Prove2Me

`BookProof.FriedrichsCanonical.exists_formExt_eq` {P : PosSymOp F} {v : F} (hv : v ∈ formDomain P) : ∃ k : FormSpace P, formExt P k = v

Proved
BookProof.FriedrichsCanonical.exists_formExt_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFriedrichsCanonical.

BookProof.FriedrichsCanonical.exists_formExt_eq {P : PosSymOp F} {v : F} (hv : v ∈ formDomain P) : ∃ k : FormSpace P, formExt P k = v

Formalization note: Lean 4 identifier BookProof.FriedrichsCanonical.exists_formExt_eq.

Preamble
-- Generated from ChapterFriedrichsCanonical.lean — theorem BookProof.FriedrichsCanonical.exists_formExt_eq
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterComplexShiftCore
import Mathlib
import Definitions.Def_ChapterFriedrichsCanonical
import Definitions.Def_ChapterFriedrichsExtension
open BookProof.FriedrichsExtension
open BookProof.FriedrichsExtension.FormDom
open BookProof.FriedrichsCanonical



open BookProof.FarisLavine BookProof.YangMillsFriedrichs BookProof.HashimotoShiftInvert
open BookProof.FriedrichsExtension BookProof.FriedrichsExtension.FormDom

noncomputable section

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]
Formal statement
theorem BookProof.FriedrichsCanonical.exists_formExt_eq {P : PosSymOp F} {v : F} (hv : v ∈ formDomain P) :
    ∃ k : FormSpace P, formExt P k = v := by sorry

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