Delete unused code and moved some lemmas into Lattice.lean

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

lean/Spa/Lattice/Unit.lean

@@ -11,17 +11,6 @@ as a base case for the iterated product `Spa/Lattice/IterProd.lean`). -/
 
 namespace Spa
 
-/-- Since a singleton type's preorder has no nonempty `<` chains,
-    they are vacuously bounded by any minimum height. -/
-lemma boundedChains_of_subsingleton (α : Type*) [Preorder α] [Subsingleton α]
-    (n : ℕ) : BoundedChains α n := fun c => by
-  by_contra hc
-  push_neg at hc
-  exact (c.step ⟨0, by omega⟩).ne (Subsingleton.elim _ _)
-
-instance : FiniteHeightLattice PUnit where
-  toLattice := inferInstance
-  longestChain := RelSeries.singleton _ PUnit.unit
-  chains_bounded := boundedChains_of_subsingleton PUnit 0
+instance : FiniteHeightLattice PUnit := FiniteHeightLattice.ofUnique PUnit
 
 end Spa