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fix
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felixwellen committed Feb 2, 2024
1 parent eda7ec4 commit 33f40fc
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions Cubical/Experiments/ZariskiLatticeBasicOpens.agda
Original file line number Diff line number Diff line change
Expand Up @@ -118,9 +118,9 @@ module Presheaf (A' : CommRing ℓ) where
lemma = PT.rec (A[1/ x ]ˣ (y ⋆ 1a) .snd) lemmaΣ
where
path1 : (y z : A) 1r ·r (y ·r 1r ·r z) ·r 1r ≡ z ·r y
path1 = solve A'
path1 _ _ = solve! A'
path2 : (xn : A) xn ≡ 1r ·r 1r ·r (1r ·r 1r ·r xn)
path2 = solve A'
path2 _ = solve! A'

lemmaΣ : Σ[ n ∈ ℕ ] Σ[ a ∈ A ] x ^ n ≡ a ·r y y ⋆ 1a ∈ A[1/ x ]ˣ
lemmaΣ (n , z , p) = [ z , (x ^ n) , PT.∣ n , refl ∣₁ ] -- xⁿ≡zy → y⁻¹ ≡ z/xⁿ
Expand Down Expand Up @@ -165,7 +165,7 @@ module Presheaf (A' : CommRing ℓ) where
·r-lcoh-≼ x y z = map ·r-lcoh-≼Σ
where
path : (x z a y zn : A) x ·r z ·r (a ·r y ·r zn) ≡ x ·r zn ·r a ·r (y ·r z)
path = solve A'
path _ _ _ _ _ = solve! A'

·r-lcoh-≼Σ : Σ[ n ∈ ℕ ] Σ[ a ∈ A ] x ^ n ≡ a ·r y
Σ[ n ∈ ℕ ] Σ[ a ∈ A ] (x ·r z) ^ n ≡ a ·r (y ·r z)
Expand Down

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