Skip to content

Implement proofs for ContinuousWithinAt.tfae and Exercises 9.4.6 & 9.4.7#438

Closed
younesselassri08-maker wants to merge 1 commit intoteorth:mainfrom
younesselassri08-maker:patch-1
Closed

Implement proofs for ContinuousWithinAt.tfae and Exercises 9.4.6 & 9.4.7#438
younesselassri08-maker wants to merge 1 commit intoteorth:mainfrom
younesselassri08-maker:patch-1

Conversation

@younesselassri08-maker
Copy link

This PR implements missing proofs for Section 9.4. Specifically, I established the equivalence of continuity definitions in "ContinuousWithinAt.tfae" (Prop 9.4.7) by bridging the topological, sequential, and metric definitions via manual logical rewriting. I implemented the proof for "ContinuousOn.restrict" (Exercise 9.4.7), demonstrating that a function continuous on a set X remains continuous on any subset Y of X. Finally, I completed Exercise 9.4.6 by proving the continuity of polynomial functions "Continuous.polynomial" using induction and the course's sum/product rules.

@teorth
Copy link
Owner

teorth commented Feb 7, 2026

Thank you, but the intention of the master repository is not to fill in the sorries that are assigned to exercises. You are free to create forks of the master repository with these proofs. You can also add hints or tips to the docstring at the start of the lean files for the exercises (this is only fully implemented for the first few chapters, but feel free to add hints for later chapters as well).

@teorth teorth closed this Feb 7, 2026
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

None yet

Development

Successfully merging this pull request may close these issues.

2 participants