diff --git a/Game/Levels/Implication/L03apply.lean b/Game/Levels/Implication/L03apply.lean index 7068e56..babf455 100644 --- a/Game/Levels/Implication/L03apply.lean +++ b/Game/Levels/Implication/L03apply.lean @@ -39,8 +39,11 @@ NewTactic apply Introduction " -In this level one of our hypotheses is an *implication*. We can use this -hypothesis with the `apply` tactic. +In this level, the hypotheses `h2` is an *implication*. It says +that *if* `x = 37` *then* `y = 42`. We can use this +hypothesis with the `apply` tactic. Remember you can click on +`apply` or any other tactic on the right to see a detailed explanation +of what it does, with examples. " /-- If $x=37$ and we know that $x=37\implies y=42$ then we can deduce $y=42$. -/ diff --git a/Game/Levels/Implication/L07intro2.lean b/Game/Levels/Implication/L07intro2.lean index 5ddb7c4..fdc4de8 100644 --- a/Game/Levels/Implication/L07intro2.lean +++ b/Game/Levels/Implication/L07intro2.lean @@ -16,7 +16,7 @@ Statement (x : ℕ) : x + 1 = y + 1 → x = y := by Hint (hidden := true) "Start with `intro h` to assume the hypothesis." intro h Hint (hidden := true) "Now `repeat rw [← succ_eq_add_one] at h` is the quickest way to - change `succ x = succ y`." + change `h` to `succ x = succ y`." repeat rw [← succ_eq_add_one] at h Hint (hidden := true) "Now `apply succ_inj at h` to cancel the `succ`s." apply succ_inj at h