`BookProof.ChapterA4f.boostZ_scales_translation` (l : ℂ) (T : Matrix (Fin 2) (Fin 2) ℂ) : (boostZ l * T * boostZ l⁻¹) 1 0 = (l⁻¹) ^ 2 * T 1 0

Proved

BookProof.ChapterA4f.boostZ_scales_translation

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4f.

BookProof.ChapterA4f.boostZ_scales_translation (l : ℂ) (T : Matrix (Fin 2) (Fin 2) ℂ) : (boostZ l * T * boostZ l⁻¹) 1 0 = (l⁻¹) ^ 2 * T 1 0

Formalization note: Lean 4 identifier BookProof.ChapterA4f.boostZ_scales_translation.

Preamble

-- Generated from ChapterA4f.lean — theorem BookProof.ChapterA4f.boostZ_scales_translation
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA5
import Mathlib
import Definitions.Def_ChapterA4f
open BookProof.ChapterA4f


open Matrix
open scoped ComplexConjugate


open BookProof.ChapterA3 BookProof.ChapterA5

Formal statement

theorem BookProof.ChapterA4f.boostZ_scales_translation (l : ℂ) (T : Matrix (Fin 2) (Fin 2) ℂ) :
    (boostZ l * T * boostZ l⁻¹) 1 0 = (l⁻¹) ^ 2 * T 1 0 := by sorry

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