Hello Everyone ,

I could appreciate some advice from more seasoned users as I work on a project that includes formalising multiple mathematical conclusions using Coq proof assistance.

My primary area of expertise is mathematics, so even though I have a bit experience with Coq, Iâ€™m currently learning about its best practices and more sophisticated capabilities.

I am concentrating on theorems from actual analysis that deal with sequences and series.

**Here are a few areas where Iâ€™m having trouble:**

**Formalising Convergence and Limits:** Iâ€™m attempting to codify the idea of a limit for a real number series. Although I can grasp the mathematical definition, Iâ€™m having trouble translating it into Coq. I would be grateful for any guidance on managing Îµ-Î´ arguments in The coq and determining limits.

**Interacting using Real Numbers:** I am finding that several operations and proofs are tedious when working with real numbers, thus I am utilising the R type from the Coq standard library. Exist any hints or resources that make utilising actual values in Coq easier?

**Inductive Illustrations and Infinite Sequence:** I have to demonstrate the convergence and sum of an infinite series, among other things. Iâ€™m still not quite sure how inductive proofs work in Coq, especially when it comes to sequences.

How can I apply induction techniques in Coq successfully for these kinds of proofs?

**General Best Practices:** It would be very beneficial to receive any general guidance on the best ways to organise proofs, handle hypotheses, and steer clear of typical mistakes.

I checked this: https://mathoverflow.net/questions/59520/how-true-are-tableau-theorems-proved-by-coq

If you know of any helpful tutorials or resources that would be appropriate for someone in my situation, please let me know.

Thank you in advance for your suggestions.