Theorems · Theorem · combinatorics
Matroid.IsCircuit.not_indep
∀ {α : Type u_1} {M : Matroid α} {C : Set α}, M.IsCircuit C → ¬M.Indep C- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 3 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.Indepstatement · cited by 367
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.IsCircuit.depproof · cited by 15
- Matroid.Dep.not_indepproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.contract_isCircuitproof · cited by 4
- Matroid.IsCircuit.minimal_not_indepproof · cited by 1
- Matroid.IsCircuit.eq_fundCircuit_of_subsetproof · cited by 0