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lines changed Original file line number Diff line number Diff line change @@ -1614,12 +1614,11 @@ m≤n⇒n∸m≤n (s≤s m≤n) = m≤n⇒m≤1+n (m≤n⇒n∸m≤n m≤n)
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∸-+-assoc (suc m) (suc n) o = ∸-+-assoc m n o
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+-∸-assoc : ∀ m {n o} → o ≤ n → (m + n) ∸ o ≡ m + (n ∸ o)
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- +-∸-assoc m (z≤n {n = n}) = begin-equality m + n ∎
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- +-∸-assoc m (s≤s {m = o} {n = n} o≤n) = begin-equality
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- (m + suc n) ∸ suc o ≡⟨ cong (_∸ suc o) (+-suc m n) ⟩
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- suc (m + n) ∸ suc o ≡⟨⟩
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- (m + n) ∸ o ≡⟨ +-∸-assoc m o≤n ⟩
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- m + (n ∸ o) ∎
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+ +-∸-assoc zero {n = _} {o = _} _ = refl
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+ +-∸-assoc (suc m) {n = n} {o = o} o≤n = begin-equality
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+ suc (m + n) ∸ o ≡⟨ ∸-suc (m≤n⇒m≤o+n m o≤n) ⟩
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+ suc ((m + n) ∸ o) ≡⟨ cong suc (+-∸-assoc m o≤n) ⟩
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+ suc (m + (n ∸ o)) ∎
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m≤n+o⇒m∸n≤o : ∀ m n {o} → m ≤ n + o → m ∸ n ≤ o
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m≤n+o⇒m∸n≤o m zero le = le
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