Proper subsets

module foundation.proper-subtypes where

Imports

open import foundation.complements-subtypes
open import foundation.inhabited-subtypes

open import foundation-core.propositions
open import foundation-core.subtypes
open import foundation-core.universe-levels

Idea

A subtype of a type is said to be proper if its complement is inhabited.

is-proper-subtype-Prop :
  {l1 l2 : Level} {A : UU l1} → subtype l2 A → Prop (l1 ⊔ l2)
is-proper-subtype-Prop P =
  is-inhabited-subtype-Prop (complement-subtype P)