Theorem: Matroid.Indep.interBasis_sInter (Matroid/Closure.lean)

State before:
α : Type u_1
ι✝ : Type u_2
M : Matroid α
F I J X Y B C R : Set α
e f x y : α
Xs Ys : Set (Set α)
ι : Type u_3
hI : M.Indep I
hXs : Xs.Nonempty
h : ∀ X ∈ Xs, M.Basis (X ∩ I) X
⊢ M.Basis (⋂₀ Xs ∩ I) (⋂₀ Xs)
Tactic:
rw [sInter_eq_biInter]
State after:
α : Type u_1
ι✝ : Type u_2
M : Matroid α
F I J X Y B C R : Set α
e f x y : α
Xs Ys : Set (Set α)
ι : Type u_3
hI : M.Indep I
hXs : Xs.Nonempty
h : ∀ X ∈ Xs, M.Basis (X ∩ I) X
⊢ M.Basis ((⋂ i ∈ Xs, i) ∩ I) (⋂ i ∈ Xs, i)

State before:
α : Type u_1
ι✝ : Type u_2
M : Matroid α
F I J X Y B C R : Set α
e f x y : α
Xs Ys : Set (Set α)
ι : Type u_3
hI : M.Indep I
hXs : Xs.Nonempty
h : ∀ X ∈ Xs, M.Basis (X ∩ I) X
⊢ M.Basis ((⋂ i ∈ Xs, i) ∩ I) (⋂ i ∈ Xs, i)
Tactic:
exact hI.interBasis_biInter hXs h
State after:
no goals