Theorems · Theorem · combinatorics
Matroid.IsBase.dep_of_insert
∀ {α : Type u_1} {M : Matroid α} {B : Set α} {e : α},
M.IsBase B → e ∉ B → autoParam (e ∈ M.E) Matroid.IsBase.dep_of_insert._auto_1 → M.Dep (insert e B)- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 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.Estatement and proof · cited by 550
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.Depstatement · cited by 76
- Set.insert_subsetproof · cited by 35
- Matroid.IsBase.subset_groundproof · cited by 30
- Set.ssubset_insertproof · cited by 6
- Matroid.IsBase.dep_of_ssubsetproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsBase.mem_of_insert_indepproof · cited by 0