`BookProof.FockQuadratic.amp_mul_le` (hω : ∀ i, 0 ≤ ω i) {P Q : Idx ι} (hPQ : deg P + deg Q ≤ 2) (b : Idx ι) (p r : ℝ) : amp P Q b * r * p ≤ sig ω b * p ^ 2 + sig ω (tgt P Q b) * r

Proved

BookProof.FockQuadratic.amp_mul_le

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFockQuadraticEsa.

BookProof.FockQuadratic.amp_mul_le (hω : ∀ i, 0 ≤ ω i) {P Q : Idx ι} (hPQ : deg P + deg Q ≤ 2) (b : Idx ι) (p r : ℝ) : amp P Q b * r * p ≤ sig ω b * p ^ 2 + sig ω (tgt P Q b) * r ^ 2

Formalization note: Lean 4 identifier BookProof.FockQuadratic.amp_mul_le.

Preamble

-- Generated from ChapterFockQuadraticEsa.lean — theorem BookProof.FockQuadratic.amp_mul_le
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterOperatorSeriesEsa
import Mathlib
import Definitions.Def_ChapterFockQuadraticEsa
import Definitions.Def_ChapterA3n
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
open BookProof.ChapterA3n
open BookProof.NavierStokesFlow.HermiteFarisLavine
open BookProof.FockQuadratic

variable {ι : Type*}
variable {ω : ι → ℝ}


open scoped ENNReal


open BookProof.FarisLavine BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.NavierStokesFlow.LpNat BookProof.OperatorSeries

noncomputable section

Formal statement

theorem BookProof.FockQuadratic.amp_mul_le (hω : ∀ i, 0 ≤ ω i) {P Q : Idx ι} (hPQ : deg P + deg Q ≤ 2) (b : Idx ι)
    (p r : ℝ) :
    amp P Q b * r * p ≤ sig ω b * p ^ 2 + sig ω (tgt P Q b) * r ^ 2 := by sorry

View graph