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https://github.com/Smaug123/agdaproofs
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19 lines
670 B
Agda
19 lines
670 B
Agda
{-# OPTIONS --warning=error --safe #-}
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open import LogicalFormulae
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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open import WellFoundedInduction
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open import Functions
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open import Orders
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open import Numbers.Naturals.Naturals
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module Numbers.Naturals.WithK where
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<NRefl : {a b : ℕ} → (p1 p2 : a <N b) → (p1 ≡ p2)
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<NRefl {a} {.(succ (p1 +N a))} (le p1 refl) (le p2 proof2) = help p1=p2 proof2
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where
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p1=p2 : p1 ≡ p2
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p1=p2 = equalityCommutative (canSubtractFromEqualityRight {p2} {a} {p1} (succInjective proof2))
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help : (p1 ≡ p2) → (pr2 : succ (p2 +N a) ≡ succ (p1 +N a)) → le p1 refl ≡ le p2 pr2
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help refl refl = refl
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