sigma — Mathlib

English

The vertices of a single-edge path e from i to j are [i, j].

Русский

Вершины пути из одного ребра e: i до j равны [i, j].

LaTeX

$$$ (e \\colon i \\to j).toPath.vertices = [i, j] $$$

Lean4

theorem sigma (h : ∀ i, (M i).Finitary) : (Matroid.sigma M).Finitary :=
  by
  refine ⟨fun I hI ↦ ?_⟩
  simp only [sigma_indep_iff] at hI ⊢
  intro i
  apply indep_of_forall_finite_subset_indep
  intro J hJI hJ
  convert hI (Sigma.mk i '' J) (by simpa) (hJ.image _) i
  rw [sigma_mk_preimage_image_eq_self]

Похожие утверждения