`BookProof.ChapterA3.upsilon_metric` (T : Matrix (Fin 2) (Fin 2) ℂ) (hT : T.det = 1) : (Upsilon T)ᵀ * minkowskiMat * Upsilon T = minkowskiMat

Proved

BookProof.ChapterA3.upsilon_metric

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3h.

BookProof.ChapterA3.upsilon_metric (T : Matrix (Fin 2) (Fin 2) ℂ) (hT : T.det = 1) : (Upsilon T)ᵀ * minkowskiMat * Upsilon T = minkowskiMat

Formalization note: Lean 4 identifier BookProof.ChapterA3.upsilon_metric.

Preamble

-- Generated from ChapterA3h.lean — theorem BookProof.ChapterA3.upsilon_metric
import Mathlib
import Definitions.Def_ChapterA3h
import Definitions.Def_ChapterA3b
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.upsilon_metric (T : Matrix (Fin 2) (Fin 2) ℂ) (hT : T.det = 1) :
    (Upsilon T)ᵀ * minkowskiMat * Upsilon T = minkowskiMat := by sorry

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