diff --git a/src/Isomorphism.lagda b/src/Isomorphism.lagda index a96dca83..09f0cff7 100644 --- a/src/Isomorphism.lagda +++ b/src/Isomorphism.lagda @@ -24,17 +24,10 @@ open Eq.≡-Reasoning In set theory, two sets are isomorphic if they are in one-to-one correspondence. Here is the formal definition of isomorphism. \begin{code} -record _InverseOf_ {A B : Set} (to : A → B) (from : B → A) : Set where - field - left-inverse-of : ∀ (x : A) → from (to x) ≡ x - right-inverse-of : ∀ (y : B) → to (from y) ≡ y -open _InverseOf_ - record _≃_ (A B : Set) : Set where field to : A → B from : B → A - -- inverse-of : to InverseOf from from∘to : ∀ (x : A) → from (to x) ≡ x to∘from : ∀ (y : B) → to (from y) ≡ y open _≃_ @@ -292,7 +285,16 @@ open ≲-Reasoning Definitions similar to those in this chapter can be found in the standard library. \begin{code} --- import Function.Inverse using (Inverse; _↔_; to; from; inverse-of; left-inverse-of; right-inverse-of) --- import Function.LeftInverse using (LeftInverse; _↞_; to; from; left-inverse-of) +import Function.Inverse using (Inverse; _↔_) +import Function.LeftInverse using (LeftInverse; _↞_) \end{code} +However, those definitions are harder to use, so we will stick with the ones given here. + + +## Unicode + +This chapter uses the following unicode. + + ≃ U+2243 ASYMPTOTICALLY EQUAL TO (\~-) + ≲ U+2272 LESS-THAN OR EQUIVALENT TO (\<~)