`BookProof.OdeUnitaryFlow.odeKoop_neg_odeKoop` (t : ℝ) (ψ : ℝ → ℂ) (x : ℝ) (hx : x ∈ flowDom (-t)) : odeKoop (-t) (odeKoop t ψ) x = ψ x

Proved

BookProof.OdeUnitaryFlow.odeKoop_neg_odeKoop

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterOdeUnitaryFlow.

BookProof.OdeUnitaryFlow.odeKoop_neg_odeKoop (t : ℝ) (ψ : ℝ → ℂ) (x : ℝ) (hx : x ∈ flowDom (-t)) : odeKoop (-t) (odeKoop t ψ) x = ψ x

Formalization note: Lean 4 identifier BookProof.OdeUnitaryFlow.odeKoop_neg_odeKoop.

Preamble

-- Generated from ChapterOdeUnitaryFlow.lean — theorem BookProof.OdeUnitaryFlow.odeKoop_neg_odeKoop
import Mathlib
import Definitions.Def_ChapterOdeUnitaryFlow
open BookProof.OdeUnitaryFlow



open MeasureTheory Filter Set
open scoped Topology ENNReal

Formal statement

theorem BookProof.OdeUnitaryFlow.odeKoop_neg_odeKoop (t : ℝ) (ψ : ℝ → ℂ) (x : ℝ) (hx : x ∈ flowDom (-t)) :
    odeKoop (-t) (odeKoop t ψ) x = ψ x := by sorry

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