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https://github.com/Smaug123/agdaproofs
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24 lines
531 B
Agda
24 lines
531 B
Agda
{-# OPTIONS --warning=error --safe --without-K #-}
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open import LogicalFormulae
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module Numbers.Naturals.Definition where
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data ℕ : Set where
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zero : ℕ
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succ : ℕ → ℕ
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infix 100 succ
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{-# BUILTIN NATURAL ℕ #-}
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succInjective : {a b : ℕ} → (succ a ≡ succ b) → a ≡ b
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succInjective {a} {.a} refl = refl
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naughtE : {a : ℕ} → zero ≡ succ a → False
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naughtE ()
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aIsNotSuccA : (a : ℕ) → (a ≡ succ a) → False
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aIsNotSuccA zero pr = naughtE pr
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aIsNotSuccA (succ a) pr = aIsNotSuccA a (succInjective pr)
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