27 lines
642 B
Lean4
27 lines
642 B
Lean4
import Game.Metadata
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import Game.MyNat.Addition
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World "Proposition"
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Level 7
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Title "(P → Q) → ((Q → R) → (P → R))"
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open MyNat
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Introduction ""
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/-- From $P \implies Q$ and $Q \implies R$ we can deduce $P \implies R$. -/
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Statement
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(P Q R : Prop) : (P → Q) → ((Q → R) → (P → R)) := by
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Hint (hidden := true)"If you start with `intro hpq` and then `intro hqr`
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the dust will clear a bit."
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intro hpq
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Hint (hidden := true) "Now try `intro hqr`."
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intro hqr
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Hint "So this level is really about showing transitivity of $\\implies$,
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if you like that sort of language."
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intro p
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apply hqr
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apply hpq
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exact p
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