Agent Skills › Prismer-AI/Prismer › theorem-proving

theorem-proving

GitHub

辅助构建、验证和排版数学证明，结合逻辑推理与计算验证。支持直接证明、反证法等，利用 LaTeX 排版及 Jupyter 进行符号或数值验证，适用于定理证明和猜想验证场景。

docker/templates/mathematician/skills/theorem-proving/SKILL.md Prismer-AI/Prismer

Trigger Scenarios

用户要求证明某个定理验证数学论据的正确性构建形式化证明通过计算检查证明正确性

Install

npx skills add Prismer-AI/Prismer --skill theorem-proving -g -y

More Options

Non-standard path

npx skills add https://github.com/Prismer-AI/Prismer/tree/main/docker/templates/mathematician/skills/theorem-proving -g -y

Use without installing

npx skills use Prismer-AI/Prismer@theorem-proving

指定 Agent (Claude Code)

npx skills add Prismer-AI/Prismer --skill theorem-proving -a claude-code -g -y

安装 repo 全部 skill

npx skills add Prismer-AI/Prismer --all -g -y

预览 repo 内 skill

npx skills add Prismer-AI/Prismer --list

SKILL.md

Frontmatter

{
    "name": "theorem-proving",
    "description": "Construct and verify mathematical proofs using LaTeX typesetting and computational verification via jupyter_execute. Use when the user asks to prove a theorem, verify a mathematical argument, construct a formal proof, or check proof correctness computationally."
}

Theorem Proving Skill

Description

Assist with constructing, verifying, and typesetting mathematical proofs. Combines rigorous logical reasoning with computational verification.

Tools Used

latex_compile - Typeset proofs and mathematical documents (auto-switches to LaTeX editor)
update_latex - Write LaTeX content to the editor for review before compiling
jupyter_execute - Verify results computationally (sympy, numpy)
update_notes - Write proof outlines and scratch work to Notes editor

Capabilities

Proof Construction

Direct proofs, proof by contradiction, proof by induction
Constructive and non-constructive existence proofs
Epsilon-delta arguments in analysis
Diagram chasing in algebra/category theory

Verification

Symbolic computation to check algebraic manipulations
Numerical examples to build intuition
Counterexample search for false conjectures
Automated checking of special cases

Typesetting

AMS theorem environments (theorem, lemma, proposition, corollary, definition)
Proper mathematical notation and spacing
Cross-references and equation numbering
Multi-part proofs with clear structure

Usage Patterns

Prove a Theorem

When user says: "Prove that [statement]"

Clarify definitions and assumptions
Outline proof strategy
Construct formal proof step-by-step
Verify key steps computationally if possible
Typeset in LaTeX with proper environments

Verify a Conjecture

When user says: "Is it true that [conjecture]?"

Test with specific examples (jupyter_execute)
Search for counterexamples
Attempt proof if examples support it
Report findings with confidence level

Tool Examples

Typeset a theorem in LaTeX

update_latex content="\\documentclass{article}\n\\usepackage{amsthm,amsmath}\n\\newtheorem{theorem}{Theorem}\n\\begin{document}\n\\begin{theorem}\nFor all $n \\geq 1$, $\\sum_{k=1}^{n} k = \\frac{n(n+1)}{2}$.\n\\end{theorem}\n\\begin{proof}\nBy induction on $n$. Base case $n=1$: $1 = \\frac{1 \\cdot 2}{2}$. Inductive step: assume true for $n$, then $\\sum_{k=1}^{n+1} k = \\frac{n(n+1)}{2} + (n+1) = \\frac{(n+1)(n+2)}{2}$.\n\\end{proof}\n\\end{document}"

Verify computationally with SymPy

jupyter_execute code="from sympy import symbols, summation, simplify\nk, n = symbols('k n', positive=True, integer=True)\nresult = simplify(summation(k, (k, 1, n)) - n*(n+1)/2)\nprint(f'Difference: {result}')  # Should be 0"