39 lines
1 KiB
Agda
39 lines
1 KiB
Agda
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{-# OPTIONS --cubical #-}
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open import Cubical.Foundations.Prelude
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data ℕ : Set where
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zero : ℕ
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suc : ℕ → ℕ
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add : ℕ → ℕ → ℕ
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add zero n = n
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add (suc m) n = add m (suc n)
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data ℤ₀ : Set where
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pos : ℕ → ℤ₀
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negsuc : ℕ → ℤ₀
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data ℤ : Set where
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z : ℕ → ℕ → ℤ
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p : (m n : ℕ) → z m n ≡ z (suc m) (suc n)
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ℤ→ℤ₀ : ℤ → ℤ₀
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ℤ→ℤ₀ (z zero zero) = pos zero
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ℤ→ℤ₀ (z zero (suc x₁)) = negsuc x₁
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ℤ→ℤ₀ (z (suc x) zero) = pos (suc x)
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ℤ→ℤ₀ (z (suc x) (suc x₁)) = ℤ→ℤ₀ (z x x₁)
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ℤ→ℤ₀ (p m n i) = ℤ→ℤ₀ {! !}
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ℤ₀→ℤ : ℤ₀ → ℤ
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ℤ₀→ℤ (pos x) = z x zero
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ℤ₀→ℤ (negsuc x) = z zero (suc x)
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ap : ∀ {A B x y} → (f : A → B) → (x ≡ y) → (f x ≡ f y)
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ap f x i = f (x i)
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add-ℤ : ℤ → ℤ → ℤ
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add-ℤ (z x x₁) (z x₂ x₃) = z (add x x₂) (add x₁ x₃)
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add-ℤ (z x x₁) (p m n i) = z (add x {! !}) {! !}
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add-ℤ (p m n i) (z x x₁) = {! !}
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add-ℤ (p m n i) (p m₁ n₁ i₁) = {! !}
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