Module: Mathlib.NumberTheory.Cyclotomic.Discriminant

Goal state before:
pp: case refine_1
n : ℕ
inst✝² : NeZero n
K : Type u
inst✝¹ : Field K
inst✝ : CharZero K
ζ : K
ce : IsCyclotomicExtension {n} ℚ K
hζ : IsPrimitiveRoot ζ n
this : NumberField K
H₁ : (aeval (IsPrimitiveRoot.powerBasis ℚ hζ).gen) (X - 1) = (subOnePowerBasis ℚ hζ).gen
H₂ : (aeval (subOnePowerBasis ℚ hζ).gen) (X + 1) = (IsPrimitiveRoot.powerBasis ℚ hζ).gen
i : Fin (IsPrimitiveRoot.powerBasis ℚ hζ).dim
j : Fin (subOnePowerBasis ℚ hζ).dim
⊢ IsIntegral ℤ (IsPrimitiveRoot.powerBasis ℚ hζ).gen

pp: case refine_2
n : ℕ
inst✝² : NeZero n
K : Type u
inst✝¹ : Field K
inst✝ : CharZero K
ζ : K
ce : IsCyclotomicExtension {n} ℚ K
hζ : IsPrimitiveRoot ζ n
this : NumberField K
H₁ : (aeval (IsPrimitiveRoot.powerBasis ℚ hζ).gen) (X - 1) = (subOnePowerBasis ℚ hζ).gen
H₂ : (aeval (subOnePowerBasis ℚ hζ).gen) (X + 1) = (IsPrimitiveRoot.powerBasis ℚ hζ).gen
i : Fin (IsPrimitiveRoot.powerBasis ℚ hζ).dim
j : Fin (subOnePowerBasis ℚ hζ).dim
⊢ minpoly ℚ (IsPrimitiveRoot.powerBasis ℚ hζ).gen =
    Polynomial.map (algebraMap ℤ ℚ) (minpoly ℤ (IsPrimitiveRoot.powerBasis ℚ hζ).gen)

pp: case refine_3
n : ℕ
inst✝² : NeZero n
K : Type u
inst✝¹ : Field K
inst✝ : CharZero K
ζ : K
ce : IsCyclotomicExtension {n} ℚ K
hζ : IsPrimitiveRoot ζ n
this : NumberField K
H₁ : (aeval (IsPrimitiveRoot.powerBasis ℚ hζ).gen) (X - 1) = (subOnePowerBasis ℚ hζ).gen
H₂ : (aeval (subOnePowerBasis ℚ hζ).gen) (X + 1) = (IsPrimitiveRoot.powerBasis ℚ hζ).gen
i : Fin (subOnePowerBasis ℚ hζ).dim
j : Fin (IsPrimitiveRoot.powerBasis ℚ hζ).dim
⊢ IsIntegral ℤ (subOnePowerBasis ℚ hζ).gen

pp: case refine_4
n : ℕ
inst✝² : NeZero n
K : Type u
inst✝¹ : Field K
inst✝ : CharZero K
ζ : K
ce : IsCyclotomicExtension {n} ℚ K
hζ : IsPrimitiveRoot ζ n
this : NumberField K
H₁ : (aeval (IsPrimitiveRoot.powerBasis ℚ hζ).gen) (X - 1) = (subOnePowerBasis ℚ hζ).gen
H₂ : (aeval (subOnePowerBasis ℚ hζ).gen) (X + 1) = (IsPrimitiveRoot.powerBasis ℚ hζ).gen
i : Fin (subOnePowerBasis ℚ hζ).dim
j : Fin (IsPrimitiveRoot.powerBasis ℚ hζ).dim
⊢ minpoly ℚ (subOnePowerBasis ℚ hζ).gen = Polynomial.map (algebraMap ℤ ℚ) (minpoly ℤ (subOnePowerBasis ℚ hζ).gen)

Tactic:
· exact hζ.isIntegral (NeZero.pos _)

Goal state after:
case refine_2
n : ℕ
inst✝² : NeZero n
K : Type u
inst✝¹ : Field K
inst✝ : CharZero K
ζ : K
ce : IsCyclotomicExtension {n} ℚ K
hζ : IsPrimitiveRoot ζ n
this : NumberField K
H₁ : (aeval (IsPrimitiveRoot.powerBasis ℚ hζ).gen) (X - 1) = (subOnePowerBasis ℚ hζ).gen
H₂ : (aeval (subOnePowerBasis ℚ hζ).gen) (X + 1) = (IsPrimitiveRoot.powerBasis ℚ hζ).gen
i : Fin (IsPrimitiveRoot.powerBasis ℚ hζ).dim
j : Fin (subOnePowerBasis ℚ hζ).dim
⊢ minpoly ℚ (IsPrimitiveRoot.powerBasis ℚ hζ).gen =
    Polynomial.map (algebraMap ℤ ℚ) (minpoly ℤ (IsPrimitiveRoot.powerBasis ℚ hζ).gen)

case refine_3
n : ℕ
inst✝² : NeZero n
K : Type u
inst✝¹ : Field K
inst✝ : CharZero K
ζ : K
ce : IsCyclotomicExtension {n} ℚ K
hζ : IsPrimitiveRoot ζ n
this : NumberField K
H₁ : (aeval (IsPrimitiveRoot.powerBasis ℚ hζ).gen) (X - 1) = (subOnePowerBasis ℚ hζ).gen
H₂ : (aeval (subOnePowerBasis ℚ hζ).gen) (X + 1) = (IsPrimitiveRoot.powerBasis ℚ hζ).gen
i : Fin (subOnePowerBasis ℚ hζ).dim
j : Fin (IsPrimitiveRoot.powerBasis ℚ hζ).dim
⊢ IsIntegral ℤ (subOnePowerBasis ℚ hζ).gen

case refine_4
n : ℕ
inst✝² : NeZero n
K : Type u
inst✝¹ : Field K
inst✝ : CharZero K
ζ : K
ce : IsCyclotomicExtension {n} ℚ K
hζ : IsPrimitiveRoot ζ n
this : NumberField K
H₁ : (aeval (IsPrimitiveRoot.powerBasis ℚ hζ).gen) (X - 1) = (subOnePowerBasis ℚ hζ).gen
H₂ : (aeval (subOnePowerBasis ℚ hζ).gen) (X + 1) = (IsPrimitiveRoot.powerBasis ℚ hζ).gen
i : Fin (subOnePowerBasis ℚ hζ).dim
j : Fin (IsPrimitiveRoot.powerBasis ℚ hζ).dim
⊢ minpoly ℚ (subOnePowerBasis ℚ hζ).gen = Polynomial.map (algebraMap ℤ ℚ) (minpoly ℤ (subOnePowerBasis ℚ hζ).gen)