`BookProof.BrstLeakage.norm_flow_sub_flow_le_cycle` {H B : E →L[ℂ] E} (hH : IsSelfAdjoint H) (hB : IsSelfAdjoint B) (tau : ℝ) (htau : 0 ≤ tau) (w : E) : ‖flow H tau w - flow B tau

Proved

BookProof.BrstLeakage.norm_flow_sub_flow_le_cycle

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBrstTruncationLeakage.

BookProof.BrstLeakage.norm_flow_sub_flow_le_cycle {H B : E →L[ℂ] E} (hH : IsSelfAdjoint H) (hB : IsSelfAdjoint B) (tau : ℝ) (htau : 0 ≤ tau) (w : E) : ‖flow H tau w - flow B tau w‖ ≤ (‖H - B‖ * tau) * ‖w‖

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

Preamble

-- Generated from ChapterBrstTruncationLeakage.lean — theorem BookProof.BrstLeakage.norm_flow_sub_flow_le_cycle
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.norm_flow_sub_flow_le_cycle {H B : E →L[ℂ] E} (hH : IsSelfAdjoint H)
    (hB : IsSelfAdjoint B) (tau : ℝ) (htau : 0 ≤ tau) (w : E) :
    ‖flow H tau w - flow B tau w‖ ≤ (‖H - B‖ * tau) * ‖w‖ := by sorry

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