Lean migration: Phases 0-2 (core lattice/chain, fixpoint, transport)

- lean/ lake project pinned to Lean v4.17.0 + mathlib v4.17.0
- Spa.Lattice: fold monotonicity, FixedHeight/BoundedChains (LTSeries-based),
  FiniteHeightLattice, chain-bottom-is-least; the rest of Lattice.agda,
  Chain.agda and Equivalence.agda lift into mathlib (see LEAN_MIGRATION.md)
- Spa.Fixedpoint: gas-based least-fixpoint computation (doStep/fix/aFix)
- Spa.Isomorphism: FixedHeight transport along monotone inverse pairs

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

lean/Spa/Isomorphism.lean

@@ -0,0 +1,58 @@
+/-
+Port of `Isomorphism.agda` (`TransportFiniteHeight`).
+
+With propositional equality this module shrinks dramatically: the Agda
+hypotheses `f-preserves-≈`, `g-preserves-≈` are free, and `f-⊔-distr` /
+`g-⊔-distr` (which in the setoid world encoded monotonicity of `f` and `g`
+w.r.t. the derived order) become plain `Monotone` hypotheses. The chain
+transport `portChain₁` / `portChain₂` is mathlib's `LTSeries.map`, using that
+a monotone injective map between partial orders is strictly monotone.
+
+Correspondence:
+  IsInverseˡ / IsInverseʳ     ↦ explicit inverse hypotheses `hfg` / `hgf`
+  f-Injective / g-Injective   ↦ local `Function.LeftInverse.injective`
+  portChain₁ / portChain₂     ↦ LTSeries.map
+  instance fixedHeight        ↦ Spa.FixedHeight.transport
+  isFiniteHeightLattice,
+  finiteHeightLattice         ↦ Spa.FiniteHeightLattice.transport
+-/
+import Spa.Lattice
+
+namespace Spa
+
+namespace FixedHeight
+
+variable {α β : Type*} [PartialOrder α] [PartialOrder β] {h : ℕ}
+
+/-- Agda: `TransportFiniteHeight.fixedHeight`. Transport a `FixedHeight`
+structure along a monotone inverse pair `f : α → β`, `g : β → α`. -/
+def transport (fh : FixedHeight α h) (f : α → β) (g : β → α)
+    (hf : Monotone f) (hg : Monotone g)
+    (hgf : ∀ a, g (f a) = a) (hfg : ∀ b, f (g b) = b) :
+    FixedHeight β h where
+  bot := f fh.bot
+  top := f fh.top
+  longestChain :=
+    fh.longestChain.map f
+      (hf.strictMono_of_injective (Function.LeftInverse.injective hgf))
+  head_longestChain := by
+    rw [LTSeries.head_map, fh.head_longestChain]
+  last_longestChain := by
+    rw [LTSeries.last_map, fh.last_longestChain]
+  length_longestChain := fh.length_longestChain
+  bounded := fun c =>
+    fh.bounded
+      (c.map g (hg.strictMono_of_injective (Function.LeftInverse.injective hfg)))
+
+end FixedHeight
+
+/-- Agda: `TransportFiniteHeight.finiteHeightLattice`. -/
+def FiniteHeightLattice.transport {α β : Type*} [Lattice α] [Lattice β]
+    (I : FiniteHeightLattice α) (f : α → β) (g : β → α)
+    (hf : Monotone f) (hg : Monotone g)
+    (hgf : ∀ a, g (f a) = a) (hfg : ∀ b, f (g b) = b) :
+    FiniteHeightLattice β where
+  height := I.height
+  fixedHeight := I.fixedHeight.transport f g hf hg hgf hfg
+
+end Spa