Theorems · Theorem · combinatorics
Matroid.Indep.exists_isBasis_subset_union_isBasis
∀ {α : Type u_1} {M : Matroid α} {I X J : Set α},
M.Indep I → I ⊆ X → M.IsBasis J X → ∃ I', M.IsBasis I' X ∧ I ⊆ I' ∧ I' ⊆ I ∪ J- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBaseproof · cited by 239
- Matroid.IsBasisstatement and proof · cited by 219
- Matroid.restrictproof · cited by 111
- Matroid.IsBasis.subset_groundproof · cited by 31
- Matroid.isBase_restrict_iffproof · cited by 11
- Matroid.Indep.indep_restrict_of_subsetproof · cited by 2
- Matroid.Indep.exists_isBase_subset_union_isBaseproof · cited by 1
- Matroid.IsBasis.isBase_restrictproof · cited by 1
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