`BookProof.ChapterLinftyMultiplication.multOp_mul` (φ ψ : α → ℂ) (hφ : MemLp φ ⊤ μ) (hψ : MemLp ψ ⊤ μ) : (multOp φ hφ).comp (multOp ψ hψ) = multOp (fun x => φ x * ψ x)...

Proved

BookProof.ChapterLinftyMultiplication.multOp_mul

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLinftyMultiplication.

BookProof.ChapterLinftyMultiplication.multOp_mul (φ ψ : α → ℂ) (hφ : MemLp φ ⊤ μ) (hψ : MemLp ψ ⊤ μ) : (multOp φ hφ).comp (multOp ψ hψ) = multOp (fun x => φ x * ψ x) (memLp_top_mul hφ hψ)

Formalization note: Lean 4 identifier BookProof.ChapterLinftyMultiplication.multOp_mul.

Preamble

-- Generated from ChapterLinftyMultiplication.lean — theorem BookProof.ChapterLinftyMultiplication.multOp_mul
import Mathlib
import Definitions.Def_ChapterLinftyMultiplication
import Theorems.Thm_BookProof_ChapterLinftyMultiplication_memLp_top_mul
open BookProof.ChapterLinftyMultiplication


noncomputable section

open MeasureTheory ENNReal Complex


variable {α : Type*} [MeasurableSpace α] {μ : Measure α}

Formal statement

theorem BookProof.ChapterLinftyMultiplication.multOp_mul (φ ψ : α → ℂ) (hφ : MemLp φ ⊤ μ) (hψ : MemLp ψ ⊤ μ) :
    (multOp φ hφ).comp (multOp ψ hψ) = multOp (fun x => φ x * ψ x) (memLp_top_mul hφ hψ) := by sorry

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