Make FiniteHeightLattice extend Lattice and derive Top/Bot

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

lean/Spa/Lattice/Bool.lean

@@ -28,13 +28,9 @@ lemma boundedChains : BoundedChains Bool 1 := fun c => by
   omega
 
 instance : FiniteHeightLattice Bool where
-  height := 1
-  longestChain :=
-    { series := (RelSeries.singleton _ (⊥ : Bool)).snoc (⊤ : Bool)
-        (by rw [RelSeries.last_singleton]; exact bot_lt_top)
-      head_series := by simp
-      last_series := by simp
-      length_series := by simp [RelSeries.snoc, RelSeries.append] }
+  toLattice := inferInstance
+  longestChain := (RelSeries.singleton _ (⊥ : Bool)).snoc (⊤ : Bool)
+    (by rw [RelSeries.last_singleton]; exact bot_lt_top)
   chains_bounded := boundedChains
 
 end Bool