fixed backticks in code spans
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@ -70,7 +70,7 @@ data Type : Set where
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\end{code}
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Terms have six constructs. Three are for the core lambda calculus:
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* Variables, `\` x`
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* Variables, `` ` x ``
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* Abstractions, `λ[ x ∶ A ] N`
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* Applications, `L · M`
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and three are for the base type, booleans:
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@ -285,7 +285,7 @@ outermost term is now `if_then_else_`, which is typed using `𝔹-E`. The
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?2 : ∅ , x ∶ 𝔹 ⊢ true ∶ 𝔹
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Again we fill in the three holes by typing C-c C-r in each. Agda observes
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that `\` x`, `false`, and `true` are typed using `Ax`, `𝔹-I₂`, and
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that `` ` x ``, `false`, and `true` are typed using `Ax`, `𝔹-I₂`, and
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`𝔹-I₁` respectively. The `Ax` rule in turn takes an argument, to show
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that `(∅ , x ∶ 𝔹) x = just 𝔹`, which can in turn be specified with a
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hole. After filling in all holes, the term is as above.
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@ -266,7 +266,7 @@ _Proof_: We show, by induction on the proof that `x` appears
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free in `M`, that, for all contexts `Γ`, if `M` is well
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typed under `Γ`, then `Γ` assigns some type to `x`.
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- If the last rule used was `free-\``, then `M = \` x`, and from
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- If the last rule used was `` free-` ``, then `M = `` `x ``, and from
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the assumption that `M` is well typed under `Γ` we have
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immediately that `Γ` assigns a type to `x`.
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@ -452,7 +452,7 @@ we show that if `∅ ⊢ V ∶ A` then `Γ ⊢ N [ x := V ] ∶ B`.
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- If `N` is a variable there are two cases to consider,
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depending on whether `N` is `x` or some other variable.
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- If `N = \` x`, then from `Γ , x ∶ A ⊢ x ∶ B`
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- If `N = `` `x ``, then from `Γ , x ∶ A ⊢ x ∶ B`
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we know that looking up `x` in `Γ , x : A` gives
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`just B`, but we already know it gives `just A`;
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applying injectivity for `just` we conclude that `A ≡ B`.
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