`BookProof.BrstUnboundedLeakage.flow_mem_of_proj` {P B : H →L[ℂ] H} (hPB : P * B = B) (t : ℝ) {x : H} (hx : P x = x) : P (flow B t x) = flow B t x

Proved

BookProof.BrstUnboundedLeakage.flow_mem_of_proj

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBrstUnboundedLeakage.

BookProof.BrstUnboundedLeakage.flow_mem_of_proj {P B : H →L[ℂ] H} (hPB : P * B = B) (t : ℝ) {x : H} (hx : P x = x) : P (flow B t x) = flow B t x

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

Preamble

-- Generated from ChapterBrstUnboundedLeakage.lean — theorem BookProof.BrstUnboundedLeakage.flow_mem_of_proj
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterBrstUnboundedLeakage
import Definitions.Def_ChapterBrstTruncationLeakage
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.flow_mem_of_proj {P B : H →L[ℂ] H} (hPB : P * B = B)
    (t : ℝ) {x : H} (hx : P x = x) : P (flow B t x) = flow B t x := by sorry

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