`BookProof.ChapterWignerSymmetry.inner_basis_sum` (b : OrthonormalBasis ι ℂ E) (v : ι → ℂ) (k : ι) : ⟪b k, ∑ j, v j • b j⟫_ℂ = v k

Proved

BookProof.ChapterWignerSymmetry.inner_basis_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWignerSymmetry.

BookProof.ChapterWignerSymmetry.inner_basis_sum (b : OrthonormalBasis ι ℂ E) (v : ι → ℂ) (k : ι) : ⟪b k, ∑ j, v j • b j⟫_ℂ = v k

Formalization note: Lean 4 identifier BookProof.ChapterWignerSymmetry.inner_basis_sum.

Preamble

-- Generated from ChapterWignerSymmetry.lean — theorem BookProof.ChapterWignerSymmetry.inner_basis_sum
import Mathlib
import Definitions.Def_ChapterWignerSymmetry
open BookProof.ChapterWignerSymmetry


open scoped InnerProductSpace ComplexConjugate
open Finset


variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]


variable {T : E → E}

variable {ι : Type*} [Fintype ι] [DecidableEq ι]
variable {S : (ι → ℂ) → (ι → ℂ)} {o : ι}

Formal statement

theorem BookProof.ChapterWignerSymmetry.inner_basis_sum (b : OrthonormalBasis ι ℂ E) (v : ι → ℂ) (k : ι) :
    ⟪b k, ∑ j, v j • b j⟫_ℂ = v k := by sorry

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