rw [Nat.lt_find_iff sorry a]
case left.hm.inl
a b : ℕ
heq : next^[a] (0, 0) = next^[b] (0, 0)
h✝ : (0, 0) ∈ Function.periodicPts next
⊢ a < Nat.find (_ : ∃ n, (fun n => 0 < n ∧ Function.IsPeriodicPt next n (0, 0)) n)
case left.hm.inl
a b : ℕ
heq : next^[a] (0, 0) = next^[b] (0, 0)
h✝ : (0, 0) ∈ Function.periodicPts next
⊢ ∀ m ≤ a, ¬(0 < m ∧ Function.IsPeriodicPt next m (0, 0))