24 lines
711 B
Plaintext
24 lines
711 B
Plaintext
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let bottomat : ℕ → ℕ → Type
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≔ ℕ-ind (λ_. ℕ → Type)
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(λ_. ⊥)
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(λn.λban. ℕ-ind (λ_. Type) ⊤ (λm.λ_. ban m))
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let fin : ℕ → Type
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≔ λn. Σ (m : ℕ) bottomat n m
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let bool : Type
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≔ fin 2
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let false : bool
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≔ (0, ★)
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let true : bool
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≔ (1, ★)
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{-
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let boolind : Π (C : bool → Type) C false → C true → Π (b : bool) C b
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≔ λC.λCf.λCt. Σ-ind ℕ (bottomat 2) C (λn.λu. ℕ-ind (λm. Id ℕ m n → C (n, u))
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(λp. ?)
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(λn.λ_.λp. ℕ-ind (λm. Id ℕ m n → C (n, u)) (λp. ?) (λm.λ_.λp. ⊥-ind (λ_. C (n, u)) ?)))
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-}
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