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Add isPropIsEquivOver. #993

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Jun 1, 2023
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6 changes: 6 additions & 0 deletions Cubical/Foundations/Equiv/Dependent.agda
Original file line number Diff line number Diff line change
Expand Up @@ -16,6 +16,7 @@ open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Equiv.HalfAdjoint
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Transport

Expand Down Expand Up @@ -54,6 +55,11 @@ isEquivOver :
→ Type _
isEquivOver {A = A} F = (a : A) → isEquiv (F a)

isPropIsEquivOver :
{f : A → B}
(F : mapOver f P Q)
→ isProp (isEquivOver {Q = Q} F)
isPropIsEquivOver F = isPropΠ (λ a → isPropIsEquiv (F a))

-- Relative version of section and retract

Expand Down