Lean migration cleanup: collapse FixedHeight struct into FiniteHeightLattice typeclass

The fable-based migration left a two-layer design (a standalone `FixedHeight α h`
struct, height carried as a type index, plus a `FiniteHeightLattice` wrapper).
This collapses it to the single `FiniteHeightLattice` typeclass (height as a
plain field, `⊥`/`⊤` via `extends Bot`/`Top`), and fixes the fallout so the
whole project builds again (`lake build` green).

- Lattice: repair `FixedHeight.bot_le` (compute the `▸` motive via a forward
  `rw`, drop the leftover `fh.length_longestChain`) and the `bot_le` alias.
- Isomorphism: transport rewritten directly onto `FiniteHeightLattice`, taking
  the source as an instance argument.
- Lattice/Prod, AboveBelow: `FixedHeight`-producing def + wrapper instance
  collapsed into one `FiniteHeightLattice` instance. `head`/`last` proofs use
  term-mode `congrArg` to bridge the `Bot`/`Top` defeq through the
  under-construction instance projection (where `rw`+`rfl` cannot).
- Lattice/IterProd: `fixedHeight` recursion now yields a `FiniteHeightLattice`
  (no height index, so the `.cast (by ring)` reassociations vanish);
  `bot_fixedHeight` reprojected onto the def's own `.bot`.
- Lattice/FiniteMap: `fixedHeight`/`bot_contains_bots` go through transport with
  the IterProd instance resolved by typeclass search; `punitFixedHeight`
  replaced by the `PUnit` instance.
- Analysis/Forward/Lattices: `botV` uses `⊥` instead of the deleted
  `FiniteHeightLattice.bot` accessor.
- Analysis/Sign: `num` case used unimported `ring`; the goal is a pure ℕ→ℤ
  cast identity, closed with `norm_cast`. Also fixes the missing `show` in
  `AboveBelow.monotone₂_of_strict` that left un-beta-reduced redexes.

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

lean/Spa/Lattice/AboveBelow.lean

@@ -175,6 +175,7 @@ theorem monotone₂_of_strict {β γ : Type*} [DecidableEq β] [DecidableEq γ]
       · rw [htopl y hy]; exact le_top' _
     · exact le_rfl
   · intro x a b hab
+    show f x a ≤ f x b
     rcases le_cases hab with rfl | rfl | rfl
     · rw [hbotr]; exact bot_le' _
     · rcases eq_or_ne x bot with rfl | hx
@@ -264,25 +265,23 @@ theorem boundedChains : BoundedChains (AboveBelow α) 2 := fun c => by
   have h2 : rank c.last ≤ 2 := by cases c.last <;> simp [rank]
   omega
 
-/-- Agda: `Plain.longestChain` and `Plain.fixedHeight` — the witness `x`
-seeds the chain `⊥ ≺ [x] ≺ ⊤` of length 2. -/
-def plainFixedHeight (x : α) : FixedHeight (AboveBelow α) 2 where
+/-- Agda: `Plain.longestChain`/`Plain.fixedHeight` and
+`Plain.isFiniteHeightLattice`/`Plain.finiteHeightLattice` — the witness
+(`default`, playing the role of the Agda module parameter `x`) seeds the chain
+`⊥ ≺ [x] ≺ ⊤` of length 2. -/
+instance [Inhabited α] : FiniteHeightLattice (AboveBelow α) where
   bot := bot
   top := top
-  longestChain :=
-    ((RelSeries.singleton _ bot).snoc (mk x)
-        (by rw [RelSeries.last_singleton]; exact bot_lt_mk x)).snoc top
-      (by rw [RelSeries.last_snoc]; exact mk_lt_top x)
-  head_longestChain := by simp
-  last_longestChain := by simp
-  length_longestChain := by simp [RelSeries.snoc, RelSeries.append]
-  bounded := boundedChains
-
-/-- Agda: `Plain.isFiniteHeightLattice` / `Plain.finiteHeightLattice`
-(`default` plays the role of the Agda module parameter `x`). -/
-instance [Inhabited α] : FiniteHeightLattice (AboveBelow α) where
   height := 2
-  fixedHeight := plainFixedHeight default
+  longest_chain :=
+    { series :=
+        ((RelSeries.singleton _ bot).snoc (mk default)
+            (by rw [RelSeries.last_singleton]; exact bot_lt_mk default)).snoc top
+          (by rw [RelSeries.last_snoc]; exact mk_lt_top default)
+      head_series := by simp
+      last_series := by simp
+      length_series := by simp [RelSeries.snoc, RelSeries.append] }
+  chains_bounded := boundedChains
 
 end AboveBelow