`BookProof.FriedrichsSquare.exists_mem_factorRel_add` (A : D →ₗ[ℂ] F) (h : F) : ∃ p : F × F, p ∈ factorRel A ∧ p.1 + p.2 = h

Proved

BookProof.FriedrichsSquare.exists_mem_factorRel_add

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFriedrichsSquareFactorization.

BookProof.FriedrichsSquare.exists_mem_factorRel_add (A : D →ₗ[ℂ] F) (h : F) : ∃ p : F × F, p ∈ factorRel A ∧ p.1 + p.2 = h

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

Preamble

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



open BookProof.FarisLavine BookProof.EsaClosure BookProof.ClosureUniqueness

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

variable [CompleteSpace F]

Formal statement

theorem BookProof.FriedrichsSquare.exists_mem_factorRel_add (A : D →ₗ[ℂ] F) (h : F) :
    ∃ p : F × F, p ∈ factorRel A ∧ p.1 + p.2 = h := by sorry

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