Theorems · Theorem · combinatorics
Matroid.IsBasis.union_isBasis_union
∀ {α : Type u_1} {M : Matroid α} {I J X Y : Set α},
M.IsBasis I X → M.IsBasis J Y → M.Indep (I ∪ J) → M.IsBasis (I ∪ J) (X ∪ Y)- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.iUnionproof · cited by 2,483
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBasisstatement and proof · cited by 219
- Set.union_eq_iUnionproof · cited by 28
- Matroid.IsBasis.iUnion_isBasis_iUnionproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.isBasis_union_of_subsetproof · cited by 2
- Matroid.IsBasis.isBasis_unionproof · cited by 2
- Matroid.IsBasis.insert_isBasis_insertproof · cited by 1