`BookProof.ChapterA.AntiUnitary.inner_map_map` (θ : AntiUnitary V) (x y : V) : inner ℂ (θ x) (θ y) = conj (inner ℂ x y)

Proved

BookProof.ChapterA.AntiUnitary.inner_map_map

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1.

BookProof.ChapterA.AntiUnitary.inner_map_map (θ : AntiUnitary V) (x y : V) : inner ℂ (θ x) (θ y) = conj (inner ℂ x y)

Formalization note: Lean 4 identifier BookProof.ChapterA.AntiUnitary.inner_map_map.

Preamble

-- Generated from ChapterA1.lean — theorem BookProof.ChapterA.AntiUnitary.inner_map_map
import Mathlib
import Definitions.Def_ChapterA1
import Definitions.Def_ChapterA
open BookProof.ChapterA
open BookProof.ChapterA

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


open scoped ComplexConjugate InnerProductSpace RealInnerProductSpace

Formal statement

theorem BookProof.ChapterA.AntiUnitary.inner_map_map (θ : AntiUnitary V) (x y : V) :
    inner ℂ (θ x) (θ y) = conj (inner ℂ x y) := by sorry

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