`BookProof.FockQuadratic.tsum_hop_reindex` {P Q : Idx ι} {F G : Idx ι → ℂ} (hF : ∀ a, ¬ P ≤ a → F a = 0) (hG : ∀ b, ¬ Q ≤ b → G b = 0) (hEq : ∀ a, P ≤ a → F a = G (tgt P...

Proved

BookProof.FockQuadratic.tsum_hop_reindex

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockQuadraticEsa.

BookProof.FockQuadratic.tsum_hop_reindex {P Q : Idx ι} {F G : Idx ι → ℂ} (hF : ∀ a, ¬ P ≤ a → F a = 0) (hG : ∀ b, ¬ Q ≤ b → G b = 0) (hEq : ∀ a, P ≤ a → F a = G (tgt P Q a)) : ∑' a, F a = ∑' b, G b

Formalization note: Lean 4 identifier BookProof.FockQuadratic.tsum_hop_reindex.

Preamble

-- Generated from ChapterFockQuadraticEsa.lean — theorem BookProof.FockQuadratic.tsum_hop_reindex
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterOperatorSeriesEsa
import Mathlib
import Definitions.Def_ChapterFockQuadraticEsa
import Definitions.Def_ChapterA3n
open BookProof.ChapterA3n
open BookProof.FockQuadratic


open scoped ENNReal


open BookProof.FarisLavine BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.NavierStokesFlow.LpNat BookProof.OperatorSeries

noncomputable section

variable {ι : Type*}

Formal statement

theorem BookProof.FockQuadratic.tsum_hop_reindex {P Q : Idx ι} {F G : Idx ι → ℂ}
    (hF : ∀ a, ¬ P ≤ a → F a = 0) (hG : ∀ b, ¬ Q ≤ b → G b = 0)
    (hEq : ∀ a, P ≤ a → F a = G (tgt P Q a)) : ∑' a, F a = ∑' b, G b := by sorry

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