## Screenshot: Code Editor with Mathematical Theorems
### Overview
The image shows a code editor interface displaying three mathematical theorems implemented in a programming language. The code includes arithmetic operations, modulo calculations, and exponentiation, with results annotated. The interface uses syntax highlighting (yellow for theorem names, green for calculations, white for other text).
### Components/Axes
- **Theorem Labels**:
- `mathd_numbertheory_254`
- `mathd_numbertheory_342`
- `mathd_algebra_304`
- **Calculations**:
- `(239 + 174 + 83) % 10`
- `54 % 6`
- `91^2`
- **Results**:
- `6`
- `0`
- `8281`
- **Annotations**:
- `: by norm_num` (repeated for all theorems)
### Content Details
1. **Theorem `mathd_numbertheory_254`**:
- Calculation: `(239 + 174 + 83) % 10`
- Result: `6`
- Color Coding:
- Theorem name: Yellow
- Calculation: Green
- Result: White
2. **Theorem `mathd_numbertheory_342`**:
- Calculation: `54 % 6`
- Result: `0`
- Color Coding:
- Theorem name: Yellow
- Calculation: Green
- Result: White
3. **Theorem `mathd_algebra_304`**:
- Calculation: `91^2`
- Result: `8281`
- Color Coding:
- Theorem name: Yellow
- Calculation: Green
- Result: White
### Key Observations
- All theorems follow the structure: `theorem <name> : <calculation> = <result> := by norm_num`.
- The `norm_num` annotation suggests a normalization function applied to results.
- Results are integers, with no decimal or fractional values.
### Interpretation
This code snippet appears to be part of a mathematical library or proof assistant, verifying arithmetic properties:
- **Modulo Operations**: The first two theorems test divisibility (e.g., `54 % 6 = 0` confirms 54 is divisible by 6).
- **Exponentiation**: The third theorem calculates `91² = 8281`, a basic algebraic identity.
- **Normalization**: The `norm_num` function may standardize results for consistency in downstream computations.
The theorems are likely automated tests or formal proofs, ensuring correctness of mathematical operations in a computational context. The use of `norm_num` implies a focus on standardized output formats, critical for integration with other systems or algorithms.
