`BookProof.ChapterA3.det_sq_of_sq_neg_one` {S : Matrix (Fin 4) (Fin 4) ℝ} (h : S * S = -1) : S.det * S.det = 1

Proved

BookProof.ChapterA3.det_sq_of_sq_neg_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3d.

BookProof.ChapterA3.det_sq_of_sq_neg_one {S : Matrix (Fin 4) (Fin 4) ℝ} (h : S * S = -1) : S.det * S.det = 1

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

Preamble

-- Generated from ChapterA3d.lean — theorem BookProof.ChapterA3.det_sq_of_sq_neg_one
import Mathlib
import Definitions.Def_ChapterA3d
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix

Formal statement

theorem BookProof.ChapterA3.det_sq_of_sq_neg_one {S : Matrix (Fin 4) (Fin 4) ℝ} (h : S * S = -1) :
    S.det * S.det = 1 := by sorry

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