`BookProof.TwoParticleSector.swapTwo_inner` (t s : X ⊗[ℂ] (X ⊗[ℂ] ℂ)) : (inner ℂ (swapTwo X t) (swapTwo X s) : ℂ) = inner ℂ t s

Proved

BookProof.TwoParticleSector.swapTwo_inner

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTwoParticleSectorEsa.

BookProof.TwoParticleSector.swapTwo_inner (t s : X ⊗[ℂ] (X ⊗[ℂ] ℂ)) : (inner ℂ (swapTwo X t) (swapTwo X s) : ℂ) = inner ℂ t s

Formalization note: Lean 4 identifier BookProof.TwoParticleSector.swapTwo_inner.

Preamble

-- Generated from ChapterTwoParticleSectorEsa.lean — theorem BookProof.TwoParticleSector.swapTwo_inner
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Definitions.Def_ChapterReducingSubspaceEsa
import Definitions.Def_ChapterTensorGraphCore
import Mathlib
import Definitions.Def_ChapterTwoParticleSectorEsa
open BookProof.TwoParticleSector



open scoped TensorProduct
open BookProof.FarisLavine BookProof.GraphCore BookProof.ReducedEsa BookProof.TensorCore

noncomputable section

variable (X : Type) [NormedAddCommGroup X] [InnerProductSpace ℂ X]
variable {X}

Formal statement

theorem BookProof.TwoParticleSector.swapTwo_inner (t s : X ⊗[ℂ] (X ⊗[ℂ] ℂ)) :
    (inner ℂ (swapTwo X t) (swapTwo X s) : ℂ) = inner ℂ t s := by sorry

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