Theorem: Matroid.Nonloop.parallel_iff_cl_eq_cl (Matroid/Parallel.lean)

State before:
α : Type u_1
M N : Matroid α
e f g : α
I X P D : Set α
he : M.Nonloop e
⊢ M.Parallel e f ↔ M.cl {e} = M.cl {f}
Tactic:
rw [Parallel, parallelClasses, Partition.rel_congr,
  (M.cl_flat ∅).rel_covByPartition_iff' ⟨he.mem_ground, he.not_loop⟩]
State after:
α : Type u_1
M N : Matroid α
e f g : α
I X P D : Set α
he : M.Nonloop e
⊢ M.cl (insert e (M.cl ∅)) = M.cl (insert f (M.cl ∅)) ↔ M.cl {e} = M.cl {f}

State before:
α : Type u_1
M N : Matroid α
e f g : α
I X P D : Set α
he : M.Nonloop e
⊢ M.cl (insert e (M.cl ∅)) = M.cl (insert f (M.cl ∅)) ↔ M.cl {e} = M.cl {f}
Tactic:
simp
State after:
no goals