Prove2Me

`BookProof.NsLagrangianDet.phase_sum` {ι : Type*} (s : Finset ι) (w : ι → Fin 3 → ℝ) (a : Fin 3 → ℝ) : ∏ i ∈ s, phase (w i) a = phase (∑ i ∈ s, w i) a

Proved
BookProof.NsLagrangianDet.phase_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsLagrangianDetConvolution.

BookProof.NsLagrangianDet.phase_sum {ι : Type*} (s : Finset ι) (w : ι → Fin 3 → ℝ) (a : Fin 3 → ℝ) : ∏ i ∈ s, phase (w i) a = phase (∑ i ∈ s, w i) a

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

Preamble
-- Generated from ChapterNsLagrangianDetConvolution.lean — theorem BookProof.NsLagrangianDet.phase_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.phase_sum {ι : Type*} (s : Finset ι) (w : ι → Fin 3 → ℝ) (a : Fin 3 → ℝ) :
    ∏ i ∈ s, phase (w i) a = phase (∑ i ∈ s, w i) a := by sorry

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