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fix
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felixwellen committed Jan 30, 2024
1 parent 029d781 commit 027f1ea
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions Cubical/Algebra/CommRing/Quotient/IdealSum.agda
Original file line number Diff line number Diff line change
Expand Up @@ -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
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