`BookProof.ChapterA.System.orthogonal_isSubsystem` (M : System 𝔽 V) (hM : IsNormal M) {W : Submodule 𝔽 V} (hW : IsSubsystem M W) : IsSubsystem M Wᗮ

Proved

BookProof.ChapterA.System.orthogonal_isSubsystem

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA.

BookProof.ChapterA.System.orthogonal_isSubsystem (M : System 𝔽 V) (hM : IsNormal M) {W : Submodule 𝔽 V} (hW : IsSubsystem M W) : IsSubsystem M Wᗮ

Formalization note: Lean 4 identifier BookProof.ChapterA.System.orthogonal_isSubsystem.

Preamble

-- Generated from ChapterA.lean — theorem BookProof.ChapterA.System.orthogonal_isSubsystem
import Mathlib
import Definitions.Def_ChapterA
open BookProof.ChapterA
open BookProof.ChapterA

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


open scoped ComplexConjugate InnerProductSpace

Formal statement

theorem BookProof.ChapterA.System.orthogonal_isSubsystem (M : System 𝔽 V) (hM : IsNormal M)
    {W : Submodule 𝔽 V} (hW : IsSubsystem M W) : IsSubsystem M Wᗮ := by sorry

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