Theorems · Theorem · combinatorics
Matroid.IsBase.eq_of_superset_spanning
∀ {α : Type u_2} {M : Matroid α} {X B : Set α}, M.IsBase B → M.Spanning X → X ⊆ B → B = X- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.IsBasestatement and proof · cited by 239
- subset_antisymmproof · cited by 150
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.IsBase.eq_of_subset_isBaseproof · cited by 7
- Matroid.Spanning.exists_isBase_subsetproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.isBase_iff_minimal_spanningproof · cited by 2