Datasets:
File size: 2,103 Bytes
50b3efe e21f84c 50b3efe e21f84c |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 |
---
license: cc0-1.0
tags:
- theorem-proving
- formal-methods
- metamath
- logic
- set-theory
- mathematics
task_categories:
- text-generation
- feature-extraction
language:
- en
size_categories:
- 10K<n<100K
---
# Metamath
A structured dataset of formally verified theorems and axioms from **Metamath**, one of the largest collections of rigorously verified mathematics in the world.
## Source
- **Repository:** https://github.com/metamath/set.mm
- **Website:** https://us.metamath.org
- **License:** CC0 1.0 (Public Domain)
## Statistics
| Property | Value |
|----------|-------|
| **Total Entries** | 72,962 |
| **Theorems** | 69,394 |
| **Axioms** | 3,568 |
| **Docstring Coverage** | 95.6% |
### Database Distribution
| Database | Entries | Description |
|----------|---------|-------------|
| set.mm | 49,410 | Classical logic and ZFC set theory |
| iset.mm | 15,953 | Intuitionistic logic and set theory |
| nf.mm | 6,245 | New Foundations set theory |
| ql.mm | 1,176 | Quantum logic |
| hol.mm | 178 | Higher-order logic |
## Schema
| Column | Type | Description |
|--------|------|-------------|
| `fact` | string | Statement in form "label : assertion" |
| `type` | string | "theorem" or "axiom" |
| `library` | string | Source database (set, iset, nf, ql, hol) |
| `imports` | list[string] | Empty (Metamath uses single-file structure) |
| `filename` | string | Source .mm file |
| `symbolic_name` | string | Theorem/axiom label |
| `docstring` | string | Description with contributor attribution |
## Metamath Syntax
Metamath uses a minimal syntax:
- `|-` indicates a provable statement
- `/\` is conjunction (AND)
- `\/` is disjunction (OR)
- `->` is implication
- `<->` is biconditional
- `-.` is negation
- `A.` is universal quantifier
- `E.` is existential quantifier
## Notable Theorems
The set.mm database includes proofs of major results:
- Fundamental Theorem of Calculus
- Prime Number Theorem
- Cauchy-Riemann equations
- Hahn-Banach theorem
- And thousands more...
## Creator
Charles Norton ([phanerozoic](https://huggingface.co/phanerozoic))
|