diff --git a/.i18n/en/Game.pot b/.i18n/en/Game.pot index 1efd046..f4b2da4 100644 --- a/.i18n/en/Game.pot +++ b/.i18n/en/Game.pot @@ -721,7 +721,8 @@ msgid "## Summary\n" msgstr "" #: Game.Levels.Addition.L05add_right_comm -msgid "`add_right_comm a b c` is a proof that `(a + b) + c = (a + c) + b`\n" +msgid "" +"`add_right_comm a b c` is a proof that `(a + b) + c = (a + c) + b`\n" "\n" "In Lean, `a + b + c` means `(a + b) + c`, so this result gets displayed\n" "as `a + b + c = a + c + b`." @@ -927,7 +928,8 @@ msgid "`mul_ne_zero a b` is a proof that if `a ≠ 0` and `b ≠ 0` then `a * b msgstr "" #: Game.Levels.Multiplication.L07mul_add -msgid "Multiplication distributes\n" +msgid "" +"Multiplication distributes\n" "over addition on the left.\n" "\n" "`mul_add a b c` is the proof that `a * (b + c) = a * b + a * c`." @@ -962,7 +964,9 @@ msgid "add_left_eq_self" msgstr "" #: Game.Levels.Multiplication -msgid "How should we define `37 * x`? Just like addition, we need to give definitions\n" +msgid "" +"How should we define `37 * x`? Just like addition, we need to give " +"definitions\n" "when $x=0$ and when $x$ is a successor.\n" "\n" "The zero case is easy: we define `37 * 0` to be `0`. Now say we know\n" @@ -974,8 +978,10 @@ msgid "How should we define `37 * x`? Just like addition, we need to give defini " * `mul_zero a : a * 0 = 0`\n" " * `mul_succ a d : a * succ d = a * d + a`\n" "\n" -"In this world, we must not only prove facts about multiplication like `a * b = b * a`,\n" -"we must also prove facts about how multiplication interacts with addition, like `a * (b + c) = a * b + a * c`.\n" +"In this world, we must not only prove facts about multiplication like `a * b " +"= b * a`,\n" +"we must also prove facts about how multiplication interacts with addition, " +"like `a * (b + c) = a * b + a * c`.\n" "Let's get started." msgstr "" @@ -1367,7 +1373,8 @@ msgid "Now `rw [← two_eq_succ_one]` will change `succ 1` into `2`." msgstr "" #: Game.Levels.Implication.L04succ_inj -msgid "# Statement\n" +msgid "" +"# Statement\n" "\n" "If $a$ and $b$ are numbers, then\n" "`succ_inj a b` is the proof that\n" @@ -1384,7 +1391,8 @@ msgid "# Statement\n" "You can think of `succ_inj` itself as a proof; it is the proof\n" "that `succ` is an injective function. In other words,\n" "`succ_inj` is a proof of\n" -"$\\forall a, b \\in \\mathbb{N}, ( \\operatorname{succ}(a) = \\operatorname{succ}(b)) \\implies a=b$.\n" +"$\\forall a, b \\in \\mathbb{N}, ( \\operatorname{succ}(a) = " +"\\operatorname{succ}(b)) \\implies a=b$.\n" "\n" "`succ_inj` was postulated as an axiom by Peano, but\n" "in Lean it can be proved using `pred`, a mathematically\n" @@ -1734,7 +1742,8 @@ msgid "If `a` and `b` are numbers, then `succ_inj a b` is a proof\n" msgstr "" #: Game.Levels.Algorithm.L02add_algo1 -msgid "In some later worlds, we're going to see some much nastier levels,\n" +msgid "" +"In some later worlds, we're going to see some much nastier levels,\n" "like `(a + a + 1) + (b + b + 1) = (a + b + 1) + (a + b + 1)`.\n" "Brackets need to be moved around, and variables need to be swapped.\n" "\n" @@ -2145,7 +2154,8 @@ msgid "We now have enough to prove that multiplication is associative,\n" msgstr "" #: Game.Levels.AdvAddition.L04add_right_eq_self -msgid "`add_right_eq_self x y` is the theorem that $x + y = x\\implies y=0.$\n" +msgid "" +"`add_right_eq_self x y` is the theorem that $x + y = x\\implies y=0.$\n" "Two ways to do it spring to mind; I'll mention them when you've solved it." msgstr "" @@ -2167,23 +2177,33 @@ msgid "Now finish in one line." msgstr "" #: Game.Levels.AdvAddition.L05add_right_eq_zero -msgid "The next result we'll need in `≤` World is that if `a + b = 0` then `a = 0` and `b = 0`.\n" +msgid "" +"The next result we'll need in `≤` World is that if `a + b = 0` then `a = 0` " +"and `b = 0`.\n" "Let's prove one of these facts in this level, and the other in the next.\n" "\n" "## A new tactic: `cases`\n" "\n" -"The `cases` tactic will split an object or hypothesis up into the possible ways\n" +"The `cases` tactic will split an object or hypothesis up into the possible " +"ways\n" "that it could have been created.\n" "\n" -"For example, sometimes you want to deal with the two cases `b = 0` and `b = succ d` separately,\n" -"but don't need the inductive hypothesis `hd` that comes with `induction b with d hd`.\n" -"In this situation you can use `cases b with d` instead. There are two ways to make\n" -"a number: it's either zero or a successor. So you will end up with two goals, one\n" +"For example, sometimes you want to deal with the two cases `b = 0` and `b = " +"succ d` separately,\n" +"but don't need the inductive hypothesis `hd` that comes with `induction b " +"with d hd`.\n" +"In this situation you can use `cases b with d` instead. There are two ways " +"to make\n" +"a number: it's either zero or a successor. So you will end up with two " +"goals, one\n" "with `b = 0` and one with `b = succ d`.\n" "\n" -"Another example: if you have a hypothesis `h : False` then you are done, because a false statement implies\n" -"any statement. Here `cases h` will close the goal, because there are *no* ways to\n" -"make a proof of `False`! So you will end up with no goals, meaning you have proved everything." +"Another example: if you have a hypothesis `h : False` then you are done, " +"because a false statement implies\n" +"any statement. Here `cases h` will close the goal, because there are *no* " +"ways to\n" +"make a proof of `False`! So you will end up with no goals, meaning you have " +"proved everything." msgstr "" #: Game @@ -2240,7 +2260,8 @@ msgid "Let's now begin our approach to the final boss,\n" msgstr "" #: Game.Levels.AdvAddition.L06add_left_eq_zero -msgid "How about this for a proof:\n" +msgid "" +"How about this for a proof:\n" "\n" "```\n" "rw [add_comm]\n" @@ -2640,7 +2661,8 @@ msgid "Let's now learn about Peano's second axiom for addition, `add_succ`." msgstr "" #: Game.Levels.LessOrEqual.L09succ_le_succ -msgid "Here's my proof:\n" +msgid "" +"Here's my proof:\n" "```\n" "cases hx with d hd\n" "use d\n" @@ -2980,15 +3002,18 @@ msgid "For all natural numbers $a$ and $b$, we have\n" msgstr "" #: Game.Levels.AdvMultiplication.L06mul_right_eq_one -msgid "# Summary\n" +msgid "" +"# Summary\n" "\n" -"The `have` tactic can be used to add new hypotheses to a level, but of course\n" +"The `have` tactic can be used to add new hypotheses to a level, but of " +"course\n" "you have to prove them.\n" "\n" "\n" "## Example\n" "\n" -"The simplest usage is like this. If you have `a` in your context and you execute\n" +"The simplest usage is like this. If you have `a` in your context and you " +"execute\n" "\n" "`have ha : a = 0`\n" "\n" @@ -3302,7 +3327,8 @@ msgid "`zero_mul x` is the proof that `0 * x = 0`.\n" msgstr "" #: Game -msgid "# Welcome to the Natural Number Game\n" +msgid "" +"# Welcome to the Natural Number Game\n" "#### An introduction to mathematical proof.\n" "\n" "In this game, we will build the basic theory of the natural\n" @@ -3322,12 +3348,15 @@ msgid "# Welcome to the Natural Number Game\n" "Note: this is a new Lean 4 version of the game containing several\n" "worlds which were not present in the old Lean 3 version. More new worlds\n" "such as Strong Induction World, Even/Odd World and Prime Number World\n" -"are in development; if you want to see their state or even help out, checkout\n" -"out the [issues in the github repo](https://github.com/leanprover-community/NNG4/issues).\n" +"are in development; if you want to see their state or even help out, " +"checkout\n" +"out the [issues in the github repo](https://github.com/leanprover-community/" +"NNG4/issues).\n" "\n" "## More\n" "\n" -"Click on the three lines in the top right and select \"Game Info\" for resources,\n" +"Click on the three lines in the top right and select \"Game Info\" for " +"resources,\n" "links, and ways to interact with the Lean community." msgstr ""