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Update Reductions.lean
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Co-Authored-By: Yaël Dillies <[email protected]>
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pitmonticone and YaelDillies committed Nov 10, 2024
1 parent 892a635 commit 64abeb0
Showing 1 changed file with 2 additions and 7 deletions.
9 changes: 2 additions & 7 deletions FLT/Basic/Reductions.lean
Original file line number Diff line number Diff line change
Expand Up @@ -254,15 +254,10 @@ lemma FreyCurve.j (P : FreyPackage) :
rw [mul_div_right_comm, EllipticCurve.j, FreyCurve.Δ'inv, FreyCurve.c₄']

private lemma j_pos_aux (a b : ℤ) (hb : b ≠ 0) : 0 < (a + b) ^ 2 - a * b := by
cases le_or_lt 0 (a * b) with
| inl h =>
rify
calc
rify
calc
(0 : ℝ) < (a ^ 2 + (a + b) ^ 2 + b ^ 2) / 2 := by positivity
_ = (a + b) ^ 2 - a * b := by ring
| inr h =>
rw [sub_pos]
exact h.trans_le (sq_nonneg _)

/-- The q-adic valuation of the j-invariant of the Frey curve is a multiple of p if 2 < q is
a prime of bad reduction. -/
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