There arguably has been a failure of communication between type theorists and "traditional" mathematicians, but Buzzard unfortunately has a bit of a history of vocally spreading less-than-accurate information about type…
Note that this proof doesn't require the axiom of choice, only excluded middle.
That sounds about correct. The naïve interpretation of AC that interprets ∃ as Σ and ∀ as Π amounts to the trivial fact that Π distributes over Σ, which has little to do with any choice principle. If you instead…
There arguably has been a failure of communication between type theorists and "traditional" mathematicians, but Buzzard unfortunately has a bit of a history of vocally spreading less-than-accurate information about type…
Note that this proof doesn't require the axiom of choice, only excluded middle.
That sounds about correct. The naïve interpretation of AC that interprets ∃ as Σ and ∀ as Π amounts to the trivial fact that Π distributes over Σ, which has little to do with any choice principle. If you instead…