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

Proved

BookProof.SmHiggsVacuum.higgsV_eq_min_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmHiggsVacuum.

BookProof.SmHiggsVacuum.higgsV_eq_min_iff {lam mu2 : ℝ} (hlam : 0 < lam) (phi : E) : higgsV lam mu2 phi = -(mu2 ^ 2 / (4 * lam)) ↔ ‖phi‖ ^ 2 = mu2 / lam

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

Preamble

-- Generated from ChapterSmHiggsVacuum.lean — theorem BookProof.SmHiggsVacuum.higgsV_eq_min_iff
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_eq_min_iff {lam mu2 : ℝ} (hlam : 0 < lam) (phi : E) :
    higgsV lam mu2 phi = -(mu2 ^ 2 / (4 * lam)) ↔ ‖phi‖ ^ 2 = mu2 / lam := by sorry

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