`BookProof.ChapterWignerSymmetry.imgBasis_apply` (hT : IsWignerSymmetry T) (i : ι) : imgBasis b T o hT i = alignPhase b T o i • T (b i)

Proved

BookProof.ChapterWignerSymmetry.imgBasis_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWignerSymmetry.

BookProof.ChapterWignerSymmetry.imgBasis_apply (hT : IsWignerSymmetry T) (i : ι) : imgBasis b T o hT i = alignPhase b T o i • T (b i)

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

Preamble

-- Generated from ChapterWignerSymmetry.lean — theorem BookProof.ChapterWignerSymmetry.imgBasis_apply
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}
variable {b : OrthonormalBasis ι ℂ E} {o : ι}

Formal statement

theorem BookProof.ChapterWignerSymmetry.imgBasis_apply (hT : IsWignerSymmetry T) (i : ι) :
    imgBasis b T o hT i = alignPhase b T o i • T (b i) := by sorry

View graph