Theorems · Definition · combinatorics
Matroid.coloops
{α : Type u_1} → Matroid α → Set αM.coloops is the set of coloops of M.
- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.dualproof · cited by 79
- Matroid.loopsproof · cited by 52
Cited by34
Results whose statement or proof uses this declaration.
- Matroid.closure_union_eq_of_subset_coloopsstatement and proof · cited by 4
- Matroid.isColoop_tfaestatement and proof · cited by 4
- Matroid.union_indep_iff_indep_of_subset_coloopsstatement and proof · cited by 3
- Matroid.isColoop_iff_forall_mem_isBaseproof · cited by 3
- Matroid.IsBasis.contract_eq_contract_deleteproof · cited by 3
- Matroid.isColoop_iff_sdiff_not_spanningproof · cited by 3
- Matroid.dual_coloopsstatement · cited by 2
- Matroid.sdiff_coloops_indep_iffstatement · cited by 2
- Matroid.sdiff_indep_iff_indep_of_subset_coloopsstatement and proof · cited by 2
- Matroid.isColoop_iff_forall_mem_closure_iff_memproof · cited by 2
- Matroid.union_coloops_indep_iffstatement · cited by 1
- Matroid.closure_inter_coloops_eqstatement and proof · cited by 1