Theorem: Matroid.Spanning.cl_superset_eq (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
S T : Set α
hS : M.Spanning S
hST : S ⊆ T
⊢ M.cl T = M.E
Tactic:
rw [← cl_inter_ground, ← spanning_iff_cl]
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
S T : Set α
hS : M.Spanning S
hST : S ⊆ T
⊢ M.Spanning (T ∩ 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
S T : Set α
hS : M.Spanning S
hST : S ⊆ T
⊢ M.Spanning (T ∩ M.E)
Tactic:
exact hS.superset (subset_inter hST hS.subset_ground)
State after:
no goals