`BookProof.ChapterWignerSymmetry.key_global` (hS : WignerCoord S o) : (∀ i, i ≠ o → ∀ v, conj (S v o) * S v i = conj (v o) * v i) ∨ (∀ i, i ≠ o → ∀ v, conj (S v o) * S v i = conj (

Proved

BookProof.ChapterWignerSymmetry.key_global

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWignerSymmetry.

BookProof.ChapterWignerSymmetry.key_global (hS : WignerCoord S o) : (∀ i, i ≠ o → ∀ v, conj (S v o) * S v i = conj (v o) * v i) ∨ (∀ i, i ≠ o → ∀ v, conj (S v o) * S v i = conj (conj (v o) * v i))

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

Preamble

-- Generated from ChapterWignerSymmetry.lean — theorem BookProof.ChapterWignerSymmetry.key_global
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.key_global (hS : WignerCoord S o) :
    (∀ i, i ≠ o → ∀ v, conj (S v o) * S v i = conj (v o) * v i) ∨
    (∀ i, i ≠ o → ∀ v, conj (S v o) * S v i = conj (conj (v o) * v i)) := by sorry

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