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

BidirTT/Check.lean

@@ -122,7 +122,7 @@ mutual
             let _ := level
             pure (.idElim motive' r' target' eq', resultTy)
         | _ => throw s!"expected Id type in idElim, got {showTy cxt.lvl eqTy}"
-    | .univ i => pure (.univ i, .univ (i + 1))
+    | .univ i => pure (.univ i.normalise, .univ i.succ')
     | .app t u => do
         let (t', tty) ← infer cxt t
         match tty with
@@ -150,12 +150,12 @@ mutual
         let (a', i) ← inferUniverse cxt a
         let va ← eval cxt.env a'
         let (b', j) ← inferUniverse (cxt.bind x va) b
-        pure (.pi a' b', .univ (Nat.max i j))
+        pure (.pi a' b', .univ (i.max' j))
     | .sig x a b => do
         let (a', i) ← inferUniverse cxt a
         let va ← eval cxt.env a'
         let (b', j) ← inferUniverse (cxt.bind x va) b
-        pure (.sig a' b', .univ (Nat.max i j))
+        pure (.sig a' b', .univ (i.max' j))
     | .ann t a => do
         let (a', _) ← inferUniverse cxt a
         let va ← eval cxt.env a'
@@ -171,7 +171,7 @@ mutual
     | .lam _ _  => throw "cannot infer type of lambda, use an annotation"
     | .pair _ _ => throw "cannot infer type of pair, use an annotation"
 
-  partial def inferUniverse (cxt : Cxt) (r : Raw) : TCM (Tm × Nat) := do
+  partial def inferUniverse (cxt : Cxt) (r : Raw) : TCM (Tm × Level) := do
     let (t, ty) ← infer cxt r
     match ty with
     | .univ level => pure (t, level)