Theorems · Theorem · combinatorics
Matroid.Indep.contract_isBase_iff
∀ {α : Type u_1} {M : Matroid α} {I B : Set α}, M.Indep I → ((M.contract I).IsBase B ↔ M.IsBase (B ∪ I) ∧ Disjoint B I)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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
- Disjointstatement and proof · cited by 2,201
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.IsBasisproof · cited by 219
- Set.subset_union_leftproof · cited by 142
- Matroid.restrictproof · cited by 111
- Matroid.contractstatement · cited by 103
- Set.union_commproof · cited by 99
- Matroid.deleteproof · cited by 86
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.Indep.contract_indep_iffproof · cited by 9