Prove2Me

`BookProof.ChapterA.realification_reducible_of_conjugation` [Nontrivial V] (M : System ℂ V) (θ : AntiUnitary V) (hθ : IsConjugation M θ) : ¬ (rxSystem M).IsIrreducible

Proved
BookProof.ChapterA.realification_reducible_of_conjugation

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1f.

BookProof.ChapterA.realification_reducible_of_conjugation [Nontrivial V] (M : System ℂ V) (θ : AntiUnitary V) (hθ : IsConjugation M θ) : ¬ (rxSystem M).IsIrreducible

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

Preamble
-- Generated from ChapterA1f.lean — theorem BookProof.ChapterA.realification_reducible_of_conjugation
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.realification_reducible_of_conjugation [Nontrivial V] (M : System ℂ V)
    (θ : AntiUnitary V) (hθ : IsConjugation M θ) : ¬ (rxSystem M).IsIrreducible := by sorry

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