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Theorems · Theorem · combinatorics

Matroid.Indep.isBasis_of_maximal_subset

∀ {α : Type u_1} {M : Matroid α} {I X : Set α},
  M.Indep I →
    I ⊆ X →
      (∀ ⦃J : Set α⦄, M.Indep J → I ⊆ J → J ⊆ X → J ⊆ I) →
        autoParam (X ⊆ M.E) Matroid.Indep.isBasis_of_maximal_subset._auto_1 → M.IsBasis I X
Defined in
Mathlib.Combinatorics.Matroid.Basic
Cited by
2 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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Matroid.map_isBasis_iff · cited by 1Matroid.map_isBasis_iffMatroid.Indep.union_isBasis_union_of_contract_isBasis · cited by 0Indep.union_isBasis_union…Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.ELE.le.antisymm · cited by 507le.antisymmMatroid.Indep · cited by 367Matroid.IndepMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.isBasis_iff · cited by 4Matroid.isBasis_iffIndep.isBasis_of_maximal_subs…CITED BYCITES

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Cited by2

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