diff --git a/Cubical/Algebra/CommRing/Quotient/IdealSum.agda b/Cubical/Algebra/CommRing/Quotient/IdealSum.agda index b7cb095de6..ae23b46491 100644 --- a/Cubical/Algebra/CommRing/Quotient/IdealSum.agda +++ b/Cubical/Algebra/CommRing/Quotient/IdealSum.agda @@ -93,12 +93,12 @@ module Construction {R : CommRing ℓ} (I J : IdealsIn R) where (subst (λ K → b - x ∈ K) (kernel≡I I) (kernelFiber R (R / I) π₁ b x π₁b≡π₁x)) - useSolver : (x b : ⟨ R ⟩) → x ≡ - (b - x) + b - useSolver = solve R + useSolver : (b : ⟨ R ⟩) → x ≡ - (b - x) + b + useSolver _ = solve! R step2 : ∀ b → b ∈ J → fst π₁ b ≡ fst π₁ x → x ∈ (I +i J) step2 b b∈J π₁b≡π₁x = - ∣ (- (b - x) , b) , (step1 b π₁b≡π₁x) , (b∈J , (x ≡⟨ useSolver x b ⟩ (- (b - x) + b) ∎)) ∣₁ + ∣ (- (b - x) , b) , (step1 b π₁b≡π₁x) , (b∈J , (x ≡⟨ useSolver b ⟩ (- (b - x) + b) ∎)) ∣₁ ψ : CommRingHom (R / (I +i J)) ((R / I) / π₁J) ψ = UniversalProperty.inducedHom R ((R / I) / π₁J) (I +i J) π πI+J≡0