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38 lines
667 B
Plaintext
38 lines
667 B
Plaintext
import NNG.Metadata
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import NNG.MyNat.Addition
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Game "NNG"
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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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"
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If you start with `intro hpq` and then `intro hqr`
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the dust will clear a bit and the level will look like this:
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```
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P Q R : Prop,
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hpq : P → Q,
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hqr : Q → R
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⊢ P → R
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```
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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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"
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Statement
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"From $P\\implies Q$ and $Q\\implies R$ we can deduce $P\\implies R$."
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(P Q R : Prop) : (P → Q) → ((Q → R) → (P → R)) := by
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intro hpq hqr
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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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Conclusion
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"
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"
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