rw [Nat.mul_succ, prod_range_add, ih (Nat.mul_mod_right (orderOf σ) n) rfl, one_mul]
case intro.succ
K : Type u_1
L : Type u_2
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : NumberField K
inst✝² : Algebra K L
inst✝¹ : IsGalois K L
inst✝ : FiniteDimensional K L
σ : L ≃ₐ[K] L
hσ : ∀ (x : L ≃ₐ[K] L), x ∈ Subgroup.zpowers σ
η : L
hη : (Algebra.norm K) η = 1
n : ℕ
ih : ∀ {a : ℕ}, a % orderOf σ = 0 → a = orderOf σ * n → ∏ i ∈ range (orderOf σ * n), (σ ^ i) ↑(ηu hη) = 1
a : ℕ
h✝ : a % orderOf σ = 0
hn✝ : a = orderOf σ * (n + 1)
⊢ ∏ i ∈ range (orderOf σ * (n + 1)), (σ ^ i) ↑(ηu hη) = 1
case intro.succ
K : Type u_1
L : Type u_2
inst✝⁵ : Field K
inst✝⁴ : Field L
inst✝³ : NumberField K
inst✝² : Algebra K L
inst✝¹ : IsGalois K L
inst✝ : FiniteDimensional K L
σ : L ≃ₐ[K] L
hσ : ∀ (x : L ≃ₐ[K] L), x ∈ Subgroup.zpowers σ
η : L
hη : (Algebra.norm K) η = 1
n : ℕ
ih : ∀ {a : ℕ}, a % orderOf σ = 0 → a = orderOf σ * n → ∏ i ∈ range (orderOf σ * n), (σ ^ i) ↑(ηu hη) = 1
a : ℕ
h✝ : a % orderOf σ = 0
hn✝ : a = orderOf σ * (n + 1)
⊢ ∏ x ∈ range (orderOf σ), (σ ^ (orderOf σ * n + x)) ↑(ηu hη) = 1