Skip to content

[Merged by Bors] - refactor(NumberTheory): golf Mathlib/NumberTheory/LegendreSymbol/GaussEisensteinLemmas #38402

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Closed
yuanyi-350 wants to merge 1 commit into from
+2 −8
Closed

[Merged by Bors] - refactor(NumberTheory): golf Mathlib/NumberTheory/LegendreSymbol/GaussEisensteinLemmas #38402

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
10 changes: 2 additions & 8 deletions Mathlib/NumberTheory/LegendreSymbol/GaussEisensteinLemmas.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -74,14 +74,8 @@ private theorem gauss_lemma_aux₁ (p : ℕ) [Fact p.Prime] {a : ℤ} (hap : (a
split_ifs <;> simp)
_ = (-1 : ZMod p) ^ #{x ∈ Ico 1 (p / 2).succ | ¬(a * x.cast : ZMod p).val ≤ p / 2} *
∏ x ∈ Ico 1 (p / 2).succ, ↑((a * x : ZMod p).valMinAbs.natAbs) := by
have :
(∏ x ∈ Ico 1 (p / 2).succ, if (a * x : ZMod p).val ≤ p / 2 then (1 : ZMod p) else -1) =
∏ x ∈ Ico 1 (p / 2).succ with ¬(a * x.cast : ZMod p).val ≤ p / 2, -1 :=
prod_bij_ne_one (fun x _ _ => x)
(fun x => by split_ifs <;> (dsimp; simp_all))
(fun _ _ _ _ _ _ => id) (fun b h _ => ⟨b, by simp_all [-not_le]⟩)
(by intros; split_ifs at * <;> simp_all)
rw [prod_mul_distrib, this, prod_const]
rw [prod_mul_distrib, Finset.prod_ite]
simp
_ = (-1 : ZMod p) ^ #{x ∈ Ico 1 (p / 2).succ | ¬(a * x.cast : ZMod p).val ≤ p / 2} *
(p / 2)! := by
rw [← prod_natCast, Finset.prod_eq_multiset_prod,
Expand Down
Loading