Theorems · Theorem · combinatorics
Matroid.IsRkFinite.iUnion
∀ {α : Type u_1} {M : Matroid α} {ι : Type u_2} [Finite ι] {Xs : ι → Set α},
(∀ (i : ι), M.IsRkFinite (Xs i)) → M.IsRkFinite (⋃ i, Xs i)A union of finitely many IsRkFinite sets is IsRkFinite.
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- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LE.le.transproof · cited by 3,151
- Finitestatement and proof · cited by 3,029
- Set.iUnionstatement and proof · cited by 2,483
- Set.Finiteproof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.closureproof · cited by 272
- Matroid.IsBasis'proof · cited by 101
- Set.subset_iUnionproof · cited by 81
- Matroid.IsRkFinitestatement and proof · cited by 53
- Matroid.exists_isBasis'proof · cited by 30
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