Theorems · Theorem · combinatorics
Matroid.IsCircuit.subset_ground
∀ {α : Type u_1} {M : Matroid α} {C : Set α}, M.IsCircuit C → C ⊆ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement · cited by 550
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.IsCircuit.depproof · cited by 15
- Matroid.Dep.subset_groundproof · cited by 7
Cited by15
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.contract_isCircuitproof · cited by 4
- Matroid.IsCircuit.ssubset_indepproof · cited by 4
- Matroid.delete_isCircuit_iffproof · cited by 4
- Matroid.isCircuit_iff_dep_forall_sdiff_singleton_indepproof · cited by 3
- Matroid.dual_rankPos_iff_exists_isCircuitproof · cited by 3
- Matroid.ext_isCircuitproof · cited by 2
- Matroid.IsCircuit.subset_closure_sdiff_singletonproof · cited by 2
- Matroid.IsCocircuit.subset_groundproof · cited by 2
- Matroid.IsCircuit.inter_isCocircuit_ne_singletonproof · cited by 2
- Matroid.IsCircuit.contract_depproof · cited by 1
- Matroid.IsCircuit.isNonloop_of_mem_of_one_lt_cardproof · cited by 0
- Matroid.IsCircuit.eRk_add_one_eqproof · cited by 0