`BookProof.ChapterA.conjFixed_ne_bot` [Nontrivial V] (θ : AntiUnitary V) (hθ : ∀ x, θ (θ x) = x) : conjFixed θ ≠ ⊥

Proved

BookProof.ChapterA.conjFixed_ne_bot

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1f.

BookProof.ChapterA.conjFixed_ne_bot [Nontrivial V] (θ : AntiUnitary V) (hθ : ∀ x, θ (θ x) = x) : conjFixed θ ≠ ⊥

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

Preamble

-- Generated from ChapterA1f.lean — theorem BookProof.ChapterA.conjFixed_ne_bot
import Mathlib
import Definitions.Def_ChapterA1f
import Definitions.Def_ChapterA1
import Definitions.Def_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_ne_bot [Nontrivial V] (θ : AntiUnitary V) (hθ : ∀ x, θ (θ x) = x) :
    conjFixed θ ≠ ⊥ := by sorry

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