Theorems · Theorem · logic and foundations

Encodable.skolem

∀ {α : Type u_1} {β : α → Type u_2} {P : (x : α) → β x → Prop} [(a : α) → Encodable (β a)]
  [(x : α) → (y : β x) → Decidable (P x y)], (∀ (x : α), ∃ y, P x y) ↔ ∃ f, ∀ (x : α), P x (f x)

A constructive version of Classical.skolem for Encodable types.

Defined in: Mathlib.Logic.Encodable.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 24 from the axioms · uses propext
Assumes: Encodable Decidable

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Encodablestatement and proof · cited by 140
Encodable.axiom_of_choiceproof · cited by 1

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