simp
case left.hm
a b : ℕ
heq : next^[a] (0, 0) = next^[b] (0, 0)
⊢ a < if h : (0, 0) ∈ Function.periodicPts next then Nat.find h else 0
case left.hm
a b : ℕ
heq : next^[a] (0, 0) = next^[b] (0, 0)
⊢ a <
    if h : (0, 0) ∈ Function.periodicPts next then
      Nat.find (_ : ∃ n, (fun n => 0 < n ∧ Function.IsPeriodicPt next n (0, 0)) n)
    else 0