Danila Fedorin
2ee32580a2
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>
29 lines
1019 B
Lean4
29 lines
1019 B
Lean4
/-
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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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/-- Agda: `Lattice/Unit.agda`'s `fixedHeight`. -/
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instance : FiniteHeightLattice PUnit where
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bot := PUnit.unit
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top := PUnit.unit
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height := 0
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longest_chain := { series := RelSeries.singleton _ PUnit.unit, head_series := refl _, last_series := refl _, length_series := refl _ }
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chains_bounded := boundedChains_of_subsingleton PUnit 0
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end Spa
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