`BookProof.BrstLeakage.flow_truncGen_mem` {P H : E →L[ℂ] E} (hP : IsIdempotentElem P) (t : ℝ) {x : E} (hx : P x = x) : P (flow (truncGen P H) t x) = flow (truncGen P H) t x

Proved

BookProof.BrstLeakage.flow_truncGen_mem

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBrstTruncationLeakage.

BookProof.BrstLeakage.flow_truncGen_mem {P H : E →L[ℂ] E} (hP : IsIdempotentElem P) (t : ℝ) {x : E} (hx : P x = x) : P (flow (truncGen P H) t x) = flow (truncGen P H) t x

Formalization note: Lean 4 identifier BookProof.BrstLeakage.flow_truncGen_mem.

Preamble

-- Generated from ChapterBrstTruncationLeakage.lean — theorem BookProof.BrstLeakage.flow_truncGen_mem
import Mathlib
import Definitions.Def_ChapterBrstTruncationLeakage
open BookProof.BrstLeakage


open NormedSpace


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

Formal statement

theorem BookProof.BrstLeakage.flow_truncGen_mem {P H : E →L[ℂ] E} (hP : IsIdempotentElem P) (t : ℝ) {x : E}
    (hx : P x = x) : P (flow (truncGen P H) t x) = flow (truncGen P H) t x := by sorry

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