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--- |
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license: cc0-1.0 |
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tags: |
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- theorem-proving |
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- formal-methods |
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- metamath |
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- logic |
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- set-theory |
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- mathematics |
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task_categories: |
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- text-generation |
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- feature-extraction |
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language: |
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- en |
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size_categories: |
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- 10K<n<100K |
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--- |
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# Metamath |
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A structured dataset of formally verified theorems and axioms from **Metamath**, one of the largest collections of rigorously verified mathematics in the world. |
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## Source |
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- **Repository:** https://github.com/metamath/set.mm |
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- **Website:** https://us.metamath.org |
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- **License:** CC0 1.0 (Public Domain) |
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## Statistics |
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| Property | Value | |
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|----------|-------| |
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| **Total Entries** | 72,962 | |
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| **Theorems** | 69,394 | |
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| **Axioms** | 3,568 | |
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| **Docstring Coverage** | 95.6% | |
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### Database Distribution |
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| Database | Entries | Description | |
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|----------|---------|-------------| |
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| set.mm | 49,410 | Classical logic and ZFC set theory | |
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| iset.mm | 15,953 | Intuitionistic logic and set theory | |
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| nf.mm | 6,245 | New Foundations set theory | |
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| ql.mm | 1,176 | Quantum logic | |
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| hol.mm | 178 | Higher-order logic | |
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## Schema |
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| Column | Type | Description | |
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|--------|------|-------------| |
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| `fact` | string | Statement in form "label : assertion" | |
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| `type` | string | "theorem" or "axiom" | |
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| `library` | string | Source database (set, iset, nf, ql, hol) | |
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| `imports` | list[string] | Empty (Metamath uses single-file structure) | |
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| `filename` | string | Source .mm file | |
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| `symbolic_name` | string | Theorem/axiom label | |
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| `docstring` | string | Description with contributor attribution | |
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## Metamath Syntax |
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Metamath uses a minimal syntax: |
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- `|-` indicates a provable statement |
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- `/\` is conjunction (AND) |
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- `\/` is disjunction (OR) |
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- `->` is implication |
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- `<->` is biconditional |
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- `-.` is negation |
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- `A.` is universal quantifier |
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- `E.` is existential quantifier |
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## Notable Theorems |
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The set.mm database includes proofs of major results: |
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- Fundamental Theorem of Calculus |
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- Prime Number Theorem |
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- Cauchy-Riemann equations |
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- Hahn-Banach theorem |
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- And thousands more... |
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## Creator |
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Charles Norton ([phanerozoic](https://huggingface.co/phanerozoic)) |
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