∀ {α : Type u_1} {a : α} (n : ℕ) {f : Fin (n + 1) → Option α},
  (f 0 = some a ∨ f 0 = none ∧ ∃ i, f i.succ = some a ∧ ∀ j < i, f j.succ = none) ↔
    (f 0 = some a ∧ (False → f 0 = none) ∧ ∀ (i : Fin n), False → f i.succ = none) ∨
      ∃ i, f i.succ = some a ∧ (True → f 0 = none) ∧ ∀ i_1 < i, f i_1.succ = none