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refactor(Channel/Determinant): use Fintype sum zero criterion #3276

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LionSR merged 1 commit into from
Jun 21, 2026
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refactor(Channel/Determinant): use Fintype sum zero criterion #3276

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7 changes: 2 additions & 5 deletions TNLean/Channel/Determinant/HilbertSchmidt.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -135,14 +135,11 @@
_ = (d : ℂ) • (1 : MatrixAlg d) := by rw [Matrix.sum_single_one]

/-- If a finite family of nonnegative reals has total sum at most `0`, then every term is `0`. -/
lemma eq_zero_of_nonneg_of_sum_le_zero {ι : Type*} [Fintype ι]

Check warning on line 138 in TNLean/Channel/Determinant/HilbertSchmidt.lean

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GitHub Actions / Check blueprint compiles without errors

Blueprint update suggested 

ChannelDeterminant.Internal.eq_zero_of_nonneg_of_sum_le_zero is changed in this PR but has no corresponding \lean{} tag in blueprint/src/chapter.
(f : ι → ℝ) (hf : ∀ i, 0 ≤ f i) (hsum : ∑ i, f i ≤ 0) :
∀ i, f i = 0 := by
intro i
have h1 : ∑ i, f i ≥ 0 := Finset.sum_nonneg (fun i _ => hf i)
have h2 : ∑ i, f i = 0 := le_antisymm hsum h1
have h3 := Finset.sum_eq_zero_iff_of_nonneg (fun i _ => hf i) |>.mp h2
exact h3 i (Finset.mem_univ i)
have hsum_zero : ∑ i, f i = 0 := le_antisymm hsum (Fintype.sum_nonneg hf)
exact fun i => congrFun ((Fintype.sum_eq_zero_iff_of_nonneg hf).mp hsum_zero) i

private lemma matrix_det_norm_one_trace_conjTranspose_mul_self_ge [NeZero d]
(A : Matrix (Fin d × Fin d) (Fin d × Fin d) ℂ) (hdet : ‖A.det‖ = 1) :
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