Theorems · Theorem · combinatorics
Matroid.Spanning.isBase_restrict_iff
∀ {α : Type u_2} {M : Matroid α} {S B : Set α}, M.Spanning S → ((M.restrict S).IsBase B ↔ M.IsBase B ∧ B ⊆ S)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.IsBasisproof · cited by 219
- Matroid.restrictstatement · cited by 111
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.IsBasis.indepproof · cited by 51
- Matroid.IsBasis.subsetproof · cited by 45
- Matroid.IsBase.indepproof · cited by 22
- Matroid.Spanning.subset_groundproof · cited by 13
- Matroid.isBasis'_iff_isBasisproof · cited by 9
- Matroid.IsBase.closure_eqproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.Indep.contract_isBase_iffproof · cited by 1
- Matroid.Restriction.isBase_iff_of_spanningproof · cited by 0