37 lines
1.1 KiB
Lean4
37 lines
1.1 KiB
Lean4
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import Game.Levels.Addition.L09add_left_comm
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World "Addition"
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Level 11
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Title "The final boss"
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namespace MyNat
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Introduction
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"
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We saw in the last level that by performing an algorithm repeating `add_assoc`
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and then applying `add_comm` and `add_left_comm` to sort variables, enables
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us to manually prove arbitrary identities involving addition of natural
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numbers. Let's now write a tactic which automates this.
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**TODO** ac_rfl tactic
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"
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macro_rules | `(tactic| ac_rfl) => `(tactic| simp only [add_assoc, add_left_comm, add_comm])
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/-- If $a, b,\ldots h$ are arbitrary natural numbers, we have
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$(d + f) + (h + (a + c)) + (g + e + b) = a + b + c + d + e + f + g + h$. -/
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Statement (a b c d e f g h : ℕ) :
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(d + f) + (h + (a + c)) + (g + e + b) = a + b + c + d + e + f + g + h := by
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ac_rfl
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NewTactic ac_rfl
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LemmaTab "Add"
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Conclusion
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"
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Congratulations! You finished addition world. Now go back to the overworld by clicking the
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home button in the top left. If you want to press on to the final boss
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of the game then go to Multiplication world next. If you are in no hurry, and would like
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to learn some more tactics, then you can try Advanced Addition World.
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"
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