(x : maxDom sym) (y : L2I ι) : HasSum (fun β => -Complex.I * S.crossA ((x : L2I ι) : ι → ℂ) ((y : ι → ℂ)) β + Complex.I * S.crossB ((x : L2I ι) : ι → ℂ) ((y : ι → ℂ)) β) (inner ℂ (hopH S x : L2I ι) y)

-- Generated from ChapterNavierStokesSignedShift.lean — theorem BookProof.NavierStokesFlow.SignedShift.SignedHop.hasSum_inner_hopH_left
import Mathlib
import Definitions.Def_ChapterNavierStokesSignedShift
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.SignedShift
open BookProof.NavierStokesFlow.LpNat BookProof.FarisLavine BookProof.NavierStokesFlow.IkebeKato BookProof.NavierStokesFlow.ShiftHamiltonian BookProof.NavierStokesFlow.AffineFiber
open BookProof.NavierStokesFlow.SignedShift.SignedHop









open scoped ENNReal




variable {ι : Type*}



variable {sym : ι → ℝ} (S : SignedHop ι sym)

theorem BookProof.NavierStokesFlow.SignedShift.SignedHop.hasSum_inner_hopH_left (x : maxDom sym) (y : L2I ι) :
    HasSum (fun β => -Complex.I * S.crossA ((x : L2I ι) : ι → ℂ) ((y : ι → ℂ)) β
        + Complex.I * S.crossB ((x : L2I ι) : ι → ℂ) ((y : ι → ℂ)) β)
      (inner ℂ (hopH S x : L2I ι) y) := by sorry