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[ fixed #1484 ] prove m<n⇒m≤1+n by composition ≤-step ∘ <⇒≤ (#1485)
The pattern matching proof is a bit awkward (as the property is, which combines two steps of information loss).
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src/Data/Nat/Properties.agda

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@@ -418,8 +418,7 @@ m<n⇒n≢0 : ∀ {m n} → m < n → n ≢ 0
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m<n⇒n≢0 (s≤s m≤n) ()
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m<n⇒m≤1+n : {m n} m < n m ≤ suc n
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m<n⇒m≤1+n (s≤s z≤n) = z≤n
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m<n⇒m≤1+n (s≤s (s≤s m<n)) = s≤s (m<n⇒m≤1+n (s≤s m<n))
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m<n⇒m≤1+n = ≤-step ∘ <⇒≤
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∀[m≤n⇒m≢o]⇒n<o : n o ( {m} m ≤ n m ≢ o) n < o
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∀[m≤n⇒m≢o]⇒n<o _ zero m≤n⇒n≢0 = contradiction refl (m≤n⇒n≢0 z≤n)

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