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Theorems · Theorem · logic and foundations

Encodable.axiom_of_choice

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

A constructive version of Classical.axiom_of_choice for Encodable types.

Defined in
Mathlib.Logic.Encodable.Basic
Cited by
1 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext
Assumes
EncodableDecidable
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Encodable.skolem · cited by 0Encodable.skolemEncodable · cited by 140EncodableEncodable.choose_spec · cited by 2Encodable.choose_specEncodable.choose · cited by 2Encodable.chooseEncodable.axiom_of_choiceCITED BYCITES

Cites3

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Cited by1

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