big refactor

Dockerfile

@@ -25,4 +25,4 @@ RUN lake clean && lake build
 
 WORKDIR /game/lake-packages/GameServer/server/build/bin/
 
-CMD ./gameserver --server /game/ NNG NNG
+CMD ./gameserver --server /game/ Game Game

Game.lean

@@ -1,15 +1,15 @@
 import GameServer.Commands
 
-import NNG.Levels.Tutorial
+import Game.Levels.Tutorial
-import NNG.Levels.Addition
+import Game.Levels.Addition
-import NNG.Levels.Multiplication
+import Game.Levels.Multiplication
-import NNG.Levels.Power
+import Game.Levels.Power
-import NNG.Levels.Function
+import Game.Levels.Function
-import NNG.Levels.Proposition
+import Game.Levels.Proposition
-import NNG.Levels.AdvProposition
+import Game.Levels.AdvProposition
-import NNG.Levels.AdvAddition
+import Game.Levels.AdvAddition
-import NNG.Levels.AdvMultiplication
+import Game.Levels.AdvMultiplication
---import NNG.Levels.Inequality
+--import Game.Levels.Inequality
 
 Game "NNG"
 Title "Natural Number Game"

Game/Doc/Definitions.lean

@@ -0,0 +1,88 @@
+import GameServer.Commands
+
+-- DefinitionDoc MyNat as "ℕ"
+-- "
+-- The Natural Numbers. These are constructed through:
+
+-- * `(0 : ℕ)`, an element called zero.
+-- * `(succ : ℕ → ℕ)`, the successor function , i.e. one is `succ 0` and two is `succ (succ 0)`.
+-- * `induction` (or `rcases`), tactics to treat the cases $n = 0$ and `n = m + 1` seperately.
+
+-- ## Game Modifications
+
+-- This notation is for our own version of the natural numbers, called `MyNat`.
+-- The natural numbers implemented in Lean's core are called `Nat`.
+
+-- If you end up getting someting of type `Nat` in this game, you probably
+-- need to write `(4 : ℕ)` to force it to be of type `MyNat`.
+
+-- *Write with `\\N`.*
+-- "
+
+-- DefinitionDoc Add as "+" "
+-- Addition on `ℕ` is defined through two axioms:
+
+-- * `add_zero (a : ℕ) : a + 0 = a`
+-- * `add_succ (a d : ℕ) : a + succ d = succ (a + d)`
+-- "
+
+-- DefinitionDoc Pow as "^" "
+-- Power on `ℕ` is defined through two axioms:
+
+-- * `pow_zero (a : ℕ) : a ^ 0 = 1`
+-- * `pow_succ (a b : ℕ) : a ^ succ b = a ^ b * a`
+
+-- ## Game-specific notes
+
+-- Note that you might need to manually specify the type of the first number:
+
+-- ```
+-- (2 : ℕ) ^ 1
+-- ```
+
+-- If you write `2 ^ 1` then lean will try to work in it's inbuild `Nat`, not in
+-- the game's natural numbers `MyNat`.
+-- "
+
+-- DefinitionDoc One as "1" "
+-- `1 : ℕ` is by definition `succ 0`. Use `one_eq_succ_zero`
+-- to change between the two.
+-- "
+
+-- DefinitionDoc False as "False" "
+-- `False` is a proposition that that is always false, in contrast to `True` which is always true.
+
+-- A proof of `False`, i.e. `(h : False)` is used to implement a contradiction: From a proof of `False`
+-- anything follows, *ad absurdum*.
+
+-- For example, \"not\" (`¬ A`) is therefore implemented as `A → False`.
+-- (\"If `A` is true then we have a contradiction.\")
+-- "
+
+-- DefinitionDoc Not as "¬" "
+-- Logical \"not\" is implemented as `¬ A := A → False`.
+
+-- *Write with `\\n`.*
+-- "
+
+-- DefinitionDoc And as "∧" "
+-- (missing)
+
+-- *Write with `\\and`.*
+-- "
+
+-- DefinitionDoc Or as "∨" "
+-- (missing)
+
+-- *Write with `\\or`.*
+-- "
+
+-- DefinitionDoc Iff as "↔" "
+-- (missing)
+
+-- *Write with `\\iff`.*
+-- "
+
+-- DefinitionDoc Mul as "*" ""
+
+-- DefinitionDoc Ne as "≠" ""

Game/Doc/Tactics.lean

@@ -0,0 +1,190 @@
+import GameServer.Commands
+
+-- TacticDoc rfl
+-- "
+-- ## Summary
+
+-- `rfl` proves goals of the form `X = X`.
+
+-- ## Details
+
+-- The `rfl` tactic will close any goal of the form `A = B`
+-- where `A` and `B` are *exactly the same thing*.
+
+-- ## Example:
+-- If it looks like this in the top right hand box:
+-- ```
+-- Objects:
+--   a b c d : ℕ
+-- Goal:
+--   (a + b) * (c + d) = (a + b) * (c + d)
+-- ```
+
+-- then `rfl` will close the goal and solve the level.
+
+-- ## Game modifications
+-- `rfl` in this game is weakened.
+
+-- The real `rfl` could also proof goals of the form `A = B` where the
+-- two sides are not *exactly identical* but merely
+-- *\"definitionally equal\"*. That means the real `rfl`
+-- could prove things like `a + 0 = a`.
+
+-- "
+
+
+-- TacticDoc rw
+-- "
+-- ## Summary
+
+-- If `h` is a proof of `X = Y`, then `rw [h]` will change
+-- all `X`s in the goal to `Y`s.
+
+-- ### Variants
+
+-- * `rw [← h]` (changes `Y` to `X`)
+-- * `rw [h] at h2` (changes `X` to `Y` in hypothesis `h2` instead of the goal)
+-- * `rw [h] at *` (changes `X` to `Y` in the goal and all hypotheses)
+
+-- ## Details
+
+-- The `rw` tactic is a way to do \"substituting in\". There
+-- are two distinct situations where use this tactics.
+
+-- 1) If `h : A = B` is a hypothesis (i.e., a proof of `A = B`)
+-- in your local context (the box in the top right)
+-- and if your goal contains one or more `A`s, then `rw [h]`
+-- will change them all to `B`'s.
+
+-- 2) The `rw` tactic will also work with proofs of theorems
+-- which are equalities (look for them in the drop down
+-- menu on the left, within Theorem Statements).
+-- For example, in world 1 level 4
+-- we learn about `add_zero x : x + 0 = x`, and `rw [add_zero]`
+-- will change `x + 0` into `x` in your goal (or fail with
+-- an error if Lean cannot find `x + 0` in the goal).
+
+-- Important note: if `h` is not a proof of the form `A = B`
+-- or `A ↔ B` (for example if `h` is a function, an implication,
+-- or perhaps even a proposition itself rather than its proof),
+-- then `rw` is not the tactic you want to use. For example,
+-- `rw (P = Q)` is never correct: `P = Q` is the true-false
+-- statement itself, not the proof.
+-- If `h : P = Q` is its proof, then `rw [h]` will work.
+
+-- Pro tip 1: If `h : A = B` and you want to change
+-- `B`s to `A`s instead, try `rw ←h` (get the arrow with `\\l` and
+-- note that this is a small letter L, not a number 1).
+
+-- ### Example:
+-- If it looks like this in the top right hand box:
+
+-- ```
+-- Objects:
+--   x y : ℕ
+-- Assumptions:
+--   h : x = y + y
+-- Goal:
+--   succ (x + 0) = succ (y + y)
+-- ```
+
+-- then
+
+-- `rw [add_zero]`
+
+-- will change the goal into `succ x = succ (y + y)`, and then
+
+-- `rw [h]`
+
+-- will change the goal into `succ (y + y) = succ (y + y)`, which
+-- can be solved with `rfl`.
+
+-- ### Example:
+
+-- You can use `rw` to change a hypothesis as well.
+-- For example, if your local context looks like this:
+
+-- ```
+-- Objects:
+--   x y : ℕ
+-- Assumptions:
+--   h1 : x = y + 3
+--   h2 : 2 * y = x
+-- Goal:
+--   y = 3
+-- ```
+-- then `rw [h1] at h2` will turn `h2` into `h2 : 2 * y = y + 3`.
+
+-- ## Game modifications
+
+-- The real `rw` tactic does automatically try to call `rfl` afterwards. We disabled this
+-- feature for the game.
+-- "
+
+-- TacticDoc induction
+-- "
+-- "
+
+-- TacticDoc exact
+-- "
+-- "
+
+-- TacticDoc apply
+-- "
+-- "
+
+-- TacticDoc intro
+-- "
+-- "
+
+-- TacticDoc «have»
+-- "
+-- "
+
+-- TacticDoc constructor
+-- "
+-- "
+
+-- TacticDoc rcases
+-- "
+-- "
+
+-- TacticDoc left
+-- "
+-- "
+
+-- TacticDoc revert
+-- "
+-- "
+
+-- TacticDoc tauto
+-- "
+-- "
+
+-- TacticDoc use
+-- "
+-- "
+
+-- TacticDoc right
+-- "
+-- "
+
+-- TacticDoc by_cases
+-- "
+-- "
+
+-- TacticDoc contradiction
+-- "
+-- "
+
+-- TacticDoc exfalso
+-- "
+-- "
+
+-- TacticDoc simp
+-- "
+-- "
+
+-- TacticDoc «repeat»
+-- "
+-- "

Game/Levels/Addition.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Addition.Level_6
+import Game.Levels.Addition.Level_6
 
 Game "NNG"
 World "Addition"
@@ -33,4 +33,4 @@ a reminder of the things you're now equipped with which we'll need in this world
 
 
 You will also find all this information in your Inventory to read the documentation.
-"
+"

Game/Levels/Addition/Level_1.lean

@@ -1,11 +1,12 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Addition"
 Level 1
 Title "the induction tactic."
 
+--namespace MyNat
 open MyNat
 
 Introduction
@@ -33,7 +34,6 @@ To prove `0 + n = n` we need to use induction on $n$. While we're here,
 note that `zero_add` is about zero add something, and `add_zero` is about something add zero.
 The names of the proofs tell you what the theorems are. Anyway, let's prove `0 + n = n`.
 "
-
 Statement MyNat.zero_add
 "For all natural numbers $n$, we have $0 + n = n$."
     (n : ℕ) : 0 + n = n := by

Game/Levels/Addition/Level_2.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Addition.Level_1
+import Game.Levels.Addition.Level_1
 
 Game "NNG"
 World "Addition"

Game/Levels/Addition/Level_3.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Addition.Level_2
+import Game.Levels.Addition.Level_2
 
 Game "NNG"
 World "Addition"

Game/Levels/Addition/Level_4.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Addition.Level_3
+import Game.Levels.Addition.Level_3
 
 Game "NNG"
 World "Addition"

Game/Levels/Addition/Level_5.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Addition.Level_4
+import Game.Levels.Addition.Level_4
 
 Game "NNG"
 World "Addition"

Game/Levels/Addition/Level_6.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Addition.Level_5
+import Game.Levels.Addition.Level_5
 
 Game "NNG"
 World "Addition"

Game/Levels/AdvAddition.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_13
+import Game.Levels.AdvAddition.Level_13
 
 Game "NNG"
 World "AdvAddition"
@@ -25,4 +25,4 @@ For `zero_ne_succ` the trick is that $X\\ne Y$ is *defined to mean*
 $X = Y\\implies{\\tt False}$. If you have played through proposition world,
 you now have the required Lean skills (i.e., you know the required
 tactics) to work with these implications.
-"
+"

Game/Levels/AdvAddition/Level_1.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.AdvAddition
+import Game.MyNat.AdvAddition
-import NNG.Levels.Addition
+import Game.Levels.Addition
 
 Game "NNG"
 World "AdvAddition"

Game/Levels/AdvAddition/Level_10.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_9
+import Game.Levels.AdvAddition.Level_9
 import Std.Tactic.RCases
 
 Game "NNG"

Game/Levels/AdvAddition/Level_11.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_10
+import Game.Levels.AdvAddition.Level_10
 
 Game "NNG"
 World "AdvAddition"

Game/Levels/AdvAddition/Level_12.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_11
+import Game.Levels.AdvAddition.Level_11
 
 
 Game "NNG"

Game/Levels/AdvAddition/Level_13.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_12
+import Game.Levels.AdvAddition.Level_12
 
 Game "NNG"
 World "AdvAddition"

Game/Levels/AdvAddition/Level_2.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_1
+import Game.Levels.AdvAddition.Level_1
 
 
 Game "NNG"

Game/Levels/AdvAddition/Level_3.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_2
+import Game.Levels.AdvAddition.Level_2
 
 
 Game "NNG"

Game/Levels/AdvAddition/Level_4.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_3
+import Game.Levels.AdvAddition.Level_3
 
 Game "NNG"
 World "AdvAddition"

Game/Levels/AdvAddition/Level_5.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_4
+import Game.Levels.AdvAddition.Level_4
 
 
 Game "NNG"

Game/Levels/AdvAddition/Level_6.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_5
+import Game.Levels.AdvAddition.Level_5
 
 Game "NNG"
 World "AdvAddition"

Game/Levels/AdvAddition/Level_7.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_6
+import Game.Levels.AdvAddition.Level_6
 
 Game "NNG"
 World "AdvAddition"

Game/Levels/AdvAddition/Level_8.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_7
+import Game.Levels.AdvAddition.Level_7
 
 
 Game "NNG"

Game/Levels/AdvAddition/Level_9.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvAddition.Level_8
+import Game.Levels.AdvAddition.Level_8
 
 Game "NNG"
 World "AdvAddition"

Game/Levels/AdvMultiplication.lean

@@ -1,7 +1,7 @@
-import NNG.Levels.AdvMultiplication.Level_1
+import Game.Levels.AdvMultiplication.Level_1
-import NNG.Levels.AdvMultiplication.Level_2
+import Game.Levels.AdvMultiplication.Level_2
-import NNG.Levels.AdvMultiplication.Level_3
+import Game.Levels.AdvMultiplication.Level_3
-import NNG.Levels.AdvMultiplication.Level_4
+import Game.Levels.AdvMultiplication.Level_4
 
 
 Game "NNG"
@@ -14,4 +14,4 @@ Welcome to Advanced Multiplication World! Before attempting this
 world you should have completed seven other worlds, including
 Multiplication World and Advanced Addition World. There are four
 levels in this world.
-"
+"

Game/Levels/AdvMultiplication/Level_1.lean

@@ -1,5 +1,5 @@
-import NNG.Levels.Multiplication
+import Game.Levels.Multiplication
-import NNG.Levels.AdvAddition
+import Game.Levels.AdvAddition
 
 Game "NNG"
 World "AdvMultiplication"

Game/Levels/AdvMultiplication/Level_2.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvMultiplication.Level_1
+import Game.Levels.AdvMultiplication.Level_1
 
 Game "NNG"
 World "AdvMultiplication"

Game/Levels/AdvMultiplication/Level_3.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvMultiplication.Level_2
+import Game.Levels.AdvMultiplication.Level_2
 
 
 Game "NNG"

Game/Levels/AdvMultiplication/Level_4.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.AdvMultiplication.Level_3
+import Game.Levels.AdvMultiplication.Level_3
 
 Game "NNG"
 World "AdvMultiplication"

Game/Levels/AdvProposition.lean

@@ -0,0 +1,23 @@
+import Game.Levels.AdvProposition.Level_1
+import Game.Levels.AdvProposition.Level_2
+import Game.Levels.AdvProposition.Level_3
+import Game.Levels.AdvProposition.Level_4
+import Game.Levels.AdvProposition.Level_5
+import Game.Levels.AdvProposition.Level_6
+import Game.Levels.AdvProposition.Level_7
+import Game.Levels.AdvProposition.Level_8
+import Game.Levels.AdvProposition.Level_9
+import Game.Levels.AdvProposition.Level_10
+
+
+Game "NNG"
+World "AdvProposition"
+Title "Advanced Proposition World"
+
+Introduction
+"
+In this world we will learn five key tactics needed to solve all the
+levels of the Natural Number Game, namely `constructor`, `rcases`, `left`, `right`, and `exfalso`.
+These, and `use` (which we'll get to in Inequality World) are all the
+tactics you will need to beat all the levels of the game.
+"

Game/Levels/AdvProposition/Level_1.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"

Game/Levels/AdvProposition/Level_10.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"
@@ -19,7 +19,7 @@ constructive logic).
 
 Statement
 "If $P$ and $Q$ are true/false statements, then
-$$(\\lnot Q\\implies \\lnot P)\\implies(P\\implies Q).$$ 
+$$(\\lnot Q\\implies \\lnot P)\\implies(P\\implies Q).$$
 "
     (P Q : Prop) : (¬ Q → ¬ P) → (P → Q) := by
   Hint "For example, you could start as always with
@@ -62,4 +62,3 @@ Get to it via the main menu.
 
 -- In fact the tactic `tauto` just kills this goal (and many other logic goals) immediately. You'll be
 -- able to use it from now on.
-

Game/Levels/AdvProposition/Level_2.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"
@@ -46,4 +46,3 @@ Statement -- and_symm
   exact p
 
 NewTactic rcases
-

Game/Levels/AdvProposition/Level_3.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"
@@ -18,7 +18,7 @@ Statement --and_trans
 $Q\\land R$ together imply $P\\land R$."
     (P Q R : Prop) : P ∧ Q → Q ∧ R → P ∧ R := by
   Hint "Here's a trick:
-  
+
   Your first steps would probably be
   ```
   intro h

Game/Levels/AdvProposition/Level_4.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"

Game/Levels/AdvProposition/Level_5.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"

Game/Levels/AdvProposition/Level_6.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"
@@ -36,4 +36,3 @@ Statement
 
 NewTactic left right
 NewDefinition Or
-

Game/Levels/AdvProposition/Level_7.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"

Game/Levels/AdvProposition/Level_8.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"

Game/Levels/AdvProposition/Level_9.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "AdvProposition"

Game/Levels/Function.lean

@@ -1,12 +1,12 @@
-import NNG.Levels.Function.Level_1
+import Game.Levels.Function.Level_1
-import NNG.Levels.Function.Level_2
+import Game.Levels.Function.Level_2
-import NNG.Levels.Function.Level_3
+import Game.Levels.Function.Level_3
-import NNG.Levels.Function.Level_4
+import Game.Levels.Function.Level_4
-import NNG.Levels.Function.Level_5
+import Game.Levels.Function.Level_5
-import NNG.Levels.Function.Level_6
+import Game.Levels.Function.Level_6
-import NNG.Levels.Function.Level_7
+import Game.Levels.Function.Level_7
-import NNG.Levels.Function.Level_8
+import Game.Levels.Function.Level_8
-import NNG.Levels.Function.Level_9
+import Game.Levels.Function.Level_9
 
 
 Game "NNG"
@@ -38,4 +38,4 @@ internally Lean stores $P$ as a \"Type\" and $p$ as a \"term\", and it uses `p :
 to mean \"$p$ is a term of type $P$\", Lean's way of expressing the idea that $p$
 is an element of the set $P$. You have seen this already – Lean has
 been writing `n : ℕ` to mean that $n$ is a natural number.
-"
+"

Game/Levels/Function/Level_1.lean

@@ -1,4 +1,4 @@
-import NNG.Metadata
+import Game.Metadata
 
 -- TODO: Cannot import level from different world.
 

Game/Levels/Function/Level_2.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Multiplication
+import Game.MyNat.Multiplication
 
 Game "NNG"
 World "Function"

Game/Levels/Function/Level_3.lean

@@ -1,4 +1,4 @@
-import NNG.Metadata
+import Game.Metadata
 
 Game "NNG"
 World "Function"

Game/Levels/Function/Level_4.lean

@@ -1,4 +1,4 @@
-import NNG.Metadata
+import Game.Metadata
 
 Game "NNG"
 World "Function"

Game/Levels/Function/Level_5.lean

@@ -1,4 +1,4 @@
-import NNG.Metadata
+import Game.Metadata
 
 Game "NNG"
 World "Function"

Game/Levels/Function/Level_6.lean

@@ -1,4 +1,4 @@
-import NNG.Metadata
+import Game.Metadata
 
 Game "NNG"
 World "Function"

Game/Levels/Function/Level_7.lean

@@ -1,4 +1,4 @@
-import NNG.Metadata
+import Game.Metadata
 
 Game "NNG"
 World "Function"
@@ -20,7 +20,7 @@ functor.
 "
 
 Statement
-"Whatever the sets $P$ and $Q$ and $F$ are, we 
+"Whatever the sets $P$ and $Q$ and $F$ are, we
 make an element of $\\operatorname{Hom}(\\operatorname{Hom}(P,Q),
 \\operatorname{Hom}(\\operatorname{Hom}(Q,F),\\operatorname{Hom}(P,F)))$."
     (P Q F : Type) : (P → Q) → ((Q → F) → (P → F)) := by

Game/Levels/Function/Level_8.lean

@@ -1,4 +1,4 @@
-import NNG.Metadata
+import Game.Metadata
 
 Game "NNG"
 World "Function"

Game/Levels/Function/Level_9.lean

@@ -1,4 +1,4 @@
-import NNG.Metadata
+import Game.Metadata
 
 Game "NNG"
 World "Function"

Game/Levels/Inequality.lean

@@ -1,20 +1,20 @@
-import NNG.Levels.Inequality.Level_1
+import Game.Levels.Inequality.Level_1
--- import NNG.Levels.Inequality.Level_2
+-- import Game.Levels.Inequality.Level_2
--- import NNG.Levels.Inequality.Level_3
+-- import Game.Levels.Inequality.Level_3
--- import NNG.Levels.Inequality.Level_4
+-- import Game.Levels.Inequality.Level_4
--- import NNG.Levels.Inequality.Level_5
+-- import Game.Levels.Inequality.Level_5
--- import NNG.Levels.Inequality.Level_6
+-- import Game.Levels.Inequality.Level_6
--- import NNG.Levels.Inequality.Level_7
+-- import Game.Levels.Inequality.Level_7
--- import NNG.Levels.Inequality.Level_8
+-- import Game.Levels.Inequality.Level_8
--- import NNG.Levels.Inequality.Level_9
+-- import Game.Levels.Inequality.Level_9
--- import NNG.Levels.Inequality.Level_10
+-- import Game.Levels.Inequality.Level_10
--- import NNG.Levels.Inequality.Level_11
+-- import Game.Levels.Inequality.Level_11
--- import NNG.Levels.Inequality.Level_12
+-- import Game.Levels.Inequality.Level_12
--- import NNG.Levels.Inequality.Level_13
+-- import Game.Levels.Inequality.Level_13
--- import NNG.Levels.Inequality.Level_14
+-- import Game.Levels.Inequality.Level_14
--- import NNG.Levels.Inequality.Level_15
+-- import Game.Levels.Inequality.Level_15
--- import NNG.Levels.Inequality.Level_16
+-- import Game.Levels.Inequality.Level_16
--- import NNG.Levels.Inequality.Level_17
+-- import Game.Levels.Inequality.Level_17
 
 Game "NNG"
 World "Inequality"
@@ -28,7 +28,7 @@ A new import, giving us a new definition. If `a` and `b` are naturals,
 `∃ (c : mynat), b = a + c`
 
 The upside-down E means \"there exists\". So in words, $a\\le b$
-if and only if there exists a natural $c$ such that $b=a+c$. 
+if and only if there exists a natural $c$ such that $b=a+c$.
 
 If you really want to change an `a ≤ b` to `∃ c, b = a + c` then
 you can do so with `rw le_iff_exists_add`:
@@ -46,5 +46,5 @@ example of this below.
 A new construction like `∃` means that we need to learn how to manipulate it.
 There are two situations. Firstly we need to know how to solve a goal
 of the form `⊢ ∃ c, ...`, and secondly we need to know how to use a hypothesis
-of the form `∃ c, ...`. 
+of the form `∃ c, ...`.
-"
+"

Game/Levels/Inequality/Level_1.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 --import Mathlib.Tactic.Ring
 
 Game "NNG"

Game/Levels/Inequality/Level_10.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_11.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_12.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_13.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_14.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_15.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_16.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_17.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_2.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
 import Mathlib.Tactic.Use
 
 Game "NNG"

Game/Levels/Inequality/Level_3.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 import Std.Tactic.RCases
 
 Game "NNG"

Game/Levels/Inequality/Level_4.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_5.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_6.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_7.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_8.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Inequality/Level_9.lean

@@ -1,6 +1,6 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.LE
+import Game.MyNat.LE
-import NNG.Tactic.Use
+import Game.Tactic.Use
 
 Game "NNG"
 World "Inequality"

Game/Levels/Multiplication.lean

@@ -1,12 +1,12 @@
-import NNG.Levels.Multiplication.Level_1
+import Game.Levels.Multiplication.Level_1
-import NNG.Levels.Multiplication.Level_2
+import Game.Levels.Multiplication.Level_2
-import NNG.Levels.Multiplication.Level_3
+import Game.Levels.Multiplication.Level_3
-import NNG.Levels.Multiplication.Level_4
+import Game.Levels.Multiplication.Level_4
-import NNG.Levels.Multiplication.Level_5
+import Game.Levels.Multiplication.Level_5
-import NNG.Levels.Multiplication.Level_6
+import Game.Levels.Multiplication.Level_6
-import NNG.Levels.Multiplication.Level_7
+import Game.Levels.Multiplication.Level_7
-import NNG.Levels.Multiplication.Level_8
+import Game.Levels.Multiplication.Level_8
-import NNG.Levels.Multiplication.Level_9
+import Game.Levels.Multiplication.Level_9
 
 
 Game "NNG"
@@ -34,4 +34,4 @@ is commutative and associative, but as well as that we will
 need to prove facts about the relationship between multiplication
 and addition, for example `a * (b + c) = a * b + a * c`, so now
 there is a lot more to do. Good luck!
-"
+"

Game/Levels/Multiplication/Level_1.lean

@@ -1,5 +1,5 @@
-import NNG.MyNat.Multiplication
+import Game.MyNat.Multiplication
-import NNG.Levels.Addition
+import Game.Levels.Addition
 
 Game "NNG"
 World "Multiplication"

Game/Levels/Multiplication/Level_2.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Multiplication.Level_1
+import Game.Levels.Multiplication.Level_1
 
 Game "NNG"
 World "Multiplication"

Game/Levels/Multiplication/Level_3.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Multiplication.Level_2
+import Game.Levels.Multiplication.Level_2
 
 Game "NNG"
 World "Multiplication"

Game/Levels/Multiplication/Level_4.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Multiplication.Level_3
+import Game.Levels.Multiplication.Level_3
 
 Game "NNG"
 World "Multiplication"

Game/Levels/Multiplication/Level_5.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Multiplication.Level_4
+import Game.Levels.Multiplication.Level_4
 
 Game "NNG"
 World "Multiplication"

Game/Levels/Multiplication/Level_6.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Multiplication.Level_5
+import Game.Levels.Multiplication.Level_5
 
 Game "NNG"
 World "Multiplication"

Game/Levels/Multiplication/Level_7.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Multiplication.Level_6
+import Game.Levels.Multiplication.Level_6
 
 Game "NNG"
 World "Multiplication"

Game/Levels/Multiplication/Level_8.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Multiplication.Level_7
+import Game.Levels.Multiplication.Level_7
 
 Game "NNG"
 World "Multiplication"
@@ -43,4 +43,4 @@ level of the world, and then we can beef up the power of `simp`.
 "
 
 -- TODO: collectible
--- instance mynat.comm_semiring : comm_semiring mynat := by structure_helper
+-- instance mynat.comm_semiring : comm_semiring mynat := by structure_helper

Game/Levels/Multiplication/Level_9.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Multiplication.Level_8
+import Game.Levels.Multiplication.Level_8
 
 Game "NNG"
 World "Multiplication"

Game/Levels/Power.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Power.Level_8
+import Game.Levels.Power.Level_8
 
 Game "NNG"
 World "Power"
@@ -26,4 +26,4 @@ Collectibles are indication that we are proving the right things.
 The levels in this world were designed by Sian Carey, a UROP student
 at Imperial College London, funded by a Mary Lister McCammon Fellowship,
 in the summer of 2019. Thanks Sian!
-"
+"

Game/Levels/Power/Level_1.lean

@@ -1,5 +1,5 @@
-import NNG.Levels.Multiplication
+import Game.Levels.Multiplication
-import NNG.MyNat.Power
+import Game.MyNat.Power
 
 Game "NNG"
 World "Power"

Game/Levels/Power/Level_2.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Power.Level_1
+import Game.Levels.Power.Level_1
 
 Game "NNG"
 World "Power"

Game/Levels/Power/Level_3.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Power.Level_2
+import Game.Levels.Power.Level_2
 
 Game "NNG"
 World "Power"

Game/Levels/Power/Level_4.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Power.Level_3
+import Game.Levels.Power.Level_3
 
 
 Game "NNG"

Game/Levels/Power/Level_5.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Power.Level_4
+import Game.Levels.Power.Level_4
 
 
 Game "NNG"

Game/Levels/Power/Level_6.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Power.Level_5
+import Game.Levels.Power.Level_5
 
 Game "NNG"
 World "Power"

Game/Levels/Power/Level_7.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Power.Level_6
+import Game.Levels.Power.Level_6
 
 Game "NNG"
 World "Power"

Game/Levels/Power/Level_8.lean

@@ -1,4 +1,4 @@
-import NNG.Levels.Power.Level_7
+import Game.Levels.Power.Level_7
 -- import Mathlib.Tactic.Ring
 
 Game "NNG"

Game/Levels/Proposition.lean

@@ -1,12 +1,12 @@
-import NNG.Levels.Proposition.Level_1
+import Game.Levels.Proposition.Level_1
-import NNG.Levels.Proposition.Level_2
+import Game.Levels.Proposition.Level_2
-import NNG.Levels.Proposition.Level_3
+import Game.Levels.Proposition.Level_3
-import NNG.Levels.Proposition.Level_4
+import Game.Levels.Proposition.Level_4
-import NNG.Levels.Proposition.Level_5
+import Game.Levels.Proposition.Level_5
-import NNG.Levels.Proposition.Level_6
+import Game.Levels.Proposition.Level_6
-import NNG.Levels.Proposition.Level_7
+import Game.Levels.Proposition.Level_7
-import NNG.Levels.Proposition.Level_8
+import Game.Levels.Proposition.Level_8
-import NNG.Levels.Proposition.Level_9 -- `cc` is not ported
+import Game.Levels.Proposition.Level_9 -- `cc` is not ported
 
 
 Game "NNG"
@@ -45,4 +45,4 @@ Here `P` is the true/false statement (the statement of proposition), and `p` is
 It's like `P` being the set and `p` being the element. In fact computer scientists
 sometimes think about the following analogy: propositions are like sets,
 and their proofs are like their elements.
-"
+"

Game/Levels/Proposition/Level_1.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Proposition"

Game/Levels/Proposition/Level_2.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Proposition"
@@ -31,7 +31,7 @@ discovered by Goedel -- these are not relevant here. Imagine we are
 working in a fixed model of mathematics, and when I say \"proof\"
 I actually mean \"truth in the model\", or \"proof in the metatheory\".
 
-## Rule of thumb: 
+## Rule of thumb:
 
 If your goal is to prove `P → Q` (i.e. that $P\\implies Q$)
 then `intro p`, meaning \"assume $p$ is a proof of $P$\", will make progress.

Game/Levels/Proposition/Level_3.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Proposition"

Game/Levels/Proposition/Level_4.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Proposition"

Game/Levels/Proposition/Level_5.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Proposition"
@@ -71,7 +71,7 @@ $P\\implies Q\\implies R$ (they are not really interested in proving abstract
 propositions, they would rather work with concrete ones such as Fermat's Last Theorem),
 so they do not have a convention for where the brackets go. It's important to
 remember Lean's convention though, or else you will get confused. If your goal
-is `P → Q → R` then you need to know whether `intro h` will create `h : P` or `h : P → Q`. 
+is `P → Q → R` then you need to know whether `intro h` will create `h : P` or `h : P → Q`.
 Make sure you understand which one.
 
 "

Game/Levels/Proposition/Level_6.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Proposition"

Game/Levels/Proposition/Level_7.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Proposition"
@@ -24,4 +24,3 @@ Statement
   apply hqr
   apply hpq
   exact p
-

Game/Levels/Proposition/Level_8.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Proposition"
@@ -69,4 +69,4 @@ NewTactic «repeat»
 NewDefinition False Not
 
 Conclusion "If you used `rw [Not]` or `rw [Not] at h` anywhere, go through your proof in
-the \"Editor Mode\" and delete them all. Observe that your proof still works."
+the \"Editor Mode\" and delete them all. Observe that your proof still works."

Game/Levels/Proposition/Level_9.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Addition
+import Game.MyNat.Addition
 
 Game "NNG"
 World "Proposition"

Game/Levels/Tutorial.lean

@@ -1,7 +1,7 @@
-import NNG.Levels.Tutorial.Level_1
+import Game.Levels.Tutorial.Level_1
-import NNG.Levels.Tutorial.Level_2
+import Game.Levels.Tutorial.Level_2
-import NNG.Levels.Tutorial.Level_3
+import Game.Levels.Tutorial.Level_3
-import NNG.Levels.Tutorial.Level_4
+import Game.Levels.Tutorial.Level_4
 
 Game "NNG"
 World "Tutorial"
@@ -12,4 +12,4 @@ Introduction
 In this world we start introducing the natural numbers `ℕ` and addition.
 
 Click on \"Next\" to dive right into it!
-"
+"

Game/Levels/Tutorial/Level_1.lean

@@ -1,5 +1,5 @@
-import NNG.Metadata
+import Game.Metadata
-import NNG.MyNat.Multiplication
+import Game.MyNat.Multiplication
 
 Game "NNG"
 World "Tutorial"