The weak limited principle of omniscience

Content created by Fredrik Bakke, Jonathan Prieto-Cubides and Egbert Rijke.

Created on 2022-08-08.
Last modified on 2024-04-11.

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


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 =
    (   Fin 2)
    ( λ f 
        ( ∀'   n  Id-Prop (Fin-Set 2) (f n) (zero-Fin 1)))
        ( ¬' (∀'   n  Id-Prop (Fin-Set 2) (f n) (zero-Fin 1)))))

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

See also

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