simp only [restrict_parallel_iff, mem_image, mem_setOf_eq, and_imp, forall_exists_index,
  loopless_iff_forall_nonloop, restrict_ground_eq, mem_image, mem_setOf_eq, restrict_nonloop_iff,
  forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
case intro
α : Type u_1
M : Matroid α
e f✝ g : α
I X P D : Set α
x y : α
f : M.parallelClasses.RepFun
⊢ (M ↾ ⇑f '' {e | M.Nonloop e}).Loopless ∧ ∀ (e f_1 : α), (M ↾ ⇑f '' {e | M.Nonloop e}).Parallel e f_1 → e = f_1
case intro
α : Type u_1
M : Matroid α
e f✝ g : α
I X P D : Set α
x y : α
f : M.parallelClasses.RepFun
⊢ (∀ (a : α), M.Nonloop a → M.Nonloop (f a) ∧ ∃ x, M.Nonloop x ∧ f x = f a) ∧
    ∀ (e f_1 : α), M.Parallel e f_1 → ∀ (x : α), M.Nonloop x → f x = e → ∀ (x : α), M.Nonloop x → f x = f_1 → e = f_1