Theorem: Matroid.Indep.base_of_ground_subset_cl (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
hI : M.Indep I
h : M.E ⊆ M.cl I
⊢ M.Base I
Tactic:
rw [← basis_ground_iff]
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
hI : M.Indep I
h : M.E ⊆ M.cl I
⊢ M.Basis I M.E

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
hI : M.Indep I
h : M.E ⊆ M.cl I
⊢ M.Basis I M.E
Tactic:
exact hI.basis_of_subset_of_subset_cl hI.subset_ground h
State after:
no goals