Theorems · Theorem · combinatorics
Matroid.disjointSum_indep_iff
∀ {α : Type u_1} {M N : Matroid α} {h : Disjoint M.E N.E} {I : Set α},
(M.disjointSum N h).Indep I ↔ M.Indep (I ∩ M.E) ∧ N.Indep (I ∩ N.E) ∧ I ⊆ M.E ∪ N.E- Defined in
- Mathlib.Combinatorics.Matroid.Sum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 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
- Disjointstatement and proof · cited by 2,201
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Matroid.restrictSubtypeproof · cited by 16
- Matroid.disjointSumstatement · cited by 8
- Function.Embedding.sumSet_preimage_inlproof · cited by 3
- Function.Embedding.sumSet_preimage_inrproof · cited by 3
- Function.Embedding.sumSet_rangeproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.Indep.eq_union_image_of_disjointSumproof · cited by 0