`BookProof.YangMillsAbelianNoGap.le_of_sq_le` {a t b : ℝ} (ht : 0 ≤ t) (hb : 0 ≤ b) (h : a ^ 2 ≤ t ^ 2 * b ^ 2) : a ≤ t * b

Proved

BookProof.YangMillsAbelianNoGap.le_of_sq_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterYangMillsAbelianNoGap.

BookProof.YangMillsAbelianNoGap.le_of_sq_le {a t b : ℝ} (ht : 0 ≤ t) (hb : 0 ≤ b) (h : a ^ 2 ≤ t ^ 2 * b ^ 2) : a ≤ t * b

Formalization note: Lean 4 identifier BookProof.YangMillsAbelianNoGap.le_of_sq_le.

Preamble

-- Generated from ChapterYangMillsAbelianNoGap.lean — theorem BookProof.YangMillsAbelianNoGap.le_of_sq_le
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterGaussCoordCombo
import Definitions.Def_ChapterSqueezedGaussStates
import Definitions.Def_ChapterYangMillsHermite
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Mathlib
import Definitions.Def_ChapterYangMillsAbelianNoGap
open BookProof.YangMillsAbelianNoGap



open MvPolynomial MeasureTheory
open BookProof.HermiteProductCore BookProof.GaussCoordCombo BookProof.SqueezedGaussStates
open BookProof.YangMillsHermite BookProof.FarisLavine BookProof.HermiteGalerkin

noncomputable section

variable {d : ℕ}

variable (vf : Fin d → ℝ) (Mf : Fin d → ℕ)

Formal statement

theorem BookProof.YangMillsAbelianNoGap.le_of_sq_le {a t b : ℝ} (ht : 0 ≤ t) (hb : 0 ≤ b)
    (h : a ^ 2 ≤ t ^ 2 * b ^ 2) : a ≤ t * b := by sorry

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