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>
This commit is contained in:
2026-06-22 18:33:48 -05:00
parent b16f14fdfd
commit 2ee32580a2
10 changed files with 115 additions and 457 deletions

View File

@@ -42,7 +42,7 @@ abbrev StateVariables : Type := FiniteMap prog.State (VariableValues L prog) pro
/-- Agda: `⊥ᵛ` (the bottom of `fixedHeightᵛ`, now found by instance search). -/
def botV [FiniteHeightLattice L] : VariableValues L prog :=
FiniteHeightLattice.bot (VariableValues L prog)
( : VariableValues L prog)
variable {L prog}