⚠ You are viewing the Cubical library. Back to Bedrock
Bedrock
English · 中文 · 日本語
On this page
Menu
Interactive contents
  • Origin
  • Reading routes
  • Dependency graph
  • Glossary
Current route:Common foundations
  • Prelude
  • Impredicativity
  • The classical boundary
  • Choice
  • The object language
  • Structures
  • Semantics
  • The Lévy hierarchy
  • Absoluteness
  • Models of ZF and ZFC
  • Syntax as sets
module Cubical.Functions.Implicit where

open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism

implicit≃Explicit : ∀ {ℓ ℓ'} {A : Type ℓ} {B : A → Type ℓ'}
  → ({a : A} → B a) ≃ ((a : A) → B a)
implicit≃Explicit = isoToEquiv isom
  where
  isom : Iso _ _
  Iso.fun isom f a = f
  Iso.inv isom f = f _
  Iso.rightInv isom f = funExt λ _ → refl
  Iso.leftInv isom f = implicitFunExt refl

Powered by Outcrop
© 2026 Bedrock Institute · content licensed CC BY-NC-SA 4.0 · Source · llms.txt