Theorems · Theorem · combinatorics
Matroid.indep_iff_forall_finite_subset_indep
∀ {α : Type u_1} {I : Set α} {M : Matroid α} [M.Finitary], M.Indep I ↔ ∀ J ⊆ I, J.Finite → M.Indep J- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.Finitary
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.Finitestatement and proof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Matroid.Indep.subsetproof · cited by 42
- Matroid.Finitarystatement and proof · cited by 11
- Matroid.Finitary.indep_of_forall_finiteproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.finiteproof · cited by 2