2026-06-09 18:48:02 -07:00
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/-
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Port of `Lattice/Unit.agda`.
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The lattice structure itself (`_⊔_`, `_⊓_`, all semilattice/lattice laws) is
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lifted into mathlib: `PUnit.instLinearOrder` provides `Lattice PUnit`.
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What remains is the fixed-height structure: the unit lattice has height 0.
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-/
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import Spa.Lattice
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namespace Spa
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/-- Chains in a subsingleton order are bounded by any `n` (Agda: the `bounded`
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field of `Lattice/Unit.agda`'s `fixedHeight`, generalized). -/
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theorem boundedChains_of_subsingleton (α : Type*) [Preorder α] [Subsingleton α]
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(n : ℕ) : BoundedChains α n := fun c => by
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by_contra hc
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push_neg at hc
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exact (c.step ⟨0, by omega⟩).ne (Subsingleton.elim _ _)
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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
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/-- Agda: `Lattice/Unit.agda`'s `fixedHeight`. -/
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def punitFixedHeight : FixedHeight PUnit 0 where
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bot := PUnit.unit
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top := PUnit.unit
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longestChain := RelSeries.singleton _ PUnit.unit
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head_longestChain := rfl
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last_longestChain := rfl
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length_longestChain := rfl
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bounded := boundedChains_of_subsingleton PUnit 0
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/-- Agda: `Lattice/Unit.agda`'s `isFiniteHeightLattice`. -/
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2026-06-09 18:48:02 -07:00
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instance : FiniteHeightLattice PUnit where
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height := 0
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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
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fixedHeight := punitFixedHeight
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2026-06-09 18:48:02 -07:00
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end Spa
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