Theorems · Theorem · combinatorics
Matroid.IsBasis.subset_closure
∀ {α : Type u_2} {M : Matroid α} {X I : Set α}, M.IsBasis I X → X ⊆ M.closure I- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 86 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_reflproof · cited by 2,061
- Matroidstatement and proof · cited by 1,258
- Matroid.closurestatement and proof · cited by 272
- Matroid.IsBasisstatement and proof · cited by 219
- Matroid.IsBasis.subset_groundproof · cited by 31
- Matroid.IsBasis.closure_eq_closureproof · cited by 13
- Matroid.closure_subset_closure_iff_subset_closureproof · cited by 3
Cited by15
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
- Matroid.Indep.inter_isBasis_biInterproof · cited by 2
- Matroid.isBasis_iff_indep_closureproof · cited by 2
- Matroid.exists_mem_finite_closure_of_mem_closureproof · cited by 1
- Matroid.Indep.inter_isBasis_closure_iff_subset_closure_interproof · cited by 1
- Matroid.IsBasis.sdiff_subset_loops_contractproof · cited by 1
- Matroid.isBasis_iff_indep_subset_closureproof · cited by 1
- Matroid.Indep.union_indep_iff_forall_notMem_closure_rightproof · cited by 1
- Matroid.isBasis_union_iff_indep_closureproof · cited by 1
- Matroid.eRk_le_one_iffproof · cited by 0
- Matroid.IsRkFinite.iUnionproof · cited by 0