`BookProof.NsLagrangianDet.det_rows_sum` {n ι R : Type*} [Fintype n] [DecidableEq n] [Fintype ι] [CommRing R] (v : n → ι → n → R) : (Matrix.of fun r c => ∑ o, v r o c).det = ∑ τ :

Proved

BookProof.NsLagrangianDet.det_rows_sum

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsLagrangianDetConvolution.

BookProof.NsLagrangianDet.det_rows_sum {n ι R : Type*} [Fintype n] [DecidableEq n] [Fintype ι] [CommRing R] (v : n → ι → n → R) : (Matrix.of fun r c => ∑ o, v r o c).det = ∑ τ : n → ι, (Matrix.of fun r c => v r (τ r) c).det

Formalization note: Lean 4 identifier BookProof.NsLagrangianDet.det_rows_sum.

Preamble

-- Generated from ChapterNsLagrangianDetConvolution.lean — theorem BookProof.NsLagrangianDet.det_rows_sum
import Mathlib
import Definitions.Def_ChapterNsLagrangianDetConvolution
open BookProof.NsLagrangianDet



open MvPolynomial Matrix

noncomputable section

variable {K : Type*} [Fintype K]

Formal statement

theorem BookProof.NsLagrangianDet.det_rows_sum {n ι R : Type*} [Fintype n] [DecidableEq n] [Fintype ι] [CommRing R]
    (v : n → ι → n → R) :
    (Matrix.of fun r c => ∑ o, v r o c).det
      = ∑ τ : n → ι, (Matrix.of fun r c => v r (τ r) c).det := by sorry

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