Abstract

This post highlights what you can do when writing mathematicial proofs (whether by hand or using a proof assistant), I hope this post helps.

Have a set of methods ready

What do you want to prove exactly? What's the tactic? What are you allowed to assume? These are the three questions you should ask yourself first before going any further.

Re-read Carefully

This save you a lot of time and avoid mistakes that can be catched now for a smoother process. Now going to the next section...

Examples of proof methods

• Proof by Construction.
• Proof by Induction.
• Brouwerian counterexample (Goodman–Myhill theorem).
• Proof by Contradiction.

Have someone else read it

The biggest one after having plans, a proof that isn't verified isn't really a proof. So you better off having someone read it and validate OR highlight issues you can fix.

Read, Read, Read!

On formal proof writing and what you're trying to prove. Don't assume anything, look it up. It will greatly help you fullfill these proofs.

Conclusion

While a short post, I hope this helps you getting started on formal proof writing and related tasks. Below are some resources for that:

• https://web.stanford.edu/class/archive/cs/cs103/cs103.1202/lectures/01/Small01.pdf (Mathematicial Proofs)
• https://shop.elsevier.com/books/an-introduction-to-writing-mathematical-proofs/bieske/978-0-443-43924-7 (An Introduction to Writing Mathematical Proofs)
• https://en.wikipedia.org/wiki/Constructive_proof (Constructive proof)