Theorems · Theorem · combinatorics
Matroid.Dep.not_indep
∀ {α : Type u_1} {M : Matroid α} {D : Set α}, M.Dep D → ¬M.Indep D- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Depstatement and proof · cited by 76
Cited by14
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.mem_of_insert_indepproof · cited by 9
- Matroid.IsCircuit.not_indepproof · cited by 3
- Matroid.IsCircuit.eq_of_dep_subsetproof · cited by 3
- Matroid.IsCircuit.finiteproof · cited by 2
- Matroid.IsCircuit.isBasis_iff_eq_sdiff_singletonproof · cited by 2
- Matroid.IsLoop.not_indep_of_memproof · cited by 2
- Matroid.Dep.dep_isRestrictionproof · cited by 1
- Matroid.Dep.eRk_lt_encardproof · cited by 1
- Matroid.isCircuit_iff_minimal_not_indepproof · cited by 1
- Matroid.IsCircuit.contract_depproof · cited by 1
- Matroid.Dep.nonemptyproof · cited by 1
- Matroid.Dep.of_isMinorproof · cited by 1