# Negation

```agda
module foundation-core.negation where
```

<details><summary>Imports</summary>

```agda
open import foundation.universe-levels

open import foundation-core.empty-types
```

</details>

## Idea

The Curry-Howard interpretation of negation in type theory is the interpretation
of the proposition `P ⇒ ⊥` using propositions as types. Thus, the negation of a
type `A` is the type `A → empty`.

## Definition

```agda
¬ : {l : Level} → UU l → UU l
¬ A = A → empty

map-neg :
  {l1 l2 : Level} {P : UU l1} {Q : UU l2} →
  (P → Q) → (¬ Q → ¬ P)
map-neg f nq p = nq (f p)
```