`BookProof.NavierStokesFlow.Carleman.tridiagOp_sum` {ι : Type*} (s : Finset ι) (cc : ι → ℕ → ℂ) : (∑ i ∈ s, tridiagOp (cc i)) = tridiagOp (fun n => ∑ i ∈ s, cc i n)

Proved

BookProof.NavierStokesFlow.Carleman.tridiagOp_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesCarleman.

BookProof.NavierStokesFlow.Carleman.tridiagOp_sum {ι : Type*} (s : Finset ι) (cc : ι → ℕ → ℂ) : (∑ i ∈ s, tridiagOp (cc i)) = tridiagOp (fun n => ∑ i ∈ s, cc i n)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.Carleman.tridiagOp_sum.

Preamble

-- Generated from ChapterNavierStokesCarleman.lean — theorem BookProof.NavierStokesFlow.Carleman.tridiagOp_sum
import Mathlib
import Definitions.Def_ChapterNavierStokesCarleman
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.Carleman


open scoped ENNReal



open LpNat DiagonalEsa FullEsa

Formal statement

theorem BookProof.NavierStokesFlow.Carleman.tridiagOp_sum {ι : Type*} (s : Finset ι) (cc : ι → ℕ → ℂ) :
    (∑ i ∈ s, tridiagOp (cc i)) = tridiagOp (fun n => ∑ i ∈ s, cc i n) := by sorry

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