Prove2Me

`BookProof.LimitCircleExample.lcSol_sq_le` (x : ℝ) : ‖lcSol x‖ ^ 2 ≤ Real.exp π * (1 + x ^ 2)⁻¹

Proved
BookProof.LimitCircleExample.lcSol_sq_le

by leonardopedro · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLimitCircleExample.

BookProof.LimitCircleExample.lcSol_sq_le (x : ℝ) : ‖lcSol x‖ ^ 2 ≤ Real.exp π * (1 + x ^ 2)⁻¹

Formalization note: Lean 4 identifier BookProof.LimitCircleExample.lcSol_sq_le.

Preamble
-- Generated from ChapterLimitCircleExample.lean — theorem BookProof.LimitCircleExample.lcSol_sq_le
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterScalaronCoreEsa
import Definitions.Def_ChapterScalaronWallEsa
import Definitions.Def_ChapterWallDeficiencyObstruction
import Mathlib
import Definitions.Def_ChapterLimitCircleExample
open BookProof.LimitCircleExample



open MeasureTheory Real
open BookProof.FarisLavine BookProof.ScalaronEsa BookProof.ScalaronWallEsa
open BookProof.WallDeficiencyObstruction

noncomputable section
Formal statement
theorem BookProof.LimitCircleExample.lcSol_sq_le (x : ℝ) : ‖lcSol x‖ ^ 2 ≤ Real.exp π * (1 + x ^ 2)⁻¹ := by sorry

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