Theorems · Theorem · combinatorics

IndepMatroid.ofFinitary_indep

∀ {α : Type u_1} (E : Set α) (Indep : Set α → Prop) (indep_empty : Indep ∅)
  (indep_subset : ∀ ⦃I J : Set α⦄, Indep J → I ⊆ J → Indep I)
  (indep_aug : ∀ ⦃I B : Set α⦄, Indep I → ¬Maximal Indep I → Maximal Indep B → ∃ x ∈ B \ I, Indep (insert x I))
  (indep_compact : ∀ (I : Set α), (∀ J ⊆ I, J.Finite → Indep J) → Indep I)
  (subset_ground : ∀ (I : Set α), Indep I → I ⊆ E),
  (IndepMatroid.ofFinitary E Indep indep_empty indep_subset indep_aug indep_compact subset_ground).Indep = Indep

Defined in

Mathlib.Combinatorics.Matroid.IndepAxioms

Cited by

0 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound