Theorems · Theorem · combinatorics
Matroid.IsBase.mem_of_insert_indep
∀ {α : Type u_1} {M : Matroid α} {B : Set α} {e : α}, M.IsBase B → M.Indep (insert e B) → e ∈ B- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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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.Indepstatement and proof · cited by 367
- Matroid.IsBasestatement and proof · cited by 239
- Set.mem_insertproof · cited by 109
- Matroid.Indep.subset_groundproof · cited by 61
- by_contraproof · cited by 60
- Matroid.Dep.not_indepproof · cited by 14
- Matroid.IsBase.dep_of_insertproof · cited by 1
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