simp [(show ¬ M.Indep (insert e _) from fun hi ↦ he <| hi.nonloop_of_mem (mem_insert _ _)), hf]
case pos
α : Type u_1
inst✝ : DecidableEq α
M M' : Matroid α
e f✝ x : α
I✝ C : Set α
he : ¬M.Nonloop e
f : α
I : Set α
hI : I ⊆ insert f M.E
hf : f ∈ I
⊢ (M.Indep (insert e (I \ {f})) ∧ (f ∈ I → e ∈ I → f = e)) ∧ I ⊆ insert f M.E ↔ M.Indep I ∧ f ∉ I
no goals