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Theorems · Theorem · combinatorics

Matroid.isBasis_iff_isBasis_closure_of_subset

∀ {α : Type u_2} {M : Matroid α} {X I : Set α},
  I ⊆ X →
    autoParam (X ⊆ M.E) Matroid.isBasis_iff_isBasis_closure_of_subset._auto_1 →
      (M.IsBasis I X ↔ M.IsBasis I (M.closure X))
Defined in
Mathlib.Combinatorics.Matroid.Closure
Cited by
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Foundations
Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
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Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.E · cited by 550Matroid.EMatroid.closure · cited by 272Matroid.closureMatroid.IsBasis · cited by 219Matroid.IsBasisMatroid.subset_closure · cited by 23Matroid.subset_closureMatroid.IsBasis.isBasis_subset · cited by 12IsBasis.isBasis_subsetMatroid.IsBasis.isBasis_closure_right · cited by 8IsBasis.isBasis_closure_r…Matroid.isBasis_iff_isBasis_c…CITED BYCITES

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