The weak limited principle of omniscience

module foundation.weak-limited-principle-of-omniscience where

Imports

open import elementary-number-theory.natural-numbers

open import foundation.disjunction
open import foundation.negation

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

open import univalent-combinatorics.standard-finite-types

Idea

The Weak Limited Principle of Omniscience asserts that for any sequence f : ℕ → Fin 2 either f n ＝ 0 for all n : ℕ or not. In particular, it is a restricted form of the law of excluded middle.

Definition

WLPO : UU lzero
WLPO =
  (f : ℕ → Fin 2) →
  type-disj-Prop
    ( Π-Prop ℕ (λ n → Id-Prop (Fin-Set 2) (f n) (zero-Fin 1)))
    ( neg-Prop (Π-Prop ℕ (λ n → Id-Prop (Fin-Set 2) (f n) (zero-Fin 1))))