Make FiniteHeightLattice extend Lattice and derive Top/Bot

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

lean/Spa/Fixedpoint.lean

@@ -6,13 +6,13 @@ namespace Fixedpoint
 
 open FiniteHeightLattice (height)
 
-variable {α : Type*} [Lattice α] [DecidableEq α] [FiniteHeightLattice α]
+variable {α : Type*} [DecidableEq α] [FiniteHeightLattice α]
 
 def doStep (f : α → α) (hf : Monotone f) :
     ∀ (g : ℕ) (c : LTSeries α), c.length + g = height (α := α) + 1 →
       c.last ≤ f c.last → {a : α // a = f a}
   | 0, c, hlen, _ =>
-    absurd (FiniteHeightLattice.chains_bounded c) (by omega)
+    absurd (FiniteHeightLattice.chains_bounded c) (by simp only [height] at hlen; omega)
   | g + 1, c, hlen, hle =>
     if heq : c.last = f c.last then
       ⟨c.last, heq⟩
@@ -39,7 +39,8 @@ lemma doStep_le (f : α → α) (hf : Monotone f)
     ∀ (g : ℕ) (c : LTSeries α) (hlen : c.length + g = height (α := α) + 1)
       (hle : c.last ≤ f c.last), c.last ≤ b →
       (doStep f hf g c hlen hle : α) ≤ b
-  | 0, c, hlen, _ => fun _ => absurd (FiniteHeightLattice.chains_bounded c) (by omega)
+  | 0, c, hlen, _ => fun _ =>
+    absurd (FiniteHeightLattice.chains_bounded c) (by simp only [height] at hlen; omega)
   | g + 1, c, hlen, hle => fun hcb => by
     rw [doStep]
     split