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lines changed Original file line number Diff line number Diff line change @@ -113,7 +113,8 @@ isCauchy (p *ₗ x) ε with p ≟ 0ℚ
113113... | no p≢0 = proj₁ (isCauchy x (1/ ∣ p ∣ * ε)) , λ {m} {n} m≥N n≥N → begin-strict
114114 ∣ lookup (map (p *_) (sequence x)) m - lookup (map (p *_) (sequence x)) n ∣
115115 ≡⟨ cong₂ (λ a b → ∣ a - b ∣) (lookup-map m (p *_) (sequence x)) (lookup-map n (p *_) (sequence x)) ⟩
116- ∣ p * lookup (sequence x) m - p * lookup (sequence x) n ∣ ≡⟨ cong (λ # → ∣ p * lookup (sequence x) m ℚ.+ # ∣) (neg-distribʳ-* p (lookup (sequence x) n)) ⟩
116+ ∣ p * lookup (sequence x) m - p * lookup (sequence x) n ∣
117+ ≡⟨ cong (λ # → ∣ p * lookup (sequence x) m ℚ.+ # ∣) (neg-distribʳ-* p (lookup (sequence x) n)) ⟩
117118 ∣ p * lookup (sequence x) m ℚ.+ p * ℚ.- lookup (sequence x) n ∣
118119 ≡⟨ cong ∣_∣ (*-distribˡ-+ p (lookup (sequence x) m) (ℚ.- lookup (sequence x) n)) ⟨
119120 ∣ p * (lookup (sequence x) m - lookup (sequence x) n) ∣
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