Theorems · Theorem · combinatorics
Matroid.Indep.isBasis_insert_iff
∀ {α : Type u_1} {M : Matroid α} {I : Set α} {e : α},
M.Indep I → (M.IsBasis I (insert e I) ↔ M.Dep (insert e I) ∨ e ∈ I)- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Eproof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBasisstatement · cited by 219
- Set.subset_insertproof · cited by 96
- Matroid.Depstatement and proof · cited by 76
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.Indep.isBasis_iff_forall_insert_depproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.Indep.mem_closure_iffproof · cited by 6
- Matroid.IsCircuit.sdiff_singleton_isBasisproof · cited by 4