Theorems · Theorem · combinatorics
Matroid.indep_iff
∀ {α : Type u_1} {M : Matroid α} {I : Set α}, M.Indep I ↔ ∃ B, M.IsBase B ∧ I ⊆ B- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 367
- Matroid.IsBasestatement · cited by 239
- Matroid.indep_iff'proof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.Indep.subsetproof · cited by 42
- Matroid.IsBase.indepproof · cited by 22
- Matroid.Indep.exists_isBase_supersetproof · cited by 18
- Matroid.Indep.exists_insert_of_not_isBaseproof · cited by 5