Theorems · Theorem · combinatorics
Matroid.IsCircuit.contract_isCircuit
∀ {α : Type u_1} {M : Matroid α} {K C : Set α}, M.IsCircuit K → C ⊂ K → (M.contract C).IsCircuit (K \ C)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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.Indepproof · cited by 367
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.contractstatement and proof · cited by 103
- Matroid.Indep.subsetproof · cited by 42
- Set.sdiff_union_selfproof · cited by 30
- LT.lt.subsetproof · cited by 20
- Set.sdiff_subset_sdiff_leftproof · cited by 20
- Set.sdiff_union_of_subsetproof · cited by 18
- Matroid.IsCircuit.subset_groundproof · cited by 15
- Set.subset_sdiff_singletonproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.contract_sdiff_isCircuitproof · cited by 2
- Matroid.IsCircuit.contractElem_isCircuitproof · cited by 0
- Matroid.IsCircuit.contract_dep_of_not_subsetproof · cited by 0
- Matroid.IsCocircuit.delete_isCocircuitproof · cited by 0