New: 98,000+ skills indexed from GitHub repos with 100+ stars · every skill safety-checkedBrowse top skillsTop skills
Esc to closeBrowse all skills
Submit a skillBrowse skills
Submit a skillBrowse skills

Agent skill

Proof Theory

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for proof theory in mathematical logic

MITAuto-check: notes

Install Proof Theory

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill proof-theory -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 proof-theory --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.claude/skills/math/mathematical-logic/proof-theory .claude/skills/proof-theory && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
proof-theory
GitHub stars
3.9k
Used in
2 other repos
Token cost
~452 tokens
SKILL.md length
134 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for proof theory in mathematical logic

  • Works in 5 steps: Proof Strategy Selection → Structural Induction → Cut Elimination → …
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Cognitive Tools Reference
  • Calls uv

What it does

Proof Theory is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for proof theory in mathematical logic

Its SKILL.md is about 450 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

The repository describes itself as: Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows. The licence is MIT.

Example prompts

  • “/proof-theory”

Requirements

  • Python 3
  • Pre-approved tools (allowed-tools): Bash, Read

Workflow steps

5 steps, taken from the first numbered list in SKILL.md.

  1. Proof Strategy Selection
  2. Structural Induction
  3. Cut Elimination
  4. Completeness/Soundness Check
  5. Proof Verification

What it can do on your machine

Read from SKILL.md and the folder at commit d07ff4b. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves these tools, so the agent can use them without asking each time:

    • Bash
    • Read

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    Shell commands in SKILL.md call:

    • uv

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md. Its commands use uv, which can reach the network depending on how they are called.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Proof Theory loads about 452 tokens when it runs. Until then it costs about 20 tokens; SKILL.md has 134 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~20
When it runs · the whole SKILL.md, loaded when a task matches
~452

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check: notes

The automated check noted patterns worth knowing about, such as sudo or a known installer.

  • NotePre-approves every shell command (allowed-tools: Bash)SKILL.md
    allowed-tools: Bash, Read

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from parcadei/Continuous-Claude-v3 at commit d07ff4b, republished under its MIT licence (© parcadei). 134 words, ~452 tokens.

Download SKILL.mdSave it as .claude/skills/proof-theory/SKILL.md (or your agent's skills folder).
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

  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/cc_math/z3_solve.py prove "P(0)"
Z3_Induction_Step
bash
uv run python -m runtime.harness scripts/cc_math/z3_solve.py prove "ForAll([n], Implies(P(n), P(n+1)))"
Z3_Soundness
bash
uv run python -m runtime.harness scripts/cc_math/z3_solve.py prove "Implies(derivable(phi), valid(phi))"
Math_Verify
bash
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.

© parcadei, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

Just SKILL.md in .claude/skills/math/mathematical-logic/proof-theory of parcadei/Continuous-Claude-v3.

Open the folder on GitHubat commit d07ff4b

Used in 2 other repositories

We found 4 copies of this SKILL.md (exact, near-identical or edited) in other folders, from 2 other GitHub owners. This page covers the copy in parcadei/Continuous-Claude-v3, which our catalogue first saw on October 7, 2026.

Compare with similar skills

Proof Theory next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

Proof Theory compared with similar skills
SkillStarsUsed inTokensAuto-checkLicenceRepo updated
Proof Theory this skillparcadei/Continuous-Claude-v33.9k2 repos~452Automated safety check: NotesMIT
Proof Strategyjeremylongshore/tons-of-skills-marketplace2.8k—~1.5kAutomated safety check: NotesMIT
Good Strategy Bad Strategywondelai/skills2.4k—~4.8kAutomated safety check: PassMIT
Product Strategyphuryn/pm-skills27k—~1.2kAutomated safety check: PassMIT
Proof Videoopenclaw/openclaw392k—~2.4kAutomated safety check: PassMIT
Vc Problem Solvingwithkynam/vibecode-pro-max-kit1.1k2 repos~1.1kAutomated safety check: PassMIT

Similar skills

  • Proof Strategy

    jeremylongshore/tons-of-skills-marketplace

    Produce a test strategy for a project or feature — risk map, test type decisions, coverage targets, CI config.

    2.8k GitHub stars~1.5k tokensUpdated today
    Testing & QAAuto-check: notes

  • Good Strategy Bad Strategy

    wondelai/skills

    Formulate and audit real strategy using Richard Rumelt's "Good Strategy Bad Strategy": an honest diagnosis, a guiding policy, and coherent action instead of goals, vision, and wishful thinking.

    2.4k GitHub stars~4.8k tokensUpdated 28 days ago
    Business, Finance & HRAuto-check passed

  • Product Strategy

    phuryn/pm-skills

    Create a comprehensive product strategy using the 9-section Product Strategy Canvas — vision, segments, costs, value propositions, trade-offs, metrics, growth, capabilities, and defensibility.

    27k GitHub stars~1.2k tokensUpdated 24 days ago
    Product & Project ManagementAuto-check passed

  • Proof Video

    openclaw/openclaw

    Add subtitles, captions, narration cues, or zoom to a proof video or PR recording using repo-local capture helpers and a system ffmpeg renderer.

    392k GitHub stars~2.4k tokensUpdated today
    Media & CreativeAuto-check passed

  • Vc Problem Solving

    withkynam/vibecode-pro-max-kit

    Apply systematic problem-solving techniques when stuck. An agent skill from withkynam/vibecode-pro-max-kit.

    1.1k GitHub starsUsed in 2 repos~1.1k tokens
    Auto-check passed

  • Launch Strategy

    alirezarezvani/claude-skills

    When the user wants to plan a product launch, feature announcement, or release strategy.

    28k GitHub stars~1.4k tokensUpdated 1 mo ago
    Marketing & SEOAuto-check passed

More from parcadei/Continuous-Claude-v3

All 141 skills in this repo

  • Tldr Deep

    parcadei/Continuous-Claude-v3

    Full 5-layer analysis of a specific function. An agent skill from parcadei/Continuous-Claude-v3.

    3.9k GitHub starsUsed in 2 repos~677 tokens
    Auto-check passed

  • Compound Learnings

    parcadei/Continuous-Claude-v3

    Transform session learnings into permanent capabilities (skills, rules, agents).

    3.9k GitHub starsUsed in 1 repo~1.6k tokens
    Auto-check: notes

  • Gradient Methods

    parcadei/Continuous-Claude-v3

    Problem-solving strategies for gradient methods in optimization

    3.9k GitHub starsUsed in 3 repos~1k tokens
    Auto-check: notes

  • Debug Hooks

    parcadei/Continuous-Claude-v3

    Systematic hook debugging workflow. An agent skill from parcadei/Continuous-Claude-v3.

    3.9k GitHub starsUsed in 1 repo~863 tokens
    Auto-check: notes

  • Math

    parcadei/Continuous-Claude-v3

    Unified math capabilities - computation, solving, and explanation.

    3.9k GitHub starsUsed in 3 repos~1.6k tokens
    Auto-check: notes

  • Math Model Selector

    parcadei/Continuous-Claude-v3

    Routes problems to appropriate mathematical frameworks using expert heuristics

    3.9k GitHub starsUsed in 3 repos~841 tokens
    Auto-check passed

Questions about Proof Theory

What does Proof Theory do?

Problem-solving strategies for proof theory in mathematical logic. Proof Theory is an agent skill from parcadei/Continuous-Claude-v3.

How do I install Proof Theory in Claude Code?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill proof-theory -a claude-code`. Or copy the skill folder (.claude/skills/math/mathematical-logic/proof-theory in parcadei/Continuous-Claude-v3) into .claude/skills/proof-theory in your project. Claude Code loads it when a task matches its description.

How do I install Proof Theory in Codex?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill proof-theory -a codex`. Or copy the skill folder (.claude/skills/math/mathematical-logic/proof-theory in parcadei/Continuous-Claude-v3) into .agents/skills/proof-theory in your project. Codex loads it when a task matches its description.

Can I use Proof Theory in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add parcadei/Continuous-Claude-v3 --skill proof-theory -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/proof-theory, .gemini/skills/proof-theory, .github/skills/proof-theory and .opencode/skills/proof-theory in your project.

What does Proof Theory need to run?

Going by SKILL.md and its folder, Proof Theory needs the command-line tools its instructions call (uv). Our summary lists: Python 3. Its frontmatter pre-approves these tools: Bash, Read.

Does Proof Theory access the network?

SKILL.md contains no URLs. Its commands use uv, which can reach the network depending on how they are called. This is read from the text; nothing was executed.

Is Proof Theory safe to install?

Our automated static check of SKILL.md found notes only (pre-approves every shell command (allowed-tools: bash)), nothing it rates as a warning. It is not a guarantee. Review the folder before installing.

What licence does Proof Theory use?

Proof Theory is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Proof Theory use?

About 452 tokens (SKILL.md is roughly 1.8k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.

What are the alternatives to Proof Theory?

Skills that share tags, products or a category with Proof Theory: Proof Strategy (jeremylongshore/tons-of-skills-marketplace, 2.8k stars), Good Strategy Bad Strategy (wondelai/skills, 2.4k stars), Product Strategy (phuryn/pm-skills, 27k stars) and Proof Video (openclaw/openclaw, 392k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Proof Theory?

parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,940 GitHub stars. The repository holds 141 skills in this directory. The repository was last updated on January 26, 2026.

Source: parcadei/Continuous-Claude-v3 on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.