Theorem: Matroid.Basis.eq_of_cl_subset (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.Basis I X
hJI : J ⊆ I
hJ : X ⊆ M.cl J
⊢ J = I
Tactic:
rw [← hI.indep.cl_inter_eq_self_of_subset hJI, inter_eq_self_of_subset_right]
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.Basis I X
hJI : J ⊆ I
hJ : X ⊆ M.cl J
⊢ I ⊆ M.cl J

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.Basis I X
hJI : J ⊆ I
hJ : X ⊆ M.cl J
⊢ I ⊆ M.cl J
Tactic:
exact hI.subset.trans hJ
State after:
no goals