`BookProof.ChapterMajoranaProp74.prop74_intertwine` (g ns : Matrix (Fin 4) (Fin 4) ℂ) (hg2 : g * g = 1) (hns2 : ns * ns = -1) (hgns : g * ns = -(ns * g)) (c s m q E : ℝ) (hcs : c ^

Proved

BookProof.ChapterMajoranaProp74.prop74_intertwine

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMajoranaProp74.

BookProof.ChapterMajoranaProp74.prop74_intertwine (g ns : Matrix (Fin 4) (Fin 4) ℂ) (hg2 : g * g = 1) (hns2 : ns * ns = -1) (hgns : g * ns = -(ns * g)) (c s m q E : ℝ) (hcs : c ^ 2 + s ^ 2 = 1) (hm : m = (c ^ 2 - s ^ 2) * E) (hq : q = 2 * c * s * E) : Qmat g ns m q * Sinv (ns * g) c s = Sinv (ns * g) c s * Rmat g E

Formalization note: Lean 4 identifier BookProof.ChapterMajoranaProp74.prop74_intertwine.

Preamble

-- Generated from ChapterMajoranaProp74.lean — theorem BookProof.ChapterMajoranaProp74.prop74_intertwine
import Definitions.Def_ChapterMajoranaFourier
import Definitions.Def_ChapterA3
import Mathlib
import Definitions.Def_ChapterMajoranaProp74
open BookProof.ChapterMajoranaProp74


open Matrix


open BookProof.ChapterMajoranaFourier
open BookProof.ChapterA3

Formal statement

theorem BookProof.ChapterMajoranaProp74.prop74_intertwine (g ns : Matrix (Fin 4) (Fin 4) ℂ)
    (hg2 : g * g = 1) (hns2 : ns * ns = -1) (hgns : g * ns = -(ns * g))
    (c s m q E : ℝ) (hcs : c ^ 2 + s ^ 2 = 1) (hm : m = (c ^ 2 - s ^ 2) * E)
    (hq : q = 2 * c * s * E) :
    Qmat g ns m q * Sinv (ns * g) c s = Sinv (ns * g) c s * Rmat g E := by sorry

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