Prove2Me

`BookProof.ChapterA.conjAU_commutesAntiUnitary` {M : System ℂ V} {N : System ℂ W} {α : V ≃ₗᵢ[ℂ] W} (hα : IsSystemIso M N α) {θ : AntiUnitary V} (hθ : CommutesAntiUnitary M θ) : Com

Proved
BookProof.ChapterA.conjAU_commutesAntiUnitary

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2d.

BookProof.ChapterA.conjAU_commutesAntiUnitary {M : System ℂ V} {N : System ℂ W} {α : V ≃ₗᵢ[ℂ] W} (hα : IsSystemIso M N α) {θ : AntiUnitary V} (hθ : CommutesAntiUnitary M θ) : CommutesAntiUnitary N (conjAU α θ)

Formalization note: Lean 4 identifier BookProof.ChapterA.conjAU_commutesAntiUnitary.

Preamble
-- Generated from ChapterA2d.lean — theorem BookProof.ChapterA.conjAU_commutesAntiUnitary
import Mathlib
import Definitions.Def_ChapterA2d
import Definitions.Def_ChapterA
import Definitions.Def_ChapterA1
open BookProof.ChapterA
open BookProof.ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace


variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]
variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℂ W] [CompleteSpace W]
Formal statement
theorem BookProof.ChapterA.conjAU_commutesAntiUnitary {M : System ℂ V} {N : System ℂ W} {α : V ≃ₗᵢ[ℂ] W}
    (hα : IsSystemIso M N α) {θ : AntiUnitary V} (hθ : CommutesAntiUnitary M θ) :
    CommutesAntiUnitary N (conjAU α θ) := by sorry

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