Theorems · Theorem · combinatorics
Matroid.union_indep_iff_indep_of_subset_coloops
∀ {α : Type u_1} {M : Matroid α} {I K : Set α}, K ⊆ M.coloops → (M.Indep (I ∪ K) ↔ M.Indep I)- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBaseproof · cited by 239
- Set.subset_union_leftproof · cited by 142
- Set.union_subsetproof · cited by 71
- Matroid.Indep.subsetproof · cited by 42
- Matroid.coloopsstatement and proof · cited by 34
- Matroid.IsBase.indepproof · cited by 22
- Matroid.Indep.exists_isBase_supersetproof · cited by 18
- Matroid.IsColoop.mem_of_isBaseproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.contract_eq_contract_deleteproof · cited by 3
- Matroid.sdiff_indep_iff_indep_of_subset_coloopsproof · cited by 2
- Matroid.union_coloops_indep_iffproof · cited by 1