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1 parent 1bd7dae commit 76ef2adCopy full SHA for 76ef2ad
src/Data/Nat/Divisibility.agda
@@ -305,4 +305,8 @@ m≤n⇒m!∣n! m≤n = help (≤⇒≤′ m≤n)
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-- Properties of quotient
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quotient∣n : ∀ {m n} (m∣n : m ∣ n) → quotient m∣n ∣ n
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-quotient∣n {m = m} m∣n = divides m (trans (_∣_.equality m∣n) (*-comm (quotient m∣n) m))
+quotient∣n {m = m} {n = n} m∣n = divides m $ begin-equality
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+ n ≡⟨ _∣_.equality m∣n ⟩
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+ quotient m∣n * m ≡⟨ *-comm (quotient m∣n) m ⟩
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+ m * quotient m∣n ∎
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+ where open ≤-Reasoning
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