`BookProof.OdeUnitaryFlow.odeKoop_conj_mul` (t : ℝ) (ρ ψ : ℝ → ℂ) (x : ℝ) (hx : x ∈ flowDom t) : odeKoop t (fun y => ρ y * odeKoop (-t) ψ y) x = ρ (mob t x) * ψ x

Proved

BookProof.OdeUnitaryFlow.odeKoop_conj_mul

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterOdeUnitaryFlow.

BookProof.OdeUnitaryFlow.odeKoop_conj_mul (t : ℝ) (ρ ψ : ℝ → ℂ) (x : ℝ) (hx : x ∈ flowDom t) : odeKoop t (fun y => ρ y * odeKoop (-t) ψ y) x = ρ (mob t x) * ψ x

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

Preamble

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



open MeasureTheory Filter Set
open scoped Topology ENNReal

Formal statement

theorem BookProof.OdeUnitaryFlow.odeKoop_conj_mul (t : ℝ) (ρ ψ : ℝ → ℂ) (x : ℝ) (hx : x ∈ flowDom t) :
    odeKoop t (fun y => ρ y * odeKoop (-t) ψ y) x = ρ (mob t x) * ψ x := by sorry

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