`BookProof.ChapterF7.l2pair_smul_left` (c : ℂ) (f g : 𝓢(ℝ, ℂ)) : l2pair (c • f) g = (starRingEnd ℂ) c * l2pair f g

Proved

BookProof.ChapterF7.l2pair_smul_left

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF7.

BookProof.ChapterF7.l2pair_smul_left (c : ℂ) (f g : 𝓢(ℝ, ℂ)) : l2pair (c • f) g = (starRingEnd ℂ) c * l2pair f g

Formalization note: Lean 4 identifier BookProof.ChapterF7.l2pair_smul_left.

Preamble

-- Generated from ChapterF7.lean — theorem BookProof.ChapterF7.l2pair_smul_left
import Mathlib
import Definitions.Def_ChapterF7
open BookProof.ChapterF7


open SchwartzMap MeasureTheory Complex
open scoped BigOperators


noncomputable section

Formal statement

theorem BookProof.ChapterF7.l2pair_smul_left (c : ℂ) (f g : 𝓢(ℝ, ℂ)) :
    l2pair (c • f) g = (starRingEnd ℂ) c * l2pair f g := by sorry

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