BookProof.ChapterWignerSymmetry.key_complex'

-- Generated from ChapterWignerSymmetry.lean — theorem BookProof.ChapterWignerSymmetry.key_complex'
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}

theorem BookProof.ChapterWignerSymmetry.key_complex_prime (a b c d : ℂ) (h1 : ‖a‖ = ‖c‖) (h2 : ‖b‖ = ‖d‖) (h3 : ‖a + b‖ = ‖c + d‖)
    (h4 : ‖conj a + (-Complex.I) * conj b‖ = ‖conj c + Complex.I * conj d‖) :
    conj a * b = conj (conj c * d) := by sorry