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>
- 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>
