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erdOne committed Nov 29, 2023
1 parent f4c6c4c commit 62b673d
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions FltRegular/NumberTheory/Hilbert92.lean
Original file line number Diff line number Diff line change
Expand Up @@ -133,7 +133,7 @@ lemma one_sub_σA_mem : 1 - σA p σ ∈ A⁰ := sorry

lemma one_sub_σA_mem_nonunit : ¬ IsUnit (1 - σA p σ) := sorry

lemma isCoprime_one_sug_σA (n : ℤ) (hn : ¬ (p : ℤ) ∣ n): IsCoprime (1 - σA p σ) n := sorry
lemma isCoprime_one_sub_σA (n : ℤ) (hn : ¬ (p : ℤ) ∣ n): IsCoprime (1 - σA p σ) n := sorry

namespace fundamentalSystemOfUnits
lemma existence [Module A G] : ∃ S : systemOfUnits p G σ r, S.IsFundamental := by
Expand Down Expand Up @@ -177,7 +177,7 @@ lemma lemma2 [Module A G] (S : systemOfUnits p G σ r) (hs : S.IsFundamental) (i
lemma lemma2' [Module A G] (S : systemOfUnits p G σ r) (hs : S.IsFundamental) (i : Fin r) (a : ℤ)
(ha : ¬ (p : ℤ) ∣ a) : ∀ g : G, (1 - σA p σ) • g ≠ a • (S.units i) := by
intro g hg
obtain ⟨x, y, e⟩ := isCoprime_one_sug_σA p σ a ha
obtain ⟨x, y, e⟩ := isCoprime_one_sub_σA p σ a ha
apply lemma2 p G σ S hs i (x • (S.units i) + y • g)
conv_rhs => rw [← one_smul A (S.units i), ← e, add_smul, ← smul_smul y, intCast_smul, ← hg]
rw [smul_add, smul_smul, smul_smul, smul_smul, mul_comm x, mul_comm y]
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