Theorems · Theorem · combinatorics
Matroid.exists_isBasis
∀ {α : Type u_1} (M : Matroid α) (X : Set α), autoParam (X ⊆ M.E) Matroid.exists_isBasis._auto_1 → ∃ I, M.IsBasis I X- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.IsBasisstatement and proof · cited by 219
- Set.empty_subsetproof · cited by 70
- Matroid.Indep.subset_isBasis_of_subsetproof · cited by 12
- Matroid.empty_indepproof · cited by 8
Cited by23
Results whose statement or proof uses this declaration.
- Matroid.Dep.exists_isCircuit_subsetproof · cited by 5
- Matroid.indep_iff_forall_notMem_closure_sdiffproof · cited by 3
- AlgebraicIndependent.matroid_closure_eqproof · cited by 3
- Matroid.map_closure_eqproof · cited by 2
- Matroid.Spanning.eRk_eqproof · cited by 2
- Matroid.exists_mem_finite_closure_of_mem_closureproof · cited by 1
- Matroid.mem_closure_insertproof · cited by 1
- Matroid.spanning_iff_eRk_le'proof · cited by 1
- Matroid.IsCircuit.contract_depproof · cited by 1
- Matroid.spanning_iff_exists_isBase_subset'proof · cited by 1
- Matroid.eRk_dual_add_eRankproof · cited by 1
- Matroid.eq_eRk_iffproof · cited by 1