Migrate Reaching.lean to projections via a generic Trace.steps

Finish the projection migration for reaching definitions by replacing the
accumulator-style runOfTrace*From definitions and their hand-rolled
re-association lemmas with a single analysis-agnostic projection:
Trace.steps / Traceₗ.steps, the chronological List of executed
(index, statement) pairs. Its four simp lemmas are one-line inductions,
with all re-association falling out of mathlib's List.append_assoc and
List.reverse_append.

Run is now an abbrev for List (State × BasicStmt) (latest-first, so
LastAssign keeps its first-match structure) and runOfTrace is just
steps.reverse.

Also hoist the generic reaches_final_post into Forward.lean, letting
analyze_correct' be stated directly about S.Post (prog.trace hrun).

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

lean/Spa/Analysis/Forward.lean

@@ -131,6 +131,15 @@ def reaches_final {s₁ s₂ : prog.State} {ρ₁ ρ₂ : Env}
   | .edge hnode hedge rest =>
     let ⟨ρin, r'⟩ := reaches_final rest; ⟨ρin, .edge_there hnode hedge _ r'⟩
 
+omit [DecidableEq L] in
+/-- Reaching the final node covers the whole trace. -/
+@[simp] lemma reaches_final_post {s₁ s₂ : prog.State} {ρ₁ ρ₂ : Env}
+    (tr : Trace prog.cfg s₁ s₂ ρ₁ ρ₂) :
+    (reaches_final tr).2.post = tr := by
+  induction tr with
+  | single hnode => rfl
+  | edge hnode hedge rest ih => simp [reaches_final, Reaches.post, ih]
+
 variable (L prog) in
 /-- Soundness at every program point reached during execution: for any node `s` visited
     by the run `hrun` (witnessed by `hr`), the analysis result over-approximates both the
@@ -148,11 +157,9 @@ theorem analyze_correct_at {ρf : Env} (hrun : EvalStmt [] prog.rootStmt ρf)
 variable (L prog) in
 theorem analyze_correct'
     {ρ : Env} (hrun : EvalStmt [] prog.rootStmt ρ) :
-    ⟦ variablesAt prog.finalState (result L prog) ⟧ (S.Post (reaches_final (prog.trace hrun)).2.post) := by
-  let idk₀ := prog.trace hrun
-  have ⟨_, idk₁⟩ := reaches_final idk₀
-  have ⟨_, idk₂⟩ := analyze_correct_at L prog hrun idk₁
-  assumption
+    ⟦ variablesAt prog.finalState (result L prog) ⟧ (S.Post (prog.trace hrun)) := by
+  have h := (analyze_correct_at L prog hrun (reaches_final (prog.trace hrun)).2).2
+  rwa [reaches_final_post] at h
 
 end