Replace hardcoded universe levels with a proper level language and constraint solving

Tests.lean

@@ -25,8 +25,12 @@ structure TestCase where
 def cases : List TestCase := [
   ⟨"U0 is typed by U1",          Examples.univ0,
     .okTy (.univ 1)⟩,
+  ⟨"U(max 0 1) is typed by U2",  Examples.univMax,
+    .okTy (.univ 2)⟩,
   ⟨"U0 subsumes into U2",        .ann (.univ 0) (.univ 2),
     .okTy (.univ 2)⟩,
+  ⟨"U0 subsumes into U(max 0 2)", .ann (.univ 0) (.univ (.max 0 2)),
+    .okTy (.univ 2)⟩,
   ⟨"Nat is typed by U0",         .nat,
     .okTy (.univ 0)⟩,
   ⟨"succ zero infers Nat",       (.succ .zero),
@@ -164,6 +168,22 @@ def runNeutralRepresentationChecks : IO Bool := do
     IO.println "fail  stuck eliminators stay in the neutral fragment"
     pure false
 
+def runLevelSolverChecks : IO Bool := do
+  let satOk :=
+    match solveLevelConstraints [(.max 0 1, 1), (1, .succ 1)] with
+    | Except.ok _ => true
+    | Except.error _ => false
+  let unsatOk :=
+    match solveLevelConstraints [(.succ 1, 1)] with
+    | Except.error err => containsText err "unsatisfiable level constraint"
+    | Except.ok _ => false
+  if satOk && unsatOk then
+    IO.println "pass  level constraints are solved consistently"
+    pure true
+  else
+    IO.println "fail  level constraints are solved consistently"
+    pure false
+
 def runPrettyPrinterChecks : IO Bool := do
   match checkTop Examples.idAnn with
   | .ok (tm, ty) =>
@@ -192,8 +212,9 @@ def main : IO UInt32 := do
   let results ← cases.mapM runCase
   let safetyOk ← runInternalSafetyChecks
   let neutralOk ← runNeutralRepresentationChecks
+  let levelOk ← runLevelSolverChecks
   let prettyOk ← runPrettyPrinterChecks
-  let allResults := results ++ [safetyOk, neutralOk, prettyOk]
+  let allResults := results ++ [safetyOk, neutralOk, levelOk, prettyOk]
   let failed := allResults.countP (· == false)
   if failed == 0 then
     IO.println s!"\n{allResults.length} passed, 0 failed"