Theorems · Theorem · combinatorics
Matroid.IsCircuit.ssubset_indep
∀ {α : Type u_1} {M : Matroid α} {C X : Set α}, M.IsCircuit C → X ⊂ C → M.Indep X- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- LT.lt.neproof · cited by 872
- Matroid.Indepstatement · cited by 367
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.Depproof · cited by 76
- LT.lt.subsetproof · cited by 20
- Matroid.IsCircuit.subset_groundproof · cited by 15
- Matroid.not_dep_iffproof · cited by 2
- Matroid.isCircuit_iffproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.sdiff_singleton_indepproof · cited by 5
- Matroid.IsCircuit.contract_isCircuitproof · cited by 4
- Matroid.IsCircuit.eq_of_not_indep_subsetproof · cited by 3
- Matroid.IsCircuit.minimal_not_indepproof · cited by 1