diff --git a/FltRegular/NumberTheory/Cyclotomic/MoreLemmas.lean b/FltRegular/NumberTheory/Cyclotomic/MoreLemmas.lean index 5a6d11fc..055a5d77 100644 --- a/FltRegular/NumberTheory/Cyclotomic/MoreLemmas.lean +++ b/FltRegular/NumberTheory/Cyclotomic/MoreLemmas.lean @@ -108,14 +108,6 @@ lemma exists_dvd_pow_sub_Int_pow (a : 𝓞 K) : ∃ b : ℤ, ↑p ∣ a ^ (p : use b, ↑u * ((hζ.unit' - 1 : 𝓞 K) * k ^ (p : ℕ)) - r rw [mul_sub, hr, add_sub_cancel_right] -lemma norm_dvd_iff {R : Type*} [CommRing R] [IsDomain R] [IsDedekindDomain R] - [Infinite R] [Module.Free ℤ R] [Module.Finite ℤ R] (x : R) (hx : Prime (Algebra.norm ℤ x)) {y : ℤ} : - Algebra.norm ℤ x ∣ y ↔ x ∣ y := by - rw [← Ideal.mem_span_singleton (y := x), ← eq_intCast (algebraMap ℤ R), ← Ideal.mem_comap, - ← Ideal.span_singleton_absNorm, Ideal.mem_span_singleton, Ideal.absNorm_span_singleton, - Int.natAbs_dvd] - rwa [Ideal.absNorm_span_singleton, ← Int.prime_iff_natAbs_prime] - section variable {α} [CommMonoidWithZero α] @@ -136,10 +128,10 @@ lemma zeta_sub_one_dvd_Int_iff {n : ℤ} : (hζ.unit' : 𝓞 K) - 1 ∣ n ↔ letI := IsCyclotomicExtension.numberField {p} ℚ K by_cases hp : p = 2 · rw [← neg_dvd (a := (p : ℤ))] - rw [← norm_Int_zeta_sub_one' hζ hp, norm_dvd_iff] + rw [← norm_Int_zeta_sub_one' hζ hp, Ideal.norm_dvd_iff] rw [norm_Int_zeta_sub_one' hζ hp, prime_neg_iff, ← Nat.prime_iff_prime_int] exact hpri.out - rw [← norm_Int_zeta_sub_one hζ hp, norm_dvd_iff] + rw [← norm_Int_zeta_sub_one hζ hp, Ideal.norm_dvd_iff] rw [norm_Int_zeta_sub_one hζ hp, ← Nat.prime_iff_prime_int] exact hpri.out