`BookProof.FriedrichsCanonical.eq_zero_of_inner_coe_eq_zero` (P : PosSymOp F) (k : FormSpace P) (h : ∀ v : FormDom P, (inner ℂ (v : FormSpace P) k : ℂ) = 0) : k = 0

Proved

BookProof.FriedrichsCanonical.eq_zero_of_inner_coe_eq_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFriedrichsCanonical.

BookProof.FriedrichsCanonical.eq_zero_of_inner_coe_eq_zero (P : PosSymOp F) (k : FormSpace P) (h : ∀ v : FormDom P, (inner ℂ (v : FormSpace P) k : ℂ) = 0) : k = 0

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

Preamble

-- Generated from ChapterFriedrichsCanonical.lean — theorem BookProof.FriedrichsCanonical.eq_zero_of_inner_coe_eq_zero
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
open BookProof.FriedrichsCanonical



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

noncomputable section

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

Formal statement

theorem BookProof.FriedrichsCanonical.eq_zero_of_inner_coe_eq_zero (P : PosSymOp F) (k : FormSpace P)
    (h : ∀ v : FormDom P, (inner ℂ (v : FormSpace P) k : ℂ) = 0) : k = 0 := by sorry

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