an example got out of sync with the text
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@ -341,7 +341,7 @@ lambda abstraction results in a single-entry table that maps the input
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`v` to the output `w`, provided that evaluating the body in an
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environment with `v` bound to its parameter produces the output `w`.
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As a simple example of this rule, we can see that the identity function
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maps `⊥` to `⊥`.
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maps `⊥` to `⊥` and also that it maps `⊥ ↦ ⊥` to `⊥ ↦ ⊥`.
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```
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id : ∅ ⊢ ★
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@ -349,11 +349,11 @@ id = ƛ # 0
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```
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```
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denot-id : ∀ {γ v} → γ ⊢ id ↓ v ↦ v
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denot-id = ↦-intro var
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denot-id1 : ∀ {γ} → γ ⊢ id ↓ ⊥ ↦ ⊥
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denot-id1 = ↦-intro var
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denot-id-two : ∀ {γ v w} → γ ⊢ id ↓ (v ↦ v) ⊔ (w ↦ w)
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denot-id-two = ⊔-intro denot-id denot-id
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denot-id2 : ∀ {γ} → γ ⊢ id ↓ (⊥ ↦ ⊥) ↦ (⊥ ↦ ⊥)
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denot-id2 = ↦-intro var
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```
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Of course, we will need tables with many rows to capture the meaning
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@ -366,12 +366,12 @@ abstraction, it pre-evaluates the function on a bunch of randomly
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chosen arguments, using many instances of the rule `↦-intro`, and then
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joins them into a big table using many instances of the rule `⊔-intro`.
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In the following we show that the identity function produces a table
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containing both of the previous results, `⊥ ↦ ⊥` and `(⊥ ↦ ⊥) ↦ (⊥ ↦
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⊥)`.
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containing both of the previous results, `⊥ ↦ ⊥` and
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`(⊥ ↦ ⊥) ↦ (⊥ ↦ ⊥)`.
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```
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denot-id3 : `∅ ⊢ id ↓ (⊥ ↦ ⊥) ⊔ (⊥ ↦ ⊥) ↦ (⊥ ↦ ⊥)
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denot-id3 = denot-id-two
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denot-id3 = ⊔-intro denot-id1 denot-id2
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```
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We most often think of the judgment `γ ⊢ M ↓ v` as taking the
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