Theorems · Theorem · combinatorics
Matroid.IsBasis.contract_isBasis_union_union
∀ {α : Type u_1} {M : Matroid α} {I J X : Set α},
M.IsBasis (J ∪ I) (X ∪ I) → Disjoint J I → Disjoint X I → (M.contract I).IsBasis J X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Disjointstatement and proof · cited by 2,201
- Matroidstatement and proof · cited by 1,258
- Matroid.IsBasisstatement and proof · cited by 219
- Set.subset_union_leftproof · cited by 142
- Matroid.contractstatement · cited by 103
- Matroid.IsBasis.subset_groundproof · cited by 31
- Set.subset_sdiffproof · cited by 29
- Matroid.IsBasis.isBasis'proof · cited by 18
- Matroid.contract_groundproof · cited by 12
- Matroid.isBasis'_iff_isBasisproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.contract_isBasis_of_isBasis'proof · cited by 2