\n ## Text Block: Mathematical Theorems ### Overview The image displays a screenshot of a terminal or code editor window containing three mathematical theorems, likely generated by a formal proof assistant system. Each theorem is presented with a unique identifier, a mathematical statement, and a proof attribution. ### Components/Axes There are no axes or charts in this image. The components are simply lines of text. ### Detailed Analysis or Content Details The text content is as follows: 1. `theorem mathd_numbertheory_254 : (239 + 174 + 83) % 10 = 6 := by norm_num` * Theorem identifier: `mathd_numbertheory_254` * Mathematical statement: `(239 + 174 + 83) % 10 = 6` * Proof attribution: `by norm_num` 2. `theorem mathd_numbertheory_342 : 54 % 6 = 0 := by norm_num` * Theorem identifier: `mathd_numbertheory_342` * Mathematical statement: `54 % 6 = 0` * Proof attribution: `by norm_num` 3. `theorem mathd_algebra_304 : 91^2 = 8281 := by norm_num` * Theorem identifier: `mathd_algebra_304` * Mathematical statement: `91^2 = 8281` * Proof attribution: `by norm_num` ### Key Observations All three theorems are proven using the `norm_num` proof tactic or strategy. The theorems cover number theory and algebra. The theorem identifiers suggest a systematic naming convention. ### Interpretation The image demonstrates the output of a formal theorem prover. The `norm_num` attribution indicates that the proofs were likely generated using a normalization or simplification tactic applied to numerical expressions. The theorems themselves are relatively simple, likely used as examples or tests within the system. The consistent use of `norm_num` suggests it is a fundamental or frequently used proof strategy within this system. The identifiers suggest the theorems are part of a larger library or database of formalized mathematical knowledge.