`BookProof.SqueezedGaussStates.coordCombo_smul_add` (i : Fin d) (c₁ c₂ : ℕ → ℝ) (α γ : ℝ) (p K : ℕ) : ((α : ℝ) : ℂ) • coordCombo i c₁ p K + ((γ : ℝ) : ℂ) •...

Proved

BookProof.SqueezedGaussStates.coordCombo_smul_add

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSqueezedGaussStates.

BookProof.SqueezedGaussStates.coordCombo_smul_add (i : Fin d) (c₁ c₂ : ℕ → ℝ) (α γ : ℝ) (p K : ℕ) : ((α : ℝ) : ℂ) • coordCombo i c₁ p K + ((γ : ℝ) : ℂ) • coordCombo i c₂ p K = coordCombo i (fun k => α * c₁ k + γ * c₂ k) p K

Formalization note: Lean 4 identifier BookProof.SqueezedGaussStates.coordCombo_smul_add.

Preamble

-- Generated from ChapterSqueezedGaussStates.lean — theorem BookProof.SqueezedGaussStates.coordCombo_smul_add
import Mathlib
import Definitions.Def_ChapterSqueezedGaussStates
import Definitions.Def_ChapterGaussCoordCombo
import Definitions.Def_ChapterHermiteProductCore
open BookProof.GaussCoordCombo
open BookProof.HermiteProductCore
open BookProof.SqueezedGaussStates



open MvPolynomial BookProof.HermiteProductCore BookProof.GaussCoordCombo

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.SqueezedGaussStates.coordCombo_smul_add (i : Fin d) (c₁ c₂ : ℕ → ℝ) (α γ : ℝ) (p K : ℕ) :
    ((α : ℝ) : ℂ) • coordCombo i c₁ p K + ((γ : ℝ) : ℂ) • coordCombo i c₂ p K
      = coordCombo i (fun k => α * c₁ k + γ * c₂ k) p K := by sorry

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