`BookProof.FriedrichsSquare.adjPairs_mono` {G H : Submodule ℂ (F × F)} (h : G ≤ H) : adjPairs H ≤ adjPairs G

Proved

BookProof.FriedrichsSquare.adjPairs_mono

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFriedrichsSquareFactorization.

BookProof.FriedrichsSquare.adjPairs_mono {G H : Submodule ℂ (F × F)} (h : G ≤ H) : adjPairs H ≤ adjPairs G

Formalization note: Lean 4 identifier BookProof.FriedrichsSquare.adjPairs_mono.

Preamble

-- Generated from ChapterFriedrichsSquareFactorization.lean — theorem BookProof.FriedrichsSquare.adjPairs_mono
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterEsaClosureCore
import Mathlib
import Definitions.Def_ChapterFriedrichsSquareFactorization
import Definitions.Def_ChapterClosureUniqueness
open BookProof.ClosureUniqueness
open BookProof.FriedrichsSquare



open BookProof.FarisLavine BookProof.EsaClosure BookProof.ClosureUniqueness

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
variable {D : Submodule ℂ F}

Formal statement

theorem BookProof.FriedrichsSquare.adjPairs_mono {G H : Submodule ℂ (F × F)} (h : G ≤ H) : adjPairs H ≤ adjPairs G := by sorry

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