`BookProof.QuantumGravityBrstCharge.sum4_swap_blocks` [AddCommMonoid α] (F : Fin d → Fin d → Fin d → Fin d → α) : ∑ l, ∑ m, ∑ j, ∑ k, F l m j k = ∑ j, ∑ k, ∑ l, ∑ m, F l...
ProvedBookProof.QuantumGravityBrstCharge.sum4_swap_blockstheoremstimepiece
Prove the following Lean 4 theorem from ChapterQuantumGravityBrstCharge.
BookProof.QuantumGravityBrstCharge.sum4_swap_blocks [AddCommMonoid α] (F : Fin d → Fin d → Fin d → Fin d → α) : ∑ l, ∑ m, ∑ j, ∑ k, F l m j k = ∑ j, ∑ k, ∑ l, ∑ m, F l m j k
Formalization note: Lean 4 identifier BookProof.QuantumGravityBrstCharge.sum4_swap_blocks.
Preamble
-- Generated from ChapterQuantumGravityBrstCharge.lean — theorem BookProof.QuantumGravityBrstCharge.sum4_swap_blocks
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterYangMillsHermite
import Definitions.Def_ChapterQuantumGravity3DGauge
import Mathlib
import Definitions.Def_ChapterQuantumGravityBrstCharge
open BookProof.QuantumGravityBrstCharge
open MvPolynomial BookProof.BRSTNilpotent BookProof.YangMillsHermite
open BookProof.QuantumGravity3DGauge
noncomputable section
variable {R : Type*} [Ring R] [Algebra ℝ R] {n : ℕ}
variable {f : Fin n → Fin n → Fin n → ℝ} {G χ β : Fin n → R}
variable {d : ℕ}
variable {α : Type*}Formal statement
theorem BookProof.QuantumGravityBrstCharge.sum4_swap_blocks [AddCommMonoid α] (F : Fin d → Fin d → Fin d → Fin d → α) :
∑ l, ∑ m, ∑ j, ∑ k, F l m j k = ∑ j, ∑ k, ∑ l, ∑ m, F l m j k := by sorry