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Theorems · Theorem · combinatorics

Matroid.IsBasis.isBasis_iUnion

∀ {α : Type u_1} {M : Matroid α} {I : Set α} {ι : Type u_2} [Nonempty ι] (X : ι → Set α),
  (∀ (i : ι), M.IsBasis I (X i)) → M.IsBasis I (⋃ i, X i)
Defined in
Mathlib.Combinatorics.Matroid.Basic
Cited by
1 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Nonempty
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matroid.IsBasis.isBasis_sUnion · cited by 0IsBasis.isBasis_sUnionSet · cited by 53352SetSet.iUnion · cited by 2483Set.iUnionMatroid · cited by 1258MatroidMatroid.Indep · cited by 367Matroid.IndepMatroid.IsBasis · cited by 219Matroid.IsBasisClassical.arbitrary · cited by 161Classical.arbitraryMatroid.IsBasis.indep · cited by 51IsBasis.indepSet.iUnion_const · cited by 11Set.iUnion_constMatroid.IsBasis.iUnion_isBasis_iUnion · cited by 2IsBasis.iUnion_isBasis_iU…IsBasis.isBasis_iUnionCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.