lean/Spa/Lattice/Unit.lean

import Spa.Lattice

namespace Spa

lemma 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
  toLattice := inferInstance
  longestChain := RelSeries.singleton _ PUnit.unit
  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
-												Adopt lemma as the default keyword

Convert every theorem to lemma (mathlib's default) except the headline results a
reader of each module seeks out: analyze_correct (Forward/Sign/Constant),
aFix_eq/aFix_le (Fixedpoint), trace (Language), and Stmt.cfg_sufficient
(Language/Properties). lemma and theorem are interchangeable keywords, so no
references change.

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

											
										
										
											2026-06-25 13:59:08 -05:00
+								lemma boundedChains_of_subsingleton (α : Type*) [Preorder α] [Subsingleton α]
-												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
+								    (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
-												Make FiniteHeightLattice extend Lattice and derive Top/Bot

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

											
										
										
											2026-06-25 18:42:28 -05:00
+								  toLattice := inferInstance
 								  longestChain := RelSeries.singleton _ PUnit.unit
-												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