make function types with an empty domain subsingletons
this is useful for the base cases of W types when i try those again closes #23
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2 changed files with 54 additions and 6 deletions
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@ -1,3 +1,5 @@
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load "misc.quox"
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namespace eta {
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def0 Π : (A : ★) → (A → ★) → ★ = λ A B ⇒ (x : A) → B x
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@ -10,4 +12,9 @@ def0 box : (A : ★) → (P : [ω.A] → ★) → (e : [ω.A]) →
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P [case1 e return A of {[x] ⇒ x}] → P e =
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λ A P e p ⇒ p
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-- not exactly η, but kinda related
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def0 from-false : (A : ★) → (P : (False → A) → ★) → (f : False → A) →
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P (λ x ⇒ void A x) → P f =
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λ A P f p ⇒ p
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}
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