Theorems · Theorem · combinatorics
Matroid.isBasis_ground_iff
∀ {α : Type u_1} {M : Matroid α} {B : Set α}, M.IsBasis B M.E ↔ M.IsBase B- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Indepproof · cited by 367
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.IsBasisstatement · cited by 219
- Maximalproof · cited by 211
- Eq.subsetproof · cited by 124
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.isBase_iff_maximal_indepproof · cited by 5
- maximal_and_iff_right_of_impproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- Matroid.IsBase.closure_eqproof · cited by 9
- Matroid.IsBase.isBasis_groundproof · cited by 4
- Matroid.IsBase.isBase_insert_sdiff_of_mem_closureproof · cited by 2
- Matroid.Coindep.delete_isBase_iffproof · cited by 2
- Matroid.comap_isBase_iffproof · cited by 1
- Matroid.spanning_iff_exists_isBase_subset'proof · cited by 1
- Matroid.eRk_dual_add_eRankproof · cited by 1
- Matroid.Indep.isBase_of_ground_subset_closureproof · cited by 1
- Matroid.isBase_iff_indep_closure_eqproof · cited by 0
- Matroid.restrictSubtype_ground_isBase_iffproof · cited by 0