Theorems · Theorem · combinatorics
Matroid.Indep.subset_isBasis_of_subset
∀ {α : Type u_1} {M : Matroid α} {I X : Set α},
M.Indep I → I ⊆ X → autoParam (X ⊆ M.E) Matroid.Indep.subset_isBasis_of_subset._auto_1 → ∃ J, M.IsBasis J X ∧ I ⊆ J- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Estatement and proof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBasisstatement · cited by 219
- Maximalproof · cited by 211
- Matroid.maximalityproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- Matroid.exists_isBasisproof · cited by 23
- Matroid.Indep.subset_isBasis'_of_subsetproof · cited by 11
- Matroid.Indep.closure_eq_setOfPred_isBasis_insertproof · cited by 6
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Matroid.Indep.augmentproof · cited by 2
- Matroid.IsBasis.exists_isBasis_inter_eq_of_supersetproof · cited by 2
- Matroid.Indep.exists_isBase_subset_spanningproof · cited by 1
- Matroid.Indep.exists_isBase_subset_union_isBaseproof · cited by 1
- Matroid.IsFlat.iInterproof · cited by 1
- Matroid.Indep.union_indep_iff_forall_notMem_closure_rightproof · cited by 1
- Matroid.exists_isBasis_subset_isBasisproof · cited by 1
- Matroid.Indep.subset_finite_isBasis_of_subset_of_isRkFiniteproof · cited by 0