Theorems · Theorem · combinatorics
Matroid.IsBasis.insert_dep
∀ {α : Type u_1} {M : Matroid α} {I X : Set α} {e : α}, M.IsBasis I X → e ∈ X \ I → M.Dep (insert e I)- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 3 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.
Cites8
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.IsBasisstatement and proof · cited by 219
- Matroid.Depstatement · cited by 76
- Matroid.IsBasis.subsetproof · cited by 45
- Set.insert_subsetproof · cited by 35
- Set.ssubset_insertproof · cited by 6
- Matroid.IsBasis.dep_of_ssubsetproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.mem_of_insert_indepproof · cited by 9
- Matroid.IsBasis.iUnion_isBasis_iUnionproof · cited by 2
- Matroid.comap_isBasis_iffproof · cited by 2