Theorems · Theorem · combinatorics
Matroid.Indep.isBase_of_maximal
∀ {α : Type u_1} {M : Matroid α} {I : Set α}, M.Indep I → (∀ ⦃J : Set α⦄, M.Indep J → I ⊆ J → I = J) → M.IsBase I- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 4 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.
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.IsBasestatement · cited by 239
- Matroid.isBase_iff_maximal_indepproof · cited by 5
- maximal_subset_iffproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.map_isBase_iffproof · cited by 5
- Matroid.Indep.isBase_of_cRank_leproof · cited by 2
- Matroid.ground_indep_iff_isBaseproof · cited by 1
- Matroid.Indep.exists_insert_of_not_maximalproof · cited by 0