`BookProof.TensorPerm.permOp_succ` (n : ℕ) (σ : Equiv.Perm (Fin (n + 1))) : permOp E (n + 1) σ = (swap0 E (n + 1) (Equiv.Perm.decomposeFin σ).1).trans (liftTail E (permOp E n (Equi

Proved

BookProof.TensorPerm.permOp_succ

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorPermutation.

BookProof.TensorPerm.permOp_succ (n : ℕ) (σ : Equiv.Perm (Fin (n + 1))) : permOp E (n + 1) σ = (swap0 E (n + 1) (Equiv.Perm.decomposeFin σ).1).trans (liftTail E (permOp E n (Equiv.Perm.decomposeFin σ).2))

Formalization note: Lean 4 identifier BookProof.TensorPerm.permOp_succ.

Preamble

-- Generated from ChapterTensorPermutation.lean — theorem BookProof.TensorPerm.permOp_succ
import Definitions.Def_ChapterGroupAverageEsa
import Mathlib
import Definitions.Def_ChapterTensorPermutation
import Definitions.Def_ChapterGaugeUnconstrainedSpectrum
import Definitions.Def_ChapterTensorGraphCore
open BookProof.ChapterGaugeUnconstrainedSpectrum
open BookProof.TensorCore
open BookProof.TensorPerm



open scoped TensorProduct
open BookProof.TensorCore BookProof.GroupAverage

noncomputable section

variable (E : BookProof.TensorCore.IPSpace)

Formal statement

theorem BookProof.TensorPerm.permOp_succ (n : ℕ) (σ : Equiv.Perm (Fin (n + 1))) :
    permOp E (n + 1) σ = (swap0 E (n + 1) (Equiv.Perm.decomposeFin σ).1).trans
      (liftTail E (permOp E n (Equiv.Perm.decomposeFin σ).2)) := by sorry

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