Theorem: Matroid.Nonloop.mem_cl_singleton (Matroid/Loop.lean)

State before:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
he : M.Nonloop e
hef : e ∈ M.cl {f}
⊢ f ∈ M.cl {e}
Tactic:
rw [← union_empty {_}, singleton_union] at *
State after:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
he : M.Nonloop e
hef : e ∈ M.cl (insert f ∅)
⊢ f ∈ M.cl (insert e ∅)

State before:
α : Type u_1
β : Type u_2
M N : Matroid α
e f : α
B L L' I X Y Z F C K : Set α
he : M.Nonloop e
hef : e ∈ M.cl (insert f ∅)
⊢ f ∈ M.cl (insert e ∅)
Tactic:
exact (M.cl_exchange (X := ∅) ⟨hef, (nonloop_iff_not_mem_cl_empty he.mem_ground).1 he⟩).1
State after:
no goals