Theorems · Theorem · combinatorics
Matroid.IsBase.insert_dep
∀ {α : Type u_1} {M : Matroid α} {B : Set α} {e : α}, M.IsBase B → e ∈ M.E \ B → M.Dep (insert e B)- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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.Indepproof · cited by 367
- Matroid.IsBasestatement and proof · cited by 239
- Set.subset_insertproof · cited by 96
- Matroid.Depstatement · cited by 76
- Set.insert_subsetproof · cited by 35
- Matroid.IsBase.subset_groundproof · cited by 30
- Matroid.not_indep_iffproof · cited by 11
- Matroid.IsBase.eq_of_subset_indepproof · cited by 8
- Set.insert_eq_selfproof · cited by 5
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