added universe polymorphism to Equality
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@ -400,7 +400,7 @@ Nonetheless, rewrite is a vital part of the Agda toolkit,
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as earlier examples have shown.
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as earlier examples have shown.
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## Extensionality {!#extensionality}
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## Extensionality {#extensionality}
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Extensionality asserts that they only way to distinguish functions is
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Extensionality asserts that they only way to distinguish functions is
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by applying them; if two functions applied to the same argument always
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by applying them; if two functions applied to the same argument always
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@ -624,3 +624,4 @@ This chapter uses the following unicode.
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⟩ U+27E9 MATHEMATICAL RIGHT ANGLE BRACKET (\>)
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⟩ U+27E9 MATHEMATICAL RIGHT ANGLE BRACKET (\>)
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∎ U+220E END OF PROOF (\qed)
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∎ U+220E END OF PROOF (\qed)
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≐ U+2250 APPROACHES THE LIMIT (\.=)
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≐ U+2250 APPROACHES THE LIMIT (\.=)
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ℓ U+2113 SCRIPT SMALL L (\ell)
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@ -17,6 +17,7 @@ distributivity.
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import Relation.Binary.PropositionalEquality as Eq
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import Relation.Binary.PropositionalEquality as Eq
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open Eq using (_≡_; refl; sym; trans; cong; cong-app)
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open Eq using (_≡_; refl; sym; trans; cong; cong-app)
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open Eq.≡-Reasoning
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open Eq.≡-Reasoning
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open Level
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\end{code}
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\end{code}
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## Function composition
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## Function composition
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@ -851,7 +851,7 @@ replacement for `_×_`. As a consequence, demonstrate an isomorphism relating
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### Exercise (`¬Any≃All¬`)
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### Exercise (`¬Any≃All¬`)
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We first generalise composition to arbitrary levels, using
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First generalise composition to arbitrary levels, using
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[universe polymorphism][unipoly].
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[universe polymorphism][unipoly].
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\begin{code}
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\begin{code}
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_∘′_ : ∀ {ℓ₁ ℓ₂ ℓ₃ : Level} {A : Set ℓ₁} {B : Set ℓ₂} {C : Set ℓ₃} → (B → C) → (A → B) → A → C
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_∘′_ : ∀ {ℓ₁ ℓ₂ ℓ₃ : Level} {A : Set ℓ₁} {B : Set ℓ₂} {C : Set ℓ₃} → (B → C) → (A → B) → A → C
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