`BookProof.BrstUnboundedLeakage.proj_mul_truncGen` : projOp V * truncGen T V hV = truncGen T V hV
ProvedBookProof.BrstUnboundedLeakage.proj_mul_truncGentheoremstimepiece
Prove the following Lean 4 theorem from ChapterBrstUnboundedLeakage.
BookProof.BrstUnboundedLeakage.proj_mul_truncGen : projOp V * truncGen T V hV = truncGen T V hV
Formalization note: Lean 4 identifier BookProof.BrstUnboundedLeakage.proj_mul_truncGen.
Preamble
-- Generated from ChapterBrstUnboundedLeakage.lean — theorem BookProof.BrstUnboundedLeakage.proj_mul_truncGen
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.proj_mul_truncGen : projOp V * truncGen T V hV = truncGen T V hV := by sorry