`BookProof.ChapterA.qembed_injective` [Nontrivial V] (θ : AntiUnitary V) (hθ : ∀ x, θ (θ x) = -x) : Function.Injective (qembed θ hθ)

Proved

BookProof.ChapterA.qembed_injective

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2c.

BookProof.ChapterA.qembed_injective [Nontrivial V] (θ : AntiUnitary V) (hθ : ∀ x, θ (θ x) = -x) : Function.Injective (qembed θ hθ)

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

Preamble

-- Generated from ChapterA2c.lean — theorem BookProof.ChapterA.qembed_injective
import Mathlib
import Definitions.Def_ChapterA2c
import Definitions.Def_ChapterA1
import Definitions.Def_ChapterA
open BookProof.ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace Quaternion


variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]

Formal statement

theorem BookProof.ChapterA.qembed_injective [Nontrivial V] (θ : AntiUnitary V) (hθ : ∀ x, θ (θ x) = -x) :
    Function.Injective (qembed θ hθ) := by sorry

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