∀ {α₁ : Type w} {m : Type w → Type w'} {β₁ : Type w} [inst : Std.Iterator α₁ m β₁] {α₂ β₂ : Type w}
  (left : Std.IterM m β₁) (memoizedLeft : Option { out // ∃ it, it.IsPlausibleOutput out }) (right : Std.IterM m β₂)
  (left_1 : Std.IterM m β₁) (memoizedLeft_1 : Option { out // ∃ it, it.IsPlausibleOutput out })
  (right_1 : Std.IterM m β₂),
  ({ left := left, memoizedLeft := memoizedLeft, right := right } =
      { left := left_1, memoizedLeft := memoizedLeft_1, right := right_1 }) =
    (left = left_1 ∧ memoizedLeft = memoizedLeft_1 ∧ right = right_1)