Theorems · Theorem · combinatorics
Matroid.IsBase.eq_of_subset_isBase
∀ {α : Type u_1} {M : Matroid α} {B₁ B₂ : Set α}, M.IsBase B₁ → M.IsBase B₂ → B₁ ⊆ B₂ → B₁ = B₂- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 7 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.
Cites5
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
- Matroid.ExchangeProperty.antichainproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Matroid.IsBase.eq_of_subset_indepproof · cited by 8
- Matroid.IsBase.eq_exchange_of_sdiff_eq_singletonproof · cited by 2
- Matroid.isBase_compl_iff_maximal_disjoint_isBaseproof · cited by 1
- Matroid.IsBase.eq_of_superset_spanningproof · cited by 1
- Matroid.IsBase.not_isBase_of_ssubsetproof · cited by 1
- Matroid.IsBase.rankPos_of_nonemptyproof · cited by 1
- Matroid.IsBase.exists_insert_of_ssubsetproof · cited by 0