`BookProof.BrstReducedTransfer.transfer_bijective` (hzero : ∀ x : H, U 0 x = x) (hgroup : ∀ (s t : ℝ) (x : H), U s (U t x) = U (s + t) x) (t : ℝ) : Function.Bijective (transfer Om

Proved

BookProof.BrstReducedTransfer.transfer_bijective

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBrstReducedTransfer.

BookProof.BrstReducedTransfer.transfer_bijective (hzero : ∀ x : H, U 0 x = x) (hgroup : ∀ (s t : ℝ) (x : H), U s (U t x) = U (s + t) x) (t : ℝ) : Function.Bijective (transfer Om U hcomm t)

Formalization note: Lean 4 identifier BookProof.BrstReducedTransfer.transfer_bijective.

Preamble

-- Generated from ChapterBrstReducedTransfer.lean — theorem BookProof.BrstReducedTransfer.transfer_bijective
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterBrstReducedTransfer
open BookProof.BrstReducedTransfer



open BookProof BookProof.ChapterStoneResolvent


variable {H : Type*} [NormedAddCommGroup H] [NormedSpace ℂ H]

variable (Om : H →L[ℂ] H)

variable {Om}
variable (Om)
variable (U : ℝ → (H →L[ℂ] H)) (hcomm : ∀ (t : ℝ) (y : H), U t (Om y) = Om (U t y))

Formal statement

theorem BookProof.BrstReducedTransfer.transfer_bijective (hzero : ∀ x : H, U 0 x = x)
    (hgroup : ∀ (s t : ℝ) (x : H), U s (U t x) = U (s + t) x) (t : ℝ) :
    Function.Bijective (transfer Om U hcomm t) := by sorry

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