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40 lines
1.0 KiB
Plaintext
40 lines
1.0 KiB
Plaintext
import NNG.Metadata
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import NNG.MyNat.Addition
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Game "NNG"
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World "AdvProposition"
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Level 1
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Title "the `split` tactic"
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open MyNat
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Introduction
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"
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In this world we will learn five key tactics needed to solve all the
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levels of the Natural Number Game, namely `split`, `cases`, `left`, `right`, and `exfalso`.
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These, and `use` (which we'll get to in Inequality World) are all the
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tactics you will need to beat all the levels of the game.
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## Level 1: the `split` tactic.
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The logical symbol `∧` means \"and\". If $P$ and $Q$ are propositions, then
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$P\\land Q$ is the proposition \"$P$ and $Q$\". If your *goal* is `P ∧ Q` then
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you can make progress with the `split` tactic, which turns one goal `⊢ P ∧ Q`
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into two goals, namely `⊢ P` and `⊢ Q`. In the level below, after a `split`,
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you will be able to finish off the goals with the `exact` tactic.
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"
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Statement
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"If $P$ and $Q$ are true, then $P\\land Q$ is true."
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(P Q : Prop) (p : P) (q : Q) : P ∧ Q := by
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constructor
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exact p
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exact q
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NewTactic constructor
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Conclusion
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"
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"
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