in report
Clean
TrivyContainer and dependency vulnerability scanner
95%
Clean
SemgrepStatic code analysis for vulnerabilities
95%
Clean
mcp-scan (Snyk)Model Context Protocol security validation
95%
Skipped
Snyk (dep)Open source security scanning
50%
Skipped
Socket.devSupply chain security analysis
50%
Skipped
VirusTotalMulti-engine malware detection
50%
Skipped
CrowdStrikeAdvanced threat intelligence
50%
Skipped
OSV-ScannerOpen Source Vulnerability database check
50%
Skipped
OWASP Dep-Check
50%
Last scanned: Jun 10, 2026, 5:58 AM4.5s1 file scanned
SKILL.md
- name:
- proof-theory
- description:
- Problem-solving strategies for proof theory in mathematical logic
- allowed-tools:
- [Bash, Read]
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.
Related Skills
vibeeval/workflow-router
development
VerifiedTrustedCommunity
Goal-based workflow orchestration - routes tasks to specialist agents based on user goals
500SKILL.mdUpdated Jun 11, 2026
vibeeval/wiring
tools
VerifiedTrustedCommunity
Wiring Verification
500SKILL.mdUpdated Jun 11, 2026
vibeeval/websocket-patterns
development
VerifiedTrustedCommunity
Connection management, room patterns, reconnection strategies, message buffering, and binary protocol design.
500SKILL.mdUpdated Jun 11, 2026
vibeeval/vp-engineering
testing
VerifiedTrustedCommunity
VP Engineering perspective - org design (team topologies), process improvement, cross-team dependencies, engineering culture, OKRs, incident management maturity, platform strategy, DX optimization, release management at scale
500SKILL.mdUpdated Jun 11, 2026