Prove2Me

`BookProof.ChapterA.conjFixed_invariant` (M : System ℂ V) (θ : AntiUnitary V) (hθ : IsConjugation M θ) : ∀ m ∈ (rxSystem M).ops, ∀ w ∈ conjFixed θ, m w ∈ conjFixed θ

Proved
BookProof.ChapterA.conjFixed_invariant

by leonardopedro · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1f.

BookProof.ChapterA.conjFixed_invariant (M : System ℂ V) (θ : AntiUnitary V) (hθ : IsConjugation M θ) : ∀ m ∈ (rxSystem M).ops, ∀ w ∈ conjFixed θ, m w ∈ conjFixed θ

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

Preamble
-- Generated from ChapterA1f.lean — theorem BookProof.ChapterA.conjFixed_invariant
import Mathlib
import Definitions.Def_ChapterA1f
import Definitions.Def_ChapterA
import Definitions.Def_ChapterA1
open BookProof.ChapterA
open BookProof.ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace RealInnerProductSpace


attribute [local instance] InnerProductSpace.rclikeToReal

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]
Formal statement
theorem BookProof.ChapterA.conjFixed_invariant (M : System ℂ V) (θ : AntiUnitary V) (hθ : IsConjugation M θ) :
    ∀ m ∈ (rxSystem M).ops, ∀ w ∈ conjFixed θ, m w ∈ conjFixed θ := by sorry

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