Theorems · Theorem · combinatorics
Matroid.Indep.subset_ground
∀ {α : Type u_1} {M : Matroid α} {I : Set α}, M.Indep I → I ⊆ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBaseproof · cited by 239
- Matroid.IsBase.subset_groundproof · cited by 30
- Matroid.Indep.exists_isBase_supersetproof · cited by 18
Cited by61
Results whose statement or proof uses this declaration.
- Matroid.Indep.eRk_eq_encardproof · cited by 15
- Matroid.ext_indepproof · cited by 15
- Matroid.indep_singletonproof · cited by 12
- Matroid.Indep.subset_isBasis'_of_subsetproof · cited by 11
- Matroid.isBasis'_iff_isBasis_inter_groundproof · cited by 11
- Matroid.isBasis_ground_iffproof · cited by 10
- Matroid.restrict_closure_eq'proof · cited by 9
- Matroid.delete_indep_iffproof · cited by 7
- Matroid.IsBasis.mapproof · cited by 6
- Matroid.map_isBase_iffproof · cited by 5
- Matroid.Indep.isNonloop_of_memproof · cited by 5
- Matroid.Indep.mem_closure_iff'proof · cited by 5