`BookProof.BrstReducedTransfer.mem_physicalStates` {x : H} : x ∈ physicalStates Om ↔ Om x = 0

Proved

BookProof.BrstReducedTransfer.mem_physicalStates

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBrstReducedTransfer.

BookProof.BrstReducedTransfer.mem_physicalStates {x : H} : x ∈ physicalStates Om ↔ Om x = 0

Formalization note: Lean 4 identifier BookProof.BrstReducedTransfer.mem_physicalStates.

Preamble

-- Generated from ChapterBrstReducedTransfer.lean — theorem BookProof.BrstReducedTransfer.mem_physicalStates
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterBrstReducedTransfer
open BookProof.BrstReducedTransfer



open BookProof BookProof.ChapterStoneResolvent


variable {H : Type*} [NormedAddCommGroup H] [NormedSpace ℂ H]

variable (Om : H →L[ℂ] H)

Formal statement

theorem BookProof.BrstReducedTransfer.mem_physicalStates {x : H} : x ∈ physicalStates Om ↔ Om x = 0 := by sorry

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