Prove2Me

`BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.stoneU_op` (t : ℝ) (x : T.domain) : T.op ⟨T.stoneU t (x : H), T.stoneU_mem_domain t x⟩ = T.stoneU t (T.op x)

Proved
BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.stoneU_op

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterStoneGenerator.

BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.stoneU_op (t : ℝ) (x : T.domain) : T.op ⟨T.stoneU t (x : H), T.stoneU_mem_domain t x⟩ = T.stoneU t (T.op x)

Formalization note: Lean 4 identifier BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.stoneU_op.

Preamble
-- Generated from ChapterStoneGenerator.lean — theorem BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.stoneU_op
import Mathlib
import Definitions.Def_ChapterStoneGenerator
import Definitions.Def_ChapterSirkTrotterKato
import Definitions.Def_ChapterStoneResolvent
import Definitions.Def_ChapterStoneUnitary
open BookProof.ChapterSirkTrotterKato
open BookProof.ChapterStoneResolvent
open BookProof.ChapterStoneResolvent


open scoped InnerProductSpace
open Filter Topology NormedSpace


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


variable (T : UnboundedSelfAdjoint H)
Formal statement
theorem BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.stoneU_op (t : ℝ) (x : T.domain) :
    T.op ⟨T.stoneU t (x : H), T.stoneU_mem_domain t x⟩ = T.stoneU t (T.op x) := by sorry

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