`BookProof.SmCar.fermi_mass_gap` {m : Fin n → ℝ} {mu : ℝ} (hmu : 0 ≤ mu) (hm : ∀ i, mu ≤ m i) (ψ : FermiFock n) (hvac : ψ ∅ = 0) : mu * ‖ψ‖ ^ 2 ≤ (inner ℂ ψ (fermiEnergy...

Proved

BookProof.SmCar.fermi_mass_gap

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmCarAlgebra.

BookProof.SmCar.fermi_mass_gap {m : Fin n → ℝ} {mu : ℝ} (hmu : 0 ≤ mu) (hm : ∀ i, mu ≤ m i) (ψ : FermiFock n) (hvac : ψ ∅ = 0) : mu * ‖ψ‖ ^ 2 ≤ (inner ℂ ψ (fermiEnergy m ψ) : ℂ).re

Formalization note: Lean 4 identifier BookProof.SmCar.fermi_mass_gap.

Preamble

-- Generated from ChapterSmCarAlgebra.lean — theorem BookProof.SmCar.fermi_mass_gap
import Mathlib
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.SmCar



open Finset

variable {n : ℕ}

Formal statement

theorem BookProof.SmCar.fermi_mass_gap {m : Fin n → ℝ} {mu : ℝ} (hmu : 0 ≤ mu) (hm : ∀ i, mu ≤ m i)
    (ψ : FermiFock n) (hvac : ψ ∅ = 0) :
    mu * ‖ψ‖ ^ 2 ≤ (inner ℂ ψ (fermiEnergy m ψ) : ℂ).re := by sorry

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