Theorems · Theorem · combinatorics
Matroid.IsBase.subset_ground
∀ {α : Type u_1} {M : Matroid α} {B : Set α}, M.IsBase B → B ⊆ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 30 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.
Cites5
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.IsBasestatement and proof · cited by 239
- Matroid.subset_groundproof · cited by 1
Cited by30
Results whose statement or proof uses this declaration.
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.ext_isBaseproof · cited by 7
- Matroid.IsBase.compl_isBase_dualproof · cited by 6
- Matroid.map_isBase_iffproof · cited by 5
- Matroid.IsBase.spanningproof · cited by 4
- Matroid.dual_isBase_iff'proof · cited by 2
- Matroid.finite_setOfPred_matroidproof · cited by 2
- Matroid.cRk_le_cardinalMkproof · cited by 2
- Matroid.isCocircuit_iff_minimal_compl_nonspanningproof · cited by 2
- Matroid.Coindep.delete_isBase_iffproof · cited by 2
- Matroid.fundCocircuit_isCocircuitproof · cited by 2
- Matroid.isBase_compl_iff_maximal_disjoint_isBaseproof · cited by 1