`BookProof.BrstUnboundedLeakage.projOp_eq_self_of_mem` {x : H} (hx : x ∈ V) : projOp V x = x

Proved

BookProof.BrstUnboundedLeakage.projOp_eq_self_of_mem

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBrstUnboundedLeakage.

BookProof.BrstUnboundedLeakage.projOp_eq_self_of_mem {x : H} (hx : x ∈ V) : projOp V x = x

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

Preamble

-- Generated from ChapterBrstUnboundedLeakage.lean — theorem BookProof.BrstUnboundedLeakage.projOp_eq_self_of_mem
import Definitions.Def_ChapterBrstTruncationLeakage
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterBrstUnboundedLeakage
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.projOp_eq_self_of_mem {x : H} (hx : x ∈ V) : projOp V x = x := by sorry

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