Update app.py

app.py

@@ -586,11 +586,13 @@ STRICT REQUIREMENTS:
 {SYMPY_GUIDELINES}
 9. For problems where the subject is Real Analysis and the question type is proof, observe the following guidelines:
     - Give detailed reasoning for each step and justify every step.
-    - In delta-epsilon proofs, explain clearly why a given choice of delta will work
+    - In delta-epsilon proofs, explain clearly why a given choice of delta will work.
+    - Ensure that every bounding argument is explicitly justified
     - Connect each step with a rationale
-    - Always justify the existence of bounds
+    - When using supremum/infimum, explain why it behaves as expected under limits, differentiation, or integration. Provide explicit justification that the supremum argument does not introduce discontinuities.
     - If you conclude certain terms vanish in a limit, clearly justify why
-    - If you state that a function has a certain characteristic, such as being Riemann integrable for example, clearly explain why
+    - If you state that a function has a certain property, such as being Riemann integrable or compact or uniformly continuous for example, clearly explain why
+    - Conclude with a brief intuitive explanation of why the result makes sense, possibly by connecting it to known theorems or simple examples.
     - In notes after the proof, if you observe aspects of the problem that might confuse students, address them."""
 
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