Module: Mathlib.AlgebraicGeometry.EllipticCurve.Reduction

Goal state before:
pp: case h.a₁
R : Type u_1
inst✝² : CommRing R
K : Type u_2
inst✝¹ : Field K
inst✝ : Algebra R K
W : WeierstrassCurve K
h₁ : ∃ r₁, (algebraMap R K) r₁ = W.a₁
h₂ : ∃ r₂, (algebraMap R K) r₂ = W.a₂
h₃ : ∃ r₃, (algebraMap R K) r₃ = W.a₃
h₄ : ∃ r₄, (algebraMap R K) r₄ = W.a₄
h₆ : ∃ r₆, (algebraMap R K) r₆ = W.a₆
⊢ W.a₁ = (algebraMap R K) h₁.choose

pp: case h.a₂
R : Type u_1
inst✝² : CommRing R
K : Type u_2
inst✝¹ : Field K
inst✝ : Algebra R K
W : WeierstrassCurve K
h₁ : ∃ r₁, (algebraMap R K) r₁ = W.a₁
h₂ : ∃ r₂, (algebraMap R K) r₂ = W.a₂
h₃ : ∃ r₃, (algebraMap R K) r₃ = W.a₃
h₄ : ∃ r₄, (algebraMap R K) r₄ = W.a₄
h₆ : ∃ r₆, (algebraMap R K) r₆ = W.a₆
⊢ W.a₂ = (algebraMap R K) h₂.choose

pp: case h.a₃
R : Type u_1
inst✝² : CommRing R
K : Type u_2
inst✝¹ : Field K
inst✝ : Algebra R K
W : WeierstrassCurve K
h₁ : ∃ r₁, (algebraMap R K) r₁ = W.a₁
h₂ : ∃ r₂, (algebraMap R K) r₂ = W.a₂
h₃ : ∃ r₃, (algebraMap R K) r₃ = W.a₃
h₄ : ∃ r₄, (algebraMap R K) r₄ = W.a₄
h₆ : ∃ r₆, (algebraMap R K) r₆ = W.a₆
⊢ W.a₃ = (algebraMap R K) h₃.choose

pp: case h.a₄
R : Type u_1
inst✝² : CommRing R
K : Type u_2
inst✝¹ : Field K
inst✝ : Algebra R K
W : WeierstrassCurve K
h₁ : ∃ r₁, (algebraMap R K) r₁ = W.a₁
h₂ : ∃ r₂, (algebraMap R K) r₂ = W.a₂
h₃ : ∃ r₃, (algebraMap R K) r₃ = W.a₃
h₄ : ∃ r₄, (algebraMap R K) r₄ = W.a₄
h₆ : ∃ r₆, (algebraMap R K) r₆ = W.a₆
⊢ W.a₄ = (algebraMap R K) h₄.choose

pp: case h.a₆
R : Type u_1
inst✝² : CommRing R
K : Type u_2
inst✝¹ : Field K
inst✝ : Algebra R K
W : WeierstrassCurve K
h₁ : ∃ r₁, (algebraMap R K) r₁ = W.a₁
h₂ : ∃ r₂, (algebraMap R K) r₂ = W.a₂
h₃ : ∃ r₃, (algebraMap R K) r₃ = W.a₃
h₄ : ∃ r₄, (algebraMap R K) r₄ = W.a₄
h₆ : ∃ r₆, (algebraMap R K) r₆ = W.a₆
⊢ W.a₆ = (algebraMap R K) h₆.choose

Tactic:
· apply h₁.choose_spec.symm

Goal state after:
case h.a₂
R : Type u_1
inst✝² : CommRing R
K : Type u_2
inst✝¹ : Field K
inst✝ : Algebra R K
W : WeierstrassCurve K
h₁ : ∃ r₁, (algebraMap R K) r₁ = W.a₁
h₂ : ∃ r₂, (algebraMap R K) r₂ = W.a₂
h₃ : ∃ r₃, (algebraMap R K) r₃ = W.a₃
h₄ : ∃ r₄, (algebraMap R K) r₄ = W.a₄
h₆ : ∃ r₆, (algebraMap R K) r₆ = W.a₆
⊢ W.a₂ = (algebraMap R K) h₂.choose

case h.a₃
R : Type u_1
inst✝² : CommRing R
K : Type u_2
inst✝¹ : Field K
inst✝ : Algebra R K
W : WeierstrassCurve K
h₁ : ∃ r₁, (algebraMap R K) r₁ = W.a₁
h₂ : ∃ r₂, (algebraMap R K) r₂ = W.a₂
h₃ : ∃ r₃, (algebraMap R K) r₃ = W.a₃
h₄ : ∃ r₄, (algebraMap R K) r₄ = W.a₄
h₆ : ∃ r₆, (algebraMap R K) r₆ = W.a₆
⊢ W.a₃ = (algebraMap R K) h₃.choose

case h.a₄
R : Type u_1
inst✝² : CommRing R
K : Type u_2
inst✝¹ : Field K
inst✝ : Algebra R K
W : WeierstrassCurve K
h₁ : ∃ r₁, (algebraMap R K) r₁ = W.a₁
h₂ : ∃ r₂, (algebraMap R K) r₂ = W.a₂
h₃ : ∃ r₃, (algebraMap R K) r₃ = W.a₃
h₄ : ∃ r₄, (algebraMap R K) r₄ = W.a₄
h₆ : ∃ r₆, (algebraMap R K) r₆ = W.a₆
⊢ W.a₄ = (algebraMap R K) h₄.choose

case h.a₆
R : Type u_1
inst✝² : CommRing R
K : Type u_2
inst✝¹ : Field K
inst✝ : Algebra R K
W : WeierstrassCurve K
h₁ : ∃ r₁, (algebraMap R K) r₁ = W.a₁
h₂ : ∃ r₂, (algebraMap R K) r₂ = W.a₂
h₃ : ∃ r₃, (algebraMap R K) r₃ = W.a₃
h₄ : ∃ r₄, (algebraMap R K) r₄ = W.a₄
h₆ : ∃ r₆, (algebraMap R K) r₆ = W.a₆
⊢ W.a₆ = (algebraMap R K) h₆.choose