Lean migration: Phase 4 (IterProd + FiniteMap lattices)

- Spa.Lattice.IterProd: k-fold product, recursive Lattice instance,
  fixed height k*hA + hB, bot = build of bottoms
- Spa.Lattice.FiniteMap: spine-pinned assoc lists ({l // l.map fst = ks});
  with = the 1100-line Map.agda collapses into positional 'combine'.
  Same lemma inventory (membership, locate, updating, GeneralizedUpdate,
  valuesAt, Provenance-union, le_of_mem_mem) — Nodup is now an explicit
  hypothesis where the Agda Map carried it intrinsically. Fixed height
  |ks|*hB still via transport along the IterProd isomorphism, which no
  longer needs Unique ks (representation is canonical).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

lean/Spa/Lattice/Unit.lean

@@ -17,16 +17,19 @@ theorem boundedChains_of_subsingleton (α : Type*) [Preorder α] [Subsingleton
   push_neg at hc
   exact (c.step ⟨0, by omega⟩).ne (Subsingleton.elim _ _)
 
-/-- Agda: `Lattice/Unit.agda`'s `fixedHeight`/`isFiniteHeightLattice`. -/
+/-- Agda: `Lattice/Unit.agda`'s `fixedHeight`. -/
+def punitFixedHeight : FixedHeight PUnit 0 where
+  bot := PUnit.unit
+  top := PUnit.unit
+  longestChain := RelSeries.singleton _ PUnit.unit
+  head_longestChain := rfl
+  last_longestChain := rfl
+  length_longestChain := rfl
+  bounded := boundedChains_of_subsingleton PUnit 0
+
+/-- Agda: `Lattice/Unit.agda`'s `isFiniteHeightLattice`. -/
 instance : FiniteHeightLattice PUnit where
   height := 0
-  fixedHeight :=
-    { bot := PUnit.unit
-      top := PUnit.unit
-      longestChain := RelSeries.singleton _ PUnit.unit
-      head_longestChain := rfl
-      last_longestChain := rfl
-      length_longestChain := rfl
-      bounded := boundedChains_of_subsingleton PUnit 0 }
+  fixedHeight := punitFixedHeight
 
 end Spa