lean/Spa/Lattice/Unit.lean

import Spa.Lattice

namespace Spa

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 _ _)

instance : FiniteHeightLattice PUnit where
  bot := PUnit.unit
  top := PUnit.unit
  height := 0
  longestChain := { series := RelSeries.singleton _ PUnit.unit, head_series := refl _, last_series := refl _, length_series := refl _ }
  chains_bounded := boundedChains_of_subsingleton PUnit 0

end Spa
-												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>

											
										
										
											2026-06-09 18:48:02 -07:00
+								import Spa.Lattice
 								namespace Spa
 								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 _ _)
-												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>

											
										
										
											2026-06-22 18:33:48 -05:00
+								instance : FiniteHeightLattice PUnit where
-												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>

											
										
										
											2026-06-09 19:12:39 -07:00
+								  bot := PUnit.unit
 								  top := PUnit.unit
-												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>

											
										
										
											2026-06-09 18:48:02 -07:00
+								  height := 0
-												Rename longest_chain to longestChain for convention

											
										
										
											2026-06-23 11:49:45 -05:00
+								  longestChain := { series := RelSeries.singleton _ PUnit.unit, head_series := refl _, last_series := refl _, length_series := refl _ }
-												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>

											
										
										
											2026-06-22 18:33:48 -05:00
+								  chains_bounded := boundedChains_of_subsingleton PUnit 0
-												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>

											
										
										
											2026-06-09 18:48:02 -07:00
 								end Spa