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39 lines
934 B
Plaintext
39 lines
934 B
Plaintext
import NNG.Metadata
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import NNG.MyNat.Addition
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Game "NNG"
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World "Function"
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Level 7
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Title "(P → Q) → ((Q → F) → (P → F))"
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open MyNat
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Introduction
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"
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Have you noticed that, in stark contrast to earlier worlds,
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we are not amassing a large collection of useful theorems?
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We really are just constructing abstract levels with sets and
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functions, and then solving them and never using the results
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ever again. Here's another one, which should hopefully be
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very easy for you now. Advanced mathematician viewers will
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know it as contravariance of $\\operatorname{Hom}(\\cdot,F)$
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functor.
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"
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Statement
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"Whatever the sets $P$ and $Q$ and $F$ are, we
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make an element of $\\operatorname{Hom}(\\operatorname{Hom}(P,Q),
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\\operatorname{Hom}(\\operatorname{Hom}(Q,F),\\operatorname{Hom}(P,F)))$."
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(P Q F : Type) : (P → Q) → ((Q → F) → (P → F)) := by
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intro f
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intro h
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intro p
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apply h
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apply f
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exact p
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Conclusion
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"
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"
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