This is an archived version pinned as of the submission of my master's thesis. An up-to-date version may be found online.

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.universal-quantification
open import foundation.universe-levels

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

open import univalent-combinatorics.standard-finite-types

Statement

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.

WLPO-Prop : Prop lzero
WLPO-Prop =
  ∀'
    ( ℕ → Fin 2)
    ( λ f →
      disjunction-Prop
        ( ∀' ℕ (λ n → Id-Prop (Fin-Set 2) (f n) (zero-Fin 1)))
        ( ¬' (∀' ℕ (λ n → Id-Prop (Fin-Set 2) (f n) (zero-Fin 1)))))

WLPO : UU lzero
WLPO = type-Prop WLPO-Prop

See also