lean/Spa/Lattice/Unit.lean

import Spa.Lattice

/-!

# Unit Lattice

This file provides a proof that in addition to being a lattice,
`PUnit` is a `Spa.FiniteHeightLattice`. This is a fairly trivial result. -/

namespace Spa

instance : FiniteHeightLattice PUnit := FiniteHeightLattice.ofUnique PUnit

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`

Write more documentation Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com> 2026-06-25 19:36:14 -05:00			`/-!`

			`# Unit Lattice`

			`This file provides a proof that in addition to being a lattice,`
Use a direct N-way unzip instead of induction over product size This makes a finite-height proof for any `Fin n -> a` lattice immediate, and precludes the need for IterProd and Prod altogether. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> 2026-06-26 11:54:34 -05:00			`PUnit` is a `Spa.FiniteHeightLattice`. This is a fairly trivial result. -/
Write more documentation Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com> 2026-06-25 19:36:14 -05:00
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			`namespace Spa`

Delete unused code and moved some lemmas into Lattice.lean Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> 2026-06-26 10:17:25 -05:00			`instance : FiniteHeightLattice PUnit := FiniteHeightLattice.ofUnique PUnit`
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`