Theorems · Theorem · combinatorics
Matroid.Indep.isBasis_of_forall_insert
∀ {α : Type u_1} {M : Matroid α} {I X : Set α}, M.Indep I → I ⊆ X → (∀ e ∈ X \ I, M.Dep (insert e I)) → M.IsBasis I X- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 5 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.
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 and proof · cited by 367
- Matroid.IsBasisstatement · cited by 219
- Matroid.Depstatement and proof · cited by 76
- Matroid.Indep.isBasis_iff_forall_insert_depproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.mapproof · cited by 6
- Matroid.Indep.isBasis_setOfPred_insert_isBasisproof · cited by 3
- Matroid.IsBasis.iUnion_isBasis_iUnionproof · cited by 2
- Matroid.comap_isBasis_iffproof · cited by 2
- Matroid.IsBase.compl_inter_isBasis_of_inter_isBasisproof · cited by 1