`BookProof.conjugateli_trans` (Θ : E ≃ₗᵢ[R] E') (A B : E ≃ₗᵢ[R] E) : conjugateₗᵢ Θ (A.trans B) = (conjugateₗᵢ Θ A).trans (conjugateₗᵢ Θ B)

Proved

BookProof.conjugateli_trans

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4.

BookProof.conjugateli_trans (Θ : E ≃ₗᵢ[R] E') (A B : E ≃ₗᵢ[R] E) : conjugateₗᵢ Θ (A.trans B) = (conjugateₗᵢ Θ A).trans (conjugateₗᵢ Θ B)

Formalization note: Lean 4 identifier BookProof.conjugateli_trans.

Preamble

-- Generated from ChapterA4.lean — theorem BookProof.conjugateₗᵢ_trans
import Mathlib
import Definitions.Def_ChapterA4
open BookProof



open MeasureTheory




variable {R E E' : Type*} [Semiring R]
    [SeminormedAddCommGroup E] [SeminormedAddCommGroup E'] [Module R E] [Module R E']

Formal statement

theorem BookProof.conjugateli_trans (Θ : E ≃ₗᵢ[R] E') (A B : E ≃ₗᵢ[R] E) :
    conjugateₗᵢ Θ (A.trans B) = (conjugateₗᵢ Θ A).trans (conjugateₗᵢ Θ B) := by sorry

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