Lean migration: Phase 3 (Unit, Prod, AboveBelow lattices)

- Spa.Lattice.Unit: PUnit fixed height 0 (lattice lifted from mathlib)
- Spa.Lattice.Prod: chain unzip + FixedHeight (h1+h2) on products
  (componentwise lattice lifted from mathlib's Prod.instLattice)
- Spa.Lattice.AboveBelow: flat lattice via Lattice.mk' (mirrors the Agda
  semilattices+absorption construction), boundedness via rank into Nat,
  Plain x ↦ plainFixedHeight x, height 2

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

lean/Spa/Lattice/Unit.lean

@@ -0,0 +1,32 @@
+/-
+Port of `Lattice/Unit.agda`.
+
+The lattice structure itself (`_⊔_`, `_⊓_`, all semilattice/lattice laws) is
+lifted into mathlib: `PUnit.instLinearOrder` provides `Lattice PUnit`.
+What remains is the fixed-height structure: the unit lattice has height 0.
+-/
+import Spa.Lattice
+
+namespace Spa
+
+/-- Chains in a subsingleton order are bounded by any `n` (Agda: the `bounded`
+field of `Lattice/Unit.agda`'s `fixedHeight`, generalized). -/
+theorem 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 _ _)
+
+/-- Agda: `Lattice/Unit.agda`'s `fixedHeight`/`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 }
+
+end Spa