`BookProof.ChapterA3.lemma48_bridge` (T : Matrix (Fin 2) (Fin 2) ℂ) (hdet : T 0 0 * T 1 1 - T 0 1 * T 1 0 = 1) (μ : Fin 4) : (Spinor T)⁻¹ * mgamma μ * Spinor T = ∑ ν, UpsilonC T ν

Proved

BookProof.ChapterA3.lemma48_bridge

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3i.

BookProof.ChapterA3.lemma48_bridge (T : Matrix (Fin 2) (Fin 2) ℂ) (hdet : T 0 0 * T 1 1 - T 0 1 * T 1 0 = 1) (μ : Fin 4) : (Spinor T)⁻¹ * mgamma μ * Spinor T = ∑ ν, UpsilonC T ν μ • mgamma ν

Formalization note: Lean 4 identifier BookProof.ChapterA3.lemma48_bridge.

Preamble

-- Generated from ChapterA3i.lean — theorem BookProof.ChapterA3.lemma48_bridge
import Mathlib
import Definitions.Def_ChapterA3i
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3h
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.lemma48_bridge (T : Matrix (Fin 2) (Fin 2) ℂ)
    (hdet : T 0 0 * T 1 1 - T 0 1 * T 1 0 = 1) (μ : Fin 4) :
    (Spinor T)⁻¹ * mgamma μ * Spinor T = ∑ ν, UpsilonC T ν μ • mgamma ν := by sorry

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