`BookProof.SmDiracYukawa.sm_fermi_N_add_one_surjective` (hom : ∀ i, 0 ≤ om i) (hc0 : 1 ≤ c0) (f : FermiFock n) : ∃ x : fullDom n, onFull (smFermiN om c0) x + (x : FermiFock n) = f

Proved

BookProof.SmDiracYukawa.sm_fermi_N_add_one_surjective

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmDiracYukawa.

BookProof.SmDiracYukawa.sm_fermi_N_add_one_surjective (hom : ∀ i, 0 ≤ om i) (hc0 : 1 ≤ c0) (f : FermiFock n) : ∃ x : fullDom n, onFull (smFermiN om c0) x + (x : FermiFock n) = f

Formalization note: Lean 4 identifier BookProof.SmDiracYukawa.sm_fermi_N_add_one_surjective.

Preamble

-- Generated from ChapterSmDiracYukawa.lean — theorem BookProof.SmDiracYukawa.sm_fermi_N_add_one_surjective
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSmDiracYukawa
import Definitions.Def_ChapterAbelianDiagonalCountable
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.ChapterAbelianDiagonalCountable
open BookProof.SmCar
open BookProof.SmDiracYukawa



open Finset Matrix
open BookProof.SmCar BookProof.FarisLavine

variable {n : ℕ}

noncomputable section

variable {hD M : Matrix (Fin n) (Fin n) ℂ} {z : ℂ} {om : Fin n → ℝ} {c0 : ℝ}

Formal statement

theorem BookProof.SmDiracYukawa.sm_fermi_N_add_one_surjective (hom : ∀ i, 0 ≤ om i) (hc0 : 1 ≤ c0)
    (f : FermiFock n) :
    ∃ x : fullDom n, onFull (smFermiN om c0) x + (x : FermiFock n) = f := by sorry

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