Theorems · Theorem · combinatorics
Matroid.IsBase.exchange_isBase_of_indep
∀ {α : Type u_1} {M : Matroid α} {B : Set α} {e f : α},
M.IsBase B → f ∉ B → M.Indep (insert f (B \ {e})) → M.IsBase (insert f (B \ {e}))- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- ENatproof · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Set.encardproof · cited by 327
- Set.inter_commproof · cited by 291
- Matroid.IsBasestatement and proof · cited by 239
- Eq.subsetproof · cited by 124
- Set.eq_empty_iff_forall_notMemproof · cited by 42
- Set.insert_subset_iffproof · cited by 35
- Set.encard_singletonproof · cited by 26
- Set.sdiff_eq_emptyproof · cited by 24
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsBase.exchange_isBase_of_indep'proof · cited by 1
- Matroid.IsBase.exchange_base_of_notMem_closureproof · cited by 1
- Matroid.insert_isBase_of_insert_indepproof · cited by 0