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Update ImpIntro.lean
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Trequetrum authored Dec 23, 2023
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Expand Up @@ -29,12 +29,3 @@ The concept behind an implication, such as `A → B`, is that there exists an ex
Where this game abstracted the idea of `A ∧ B` into a tuple holding evidence for `A` and evidence for `B`. The way we store evidence like `A → B` is with a function that takes evidence for `A` and produces evidence for `B`.\\
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`h : A → B` reads `h` is evidence for `A → B`. While real-world analogues can be anything, the abstract machinery used in this game will always be a function.
# An Aside for Programmers
If you've done some programming, this might be interesting context. It won't be important for completing any levels.\\
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In the broader context of the Lean programming language, any function that returns evidence for a proposition, is itself also evidence for a proposition. We won't be building any other sort of function in this game.\\
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The function space constructor “`→`” is not overloaded. We won't get into the weeds; suffice it to say that the rules for implication in a proof system for natural deduction correspond exactly to the rules governing abstraction and application for functions.
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