Étienne Miquey

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The dependent sum type of Martin-Löf's type theory provides a strong existential elimination , which allows to prove the full axiom of choice. The proof is simple and constructive: AC A := λH.(λx. wit(Hx), λx. prf(Hx)) : ∀x A ∃y B P (x, y) → ∃f A→B ∀x A P (x, f (x)) where wit and prf are the first and second projections of a strong existential quantifier.(More)
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