`BookProof.Complexification.Cx.complexify_isSubsystem` (M : System ℝ W) {Y : Submodule ℝ W} (hY : (M).IsSubsystem Y) : (cxSystem M).IsSubsystem (complexify Y)

Proved

BookProof.Complexification.Cx.complexify_isSubsystem

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA1b.

BookProof.Complexification.Cx.complexify_isSubsystem (M : System ℝ W) {Y : Submodule ℝ W} (hY : (M).IsSubsystem Y) : (cxSystem M).IsSubsystem (complexify Y)

Formalization note: Lean 4 identifier BookProof.Complexification.Cx.complexify_isSubsystem.

Preamble

-- Generated from ChapterA1b.lean — theorem BookProof.Complexification.Cx.complexify_isSubsystem
import Mathlib
import Definitions.Def_ChapterA1b
import Definitions.Def_ChapterA
import Definitions.Def_Complexification
open BookProof.ChapterA
open BookProof.ChapterA
open BookProof.Complexification
open BookProof.Complexification.Cx


open scoped RealInnerProductSpace
open BookProof.ChapterA


variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℝ W]

variable [CompleteSpace W]

Formal statement

theorem BookProof.Complexification.Cx.complexify_isSubsystem (M : System ℝ W) {Y : Submodule ℝ W}
    (hY : (M).IsSubsystem Y) : (cxSystem M).IsSubsystem (complexify Y) := by sorry

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