Theorems · Theorem · combinatorics
Matroid.IsCircuit.dep
∀ {α : Type u_1} {M : Matroid α} {C : Set α}, M.IsCircuit C → M.Dep C- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.IsCircuitstatement and proof · cited by 108
- Matroid.Depstatement · cited by 76
- Minimal.propproof · cited by 23
Cited by15
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.subset_groundproof · cited by 15
- Matroid.IsCircuit.sdiff_singleton_isBasisproof · cited by 4
- Matroid.IsCircuit.nonemptyproof · cited by 3
- Matroid.IsCircuit.not_indepproof · cited by 3
- Matroid.IsCircuit.eq_of_subset_isCircuitproof · cited by 3
- Matroid.IsCircuit.finiteproof · cited by 2
- Matroid.IsCircuit.isBasis_iff_eq_sdiff_singletonproof · cited by 2
- Matroid.IsCircuit.contract_depproof · cited by 1
- Matroid.dep_iff_superset_isCircuitproof · cited by 0
- Matroid.dep_iff_superset_isCircuit'proof · cited by 0
- Matroid.IsCircuit.not_ssubsetproof · cited by 0
- Matroid.IsCircuit.eq_fundCircuit_of_subsetproof · cited by 0