import GameServer.Commands import NNG.Levels.Tutorial import NNG.Levels.Addition import NNG.Levels.Multiplication import NNG.Levels.Power import NNG.Levels.Function import NNG.Levels.Proposition import NNG.Levels.AdvProposition import NNG.Levels.AdvAddition import NNG.Levels.AdvMultiplication import NNG.Levels.Inequality Game "NNG" Title "Natural Number Game" Introduction " # Natural Number Game ##### version 2.0.1 Welcome to the natural number game -- a game which shows the power of induction. In this game, you get own version of the natural numbers, in an interactive theorem prover called Lean. Your version of the natural numbers satisfies something called the principle of mathematical induction, and a couple of other things too (Peano's axioms). Unfortunately, nobody has proved any theorems about these natural numbers yet! For example, addition will be defined for you, but nobody has proved that `x + y = y + x` yet. This is your job. You're going to prove mathematical theorems using the Lean theorem prover. In other words, you're going to solve levels in a computer game. You're going to prove these theorems using *tactics*. The introductory world, Tutorial World, will take you through some of these tactics. During your proofs, the assistant shows your \"goal\" (i.e. what you're supposed to be proving) and keeps track of the state of your proof. Click on the blue \"Tutorial World\" to start your journey! ## Save progress The game stores your progress locally in your browser storage. If you delete it, your progress will be lost! (usually the *website data* gets deleted together with cookies.) ## Credits * **Content and Lean3-version:** Kevin Buzzard, Mohammad Pedramfar * **Game Engine:** Alexander Bentkamp, Jon Eugster, Patrick Massot ## Resources * The [Lean Zulip chat] forum * [Original Lean3 version](https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/) * [A textbook-style (lean4) version of the NN-game](https://lovettsoftware.com/NaturalNumbers/TutorialWorld/Level1.lean.html) " Path Tutorial → Addition → Function → Proposition → AdvProposition → AdvAddition Path AdvAddition → AdvMultiplication → Inequality Path Addition → Multiplication → AdvMultiplication Path Multiplication → Power MakeGame