Theorems · Theorem · combinatorics
Matroid.IsBasis.subset_ground
∀ {α : Type u_1} {M : Matroid α} {I X : Set α}, M.IsBasis I X → X ⊆ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 550
- Matroid.IsBasisstatement and proof · cited by 219
Cited by31
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.subset_closureproof · cited by 15
- Matroid.IsBasis.isBasis_subsetproof · cited by 12
- Matroid.Indep.closure_eq_setOfPred_isBasis_insertproof · cited by 6
- Matroid.IsBasis.mapproof · cited by 6
- Matroid.delete_isBasis_iffproof · cited by 4
- Matroid.map_isBasis_iff'proof · cited by 3
- Matroid.IsBasis.contract_eq_contract_deleteproof · cited by 3
- Matroid.Indep.isBasis_setOfPred_insert_isBasisproof · cited by 3
- Matroid.ground_isFlatproof · cited by 2
- Matroid.comap_isBasis_iffproof · cited by 2
- Matroid.IsBasis.iUnion_isBasis_iUnionproof · cited by 2
- Matroid.IsBasis.restrict_isBaseproof · cited by 2