Theorems · Theorem · combinatorics
Matroid.IsBasis.indep
∀ {α : Type u_1} {M : Matroid α} {I X : Set α}, M.IsBasis I X → M.Indep I- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 51 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.Indepstatement · cited by 367
- Matroid.IsBasisstatement and proof · cited by 219
Cited by51
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.closure_eq_closureproof · cited by 13
- Matroid.IsBasis.isBasis_subsetproof · cited by 12
- Matroid.IsBasis.eRk_eq_encardproof · cited by 7
- Matroid.Indep.closure_eq_setOfPred_isBasis_insertproof · cited by 6
- Matroid.IsBasis.mapproof · cited by 6
- Matroid.Dep.exists_isCircuit_subsetproof · cited by 5
- Matroid.comap_isBasis'_iffproof · cited by 4
- Matroid.IsBasis.eRk_eq_eRkproof · cited by 3
- Matroid.indep_iff_forall_notMem_closure_sdiffproof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Matroid.IsBase.isBase_of_isBasis_supersetproof · cited by 3
- Matroid.map_isBasis_iff'proof · cited by 3