Created
April 7, 2020 11:09
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| ℕ-induction : (A : ℕ → 𝓤 ̇ ) → A 0 → ((n : ℕ) → A n → A (succ n)) → (n : ℕ) → A n | |
| ℕ-induction A a₀ f = h where h : (n : ℕ) → A n | |
| h 0 = a₀ | |
| h (succ n) = f n (h n) | |
| ℕ-recursion : (X : 𝓤 ̇ ) → X → (ℕ → X → X) → ℕ → X | |
| ℕ-recursion X = ℕ-induction (λ _ → X) | |
| ℕ-iteration : (X : 𝓤 ̇ ) → X → (X → X) → ℕ → X | |
| ℕ-iteration X x f = ℕ-recursion X x (λ _ x → f x) |
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