Theorems · Theorem · combinatorics
Matroid.Indep.exists_insert_of_not_isBase
∀ {α : Type u_1} {M : Matroid α} {B I : Set α}, M.Indep I → ¬M.IsBase I → M.IsBase B → ∃ e ∈ B \ I, M.Indep (insert e I)- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 5 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.
Cites15
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.Indepstatement and proof · cited by 367
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.Indep.subsetproof · cited by 42
- Set.insert_subsetproof · cited by 35
- Matroid.IsBase.indepproof · cited by 22
- Matroid.Indep.exists_isBase_supersetproof · cited by 18
- Set.notMem_subsetproof · cited by 18
- Set.insert_subset_insertproof · cited by 18
- LE.le.ssubset_of_neproof · cited by 16
- Set.subset_sdiff_singletonproof · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.IsBase.isBase_of_isBasis_supersetproof · cited by 3
- Matroid.IsBase.exists_insert_of_ssubsetproof · cited by 0
- Matroid.Indep.exists_insert_of_not_isBasisproof · cited by 0
- Matroid.Indep.exists_insert_of_not_maximalproof · cited by 0
- Matroid.Indep.isBase_of_forall_insertproof · cited by 0