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A first guide to the Lean 4 Proof Assistant. To learn for free on Brilliant, go to https://brilliant.org/AnkYog . You’ll also get 20% off an annual premium subscription. You can try out Lean at Lean 4 Web: https://live.lean-lang.org/ (no installation required) The code for the video is given at https://github.com/AnkYog/LeanTutorial1 You can copy this code into Lean 4 Web to follow along the video. Learning Lean 4: https://leanprover-community.github.i... Proof assistants are insane - Errors that might take months to find can be done in minutes. Math problems become open-source projects as anyone can contribute verified math code. AIs now have an environment to learn and generate verified math proofs. This video is the ultimate tutorial on the Lean 4 proof assistant. By the end, we’ll be able to formalize these three big proofs: 1. An irrational number raised to the power of an irrational number can be rational (using the law of the excluded middle) 2. The existence of infinite primes (using a proof by contradiction) 3. Every onto function has a right inverse (using the axiom of choice) This video was sponsored by Brilliant. Twitter: / ank_yog 00:00 Intro 00:46 Basic Syntax 01:41 Prop-as-Types 03:28 Tactic Mode 04:09 Mathlib 07:00 Intro and Elim Rules 08:52 Proof: 10 is even 09:43 Proof: If a number is even, 2 divides it 12:53 Define PrimeNum 13:19 Proof: 1 is not prime 14:18 Proof: 9 is not prime 16:01 Proof: 5 is prime 19:37 Final 3 Proofs 20:01 Irrational to the power Irrational can be Rational 24:44 There exist infinite primes 31:22 Every onto (surjective) function has a right inverse 34:21 End