rw [←Function.IsPeriodicPt] at foo
case left.hm.inr
a b : ℕ
heq : next^[a] (0, 0) = next^[b] (0, 0)
h✝ : (0, 0) ∉ Function.periodicPts next
foo : Function.IsFixedPt next^[a - b] (0, 0)
⊢ a < 0
case left.hm.inr
a b : ℕ
heq : next^[a] (0, 0) = next^[b] (0, 0)
h✝ : (0, 0) ∉ Function.periodicPts next
foo : Function.IsPeriodicPt next (a - b) (0, 0)
⊢ a < 0