Theorems · Theorem · combinatorics
Matroid.IsBasis.isBasis_subset
∀ {α : Type u_1} {M : Matroid α} {I X Y : Set α}, M.IsBasis I X → I ⊆ Y → Y ⊆ X → M.IsBasis I Y- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Indepproof · cited by 367
- Matroid.IsBasisstatement and proof · cited by 219
- Matroid.IsBasis.indepproof · cited by 51
- Matroid.IsBasis.subset_groundproof · cited by 31
- Matroid.IsBasis.eq_of_subset_indepproof · cited by 8
- Matroid.isBasis_iffproof · cited by 4
Cited by12
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.closure_eq_closureproof · cited by 13
- Matroid.Indep.isBasis_of_subset_of_subset_closureproof · cited by 8
- Matroid.Indep.closure_eq_setOfPred_isBasis_insertproof · cited by 6
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Matroid.isBasis_iff_indep_closureproof · cited by 2
- Matroid.Coindep.delete_isBase_iffproof · cited by 2
- Matroid.IsBasis.isBasis_of_isBasis_of_subset_of_subsetproof · cited by 1
- Matroid.IsBasis.contract_sdiff_isBasis_sdiffproof · cited by 1
- Matroid.isBasis_union_iff_indep_closureproof · cited by 1
- Matroid.isBasis'_iff_isBasis_closureproof · cited by 0
- Matroid.isBasis_iff_isBasis_closure_of_subsetproof · cited by 0
- Matroid.isBasis_iff_isBasis_closure_of_subset'proof · cited by 0