simp_rw [f1k₂, ite_smul, sum_ite, filter_filter, ← Ne.eq_def, ne_and_eq_iff_right
  (show 0 ≠ 2 by norm_num), Finset.range_filter_eq]
p : ℕ
hpri : p.Prime
a b c : ℤ
ζ : 𝓞 (CyclotomicField ⟨p, ⋯⟩ ℚ)
hp5 : 5 ≤ p
hζ : IsPrimitiveRoot ζ p
caseI : ¬↑p ∣ a * b * c
k₁ k₂ : Fin p
this : Fact (↑⟨p, ⋯⟩).Prime
habs : ↑k₂ = 1
hcong : ↑↑k₁ ≡ 1 + 1 [ZMOD ↑p]
hdiv : ↑p ∣ ↑a - ↑a * ζ ^ 2
⊢ ∑ j ∈ range p, f1k₂ a j • ζ ^ j = ↑a - ↑a * ζ ^ 2
p : ℕ
hpri : p.Prime
a b c : ℤ
ζ : 𝓞 (CyclotomicField ⟨p, ⋯⟩ ℚ)
hp5 : 5 ≤ p
hζ : IsPrimitiveRoot ζ p
caseI : ¬↑p ∣ a * b * c
k₁ k₂ : Fin p
this : Fact (↑⟨p, ⋯⟩).Prime
habs : ↑k₂ = 1
hcong : ↑↑k₁ ≡ 1 + 1 [ZMOD ↑p]
hdiv : ↑p ∣ ↑a - ↑a * ζ ^ 2
⊢ ∑ x ∈ if 0 < p then {0} else ∅, a • ζ ^ x +
      (∑ x ∈ if 2 < p then {2} else ∅, -a • ζ ^ x + ∑ x ∈ filter (fun a => a ≠ 0 ∧ a ≠ 2) (range p), 0 • ζ ^ x) =
    ↑a - ↑a * ζ ^ 2