`BookProof.ChapterA3.hasLambda_mul` {S₁ S₂ Λ₁ Λ₂ : Matrix (Fin 4) (Fin 4) ℝ} (_h1 : IsUnit S₁.det) (_h2 : IsUnit S₂.det) (hL1 : HasLambda S₁ Λ₁) (hL2 : HasLambda S₂ Λ₂)...

Proved

BookProof.ChapterA3.hasLambda_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3c.

BookProof.ChapterA3.hasLambda_mul {S₁ S₂ Λ₁ Λ₂ : Matrix (Fin 4) (Fin 4) ℝ} (_h1 : IsUnit S₁.det) (_h2 : IsUnit S₂.det) (hL1 : HasLambda S₁ Λ₁) (hL2 : HasLambda S₂ Λ₂) : HasLambda (S₁ * S₂) (Λ₁ * Λ₂)

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

Preamble

-- Generated from ChapterA3c.lean — theorem BookProof.ChapterA3.hasLambda_mul
import Mathlib
import Definitions.Def_ChapterA3c
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.hasLambda_mul {S₁ S₂ Λ₁ Λ₂ : Matrix (Fin 4) (Fin 4) ℝ}
    (_h1 : IsUnit S₁.det) (_h2 : IsUnit S₂.det)
    (hL1 : HasLambda S₁ Λ₁) (hL2 : HasLambda S₂ Λ₂) :
    HasLambda (S₁ * S₂) (Λ₁ * Λ₂) := by sorry

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