Theorems · Theorem · combinatorics

IndepMatroid.ofFinite_E

∀ {α : Type u_1} {E : Set α} (hE : E.Finite) (Indep : Set α → Prop) (indep_empty : Indep ∅)
  (indep_subset : ∀ ⦃I J : Set α⦄, Indep J → I ⊆ J → Indep I)
  (indep_aug : ∀ ⦃I J : Set α⦄, Indep I → Indep J → I.ncard < J.ncard → ∃ e ∈ J, e ∉ I ∧ Indep (insert e I))
  (subset_ground : ∀ ⦃I : Set α⦄, Indep I → I ⊆ E),
  (IndepMatroid.ofFinite hE Indep indep_empty indep_subset indep_aug subset_ground).E = E

Defined in

Mathlib.Combinatorics.Matroid.IndepAxioms

Cited by

0 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound