Theorems · Theorem · combinatorics
Matroid.IsBase.exchange
∀ {α : Type u_1} {M : Matroid α} {B₁ B₂ : Set α} {e : α},
M.IsBase B₁ → M.IsBase B₂ → e ∈ B₁ \ B₂ → ∃ y ∈ B₂ \ B₁, M.IsBase (insert y (B₁ \ {e}))- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.IsBasestatement and proof · cited by 239
- Matroid.isBase_exchangeproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.Indep.exists_insert_of_not_isBaseproof · cited by 5
- Matroid.IsBase.eq_exchange_of_sdiff_eq_singletonproof · cited by 2
- Matroid.IsBase.compl_inter_isBasis_of_inter_isBasisproof · cited by 1
- Matroid.IsBasis.exchangeproof · cited by 1
- Matroid.IsBase.exchange_memproof · cited by 0