ofExistsFiniteIsBase_rankFinite — Mathlib

English

The finite-base construction yields a matroid whose base predicate is preserved.

Русский

Конструкция с конечной базой порождает матроид, база которого сохраняется.

LaTeX

$$$\\mathrm{ofExistsFiniteIsBase} E IsBase exists_finite_base isBase_exchange subset_ground$.IsBase = IsBase$$

Lean4

instance ofExistsFiniteIsBase_rankFinite (E : Set α) IsBase exists_finite_base isBase_exchange subset_ground :
    RankFinite (Matroid.ofExistsFiniteIsBase E IsBase exists_finite_base isBase_exchange subset_ground) :=
  by
  obtain ⟨B, hB, hfin⟩ := exists_finite_base
  exact Matroid.IsBase.rankFinite_of_finite (by simpa) hfin

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