Theorems · Theorem · combinatorics
Matroid.Indep.inter_isBasis_iInter
∀ {α : Type u_2} {M : Matroid α} {ι : Sort u_3} {I : Set α} [Nonempty ι] {X : ι → Set α},
M.Indep I → (∀ (i : ι), M.IsBasis (X i ∩ I) (X i)) → M.IsBasis ((⋂ i, X i) ∩ I) (⋂ i, X i)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
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Cites11
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
- Set.univproof · cited by 3,945
- Matroidstatement and proof · cited by 1,258
- Set.iInterstatement and proof · cited by 1,084
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBasisstatement and proof · cited by 219
- Set.iInter_congr_Propproof · cited by 170
- Set.univ_nonemptyproof · cited by 21
- Set.iInter_trueproof · cited by 17
- Matroid.Indep.inter_isBasis_biInterproof · cited by 2
- Set.iInter_plift_downproof · cited by 2
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