`BookProof.SmHiggsVacuum.higgsV_ge_min` {lam mu2 : ℝ} (hlam : 0 < lam) (phi : E) : -(mu2 ^ 2 / (4 * lam)) ≤ higgsV lam mu2 phi

Proved

BookProof.SmHiggsVacuum.higgsV_ge_min

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmHiggsVacuum.

BookProof.SmHiggsVacuum.higgsV_ge_min {lam mu2 : ℝ} (hlam : 0 < lam) (phi : E) : -(mu2 ^ 2 / (4 * lam)) ≤ higgsV lam mu2 phi

Formalization note: Lean 4 identifier BookProof.SmHiggsVacuum.higgsV_ge_min.

Preamble

-- Generated from ChapterSmHiggsVacuum.lean — theorem BookProof.SmHiggsVacuum.higgsV_ge_min
import Mathlib
import Definitions.Def_ChapterSmHiggsVacuum
open BookProof.SmHiggsVacuum



open Finset

noncomputable section

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]

Formal statement

theorem BookProof.SmHiggsVacuum.higgsV_ge_min {lam mu2 : ℝ} (hlam : 0 < lam) (phi : E) :
    -(mu2 ^ 2 / (4 * lam)) ≤ higgsV lam mu2 phi := by sorry

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