Theorems · Theorem · combinatorics
Matroid.IsBasis.spanning_iff_spanning
∀ {α : Type u_2} {M : Matroid α} {X I : Set α}, M.IsBasis I X → (M.Spanning I ↔ M.Spanning X)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Eproof · cited by 550
- Matroid.closureproof · cited by 272
- Matroid.IsBasisstatement and proof · cited by 219
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.IsBasis.subset_groundproof · cited by 31
- Matroid.IsBasis.closure_eq_closureproof · cited by 13
- Matroid.spanning_iff_closure_eqproof · cited by 7
- Matroid.IsBasis.left_subset_groundproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.isBase_of_spanningproof · cited by 2
- Matroid.Spanning.isBase_restrict_iffproof · cited by 2