`BookProof.ChapterA3.lambdaOf_mul` {S₁ S₂ : Matrix (Fin 4) (Fin 4) ℝ} (h1 : IsPin S₁) (h2 : IsPin S₂) : LambdaOf (S₁ * S₂) = LambdaOf S₁ * LambdaOf S₂

Proved

BookProof.ChapterA3.lambdaOf_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3c.

BookProof.ChapterA3.lambdaOf_mul {S₁ S₂ : Matrix (Fin 4) (Fin 4) ℝ} (h1 : IsPin S₁) (h2 : IsPin S₂) : LambdaOf (S₁ * S₂) = LambdaOf S₁ * LambdaOf S₂

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

Preamble

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


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.lambdaOf_mul {S₁ S₂ : Matrix (Fin 4) (Fin 4) ℝ}
    (h1 : IsPin S₁) (h2 : IsPin S₂) :
    LambdaOf (S₁ * S₂) = LambdaOf S₁ * LambdaOf S₂ := by sorry

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