`BookProof.FriedrichsCanonical.friedrichsOp_apply` (P : PosSymOp F) (hdense : Dense (P.dom : Set F)) (y : friedrichsDomain P) : friedrichsOp P hdense y = preim (friedrichsResolvent

Proved

BookProof.FriedrichsCanonical.friedrichsOp_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFriedrichsCanonical.

BookProof.FriedrichsCanonical.friedrichsOp_apply (P : PosSymOp F) (hdense : Dense (P.dom : Set F)) (y : friedrichsDomain P) : friedrichsOp P hdense y = preim (friedrichsResolvent P) y - ((1 : ℝ) : ℂ) • (y : F)

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

Preamble

-- Generated from ChapterFriedrichsCanonical.lean — theorem BookProof.FriedrichsCanonical.friedrichsOp_apply
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterComplexShiftCore
import Mathlib
import Definitions.Def_ChapterFriedrichsCanonical
import Definitions.Def_ChapterFriedrichsExtension
import Definitions.Def_ChapterHashimotoShiftInvert
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.friedrichsOp_apply (P : PosSymOp F) (hdense : Dense (P.dom : Set F))
    (y : friedrichsDomain P) :
    friedrichsOp P hdense y
      = preim (friedrichsResolvent P) y - ((1 : ℝ) : ℂ) • (y : F) := by sorry

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