Prove2Me

`BookProof.BrstUnboundedLeakage.defect_eq_truncDefect` {y : H} (hy : y ∈ V) : T.op ⟨y, hV hy⟩ - truncGen T V hV y = truncDefect T V hV y

Proved
BookProof.BrstUnboundedLeakage.defect_eq_truncDefect

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBrstUnboundedLeakage.

BookProof.BrstUnboundedLeakage.defect_eq_truncDefect {y : H} (hy : y ∈ V) : T.op ⟨y, hV hy⟩ - truncGen T V hV y = truncDefect T V hV y

Formalization note: Lean 4 identifier BookProof.BrstUnboundedLeakage.defect_eq_truncDefect.

Preamble
-- Generated from ChapterBrstUnboundedLeakage.lean — theorem BookProof.BrstUnboundedLeakage.defect_eq_truncDefect
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterBrstUnboundedLeakage
import Definitions.Def_ChapterBrstTruncationLeakage
import Definitions.Def_ChapterStoneResolvent
open BookProof.BrstLeakage
open BookProof.BrstUnboundedLeakage


open NormedSpace Filter Topology
open scoped InnerProductSpace


open BookProof.BrstLeakage BookProof.ChapterStoneResolvent

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

variable (T : UnboundedSelfAdjoint H)
variable (V : Submodule ℂ H) [FiniteDimensional ℂ V] (hV : V ≤ T.domain)
Formal statement
theorem BookProof.BrstUnboundedLeakage.defect_eq_truncDefect {y : H} (hy : y ∈ V) :
    T.op ⟨y, hV hy⟩ - truncGen T V hV y = truncDefect T V hV y := by sorry

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