diff --git a/lib/Quox/Syntax/Qty.idr b/lib/Quox/Syntax/Qty.idr
index 0db17b5..86672b6 100644
--- a/lib/Quox/Syntax/Qty.idr
+++ b/lib/Quox/Syntax/Qty.idr
@@ -83,10 +83,11 @@ compat pi rh  = pi == rh
 
 ||| "π ∨ ρ"
 |||
-||| returns some quantity τ where π ≤ τ and ρ ≤ τ, if one exists.
+||| returns a quantity τ with π ≤ τ and ρ ≤ τ.
+||| if π = ρ, then it's that, otherwise it's ω.
 public export
-lub : Qty -> Qty -> Maybe Qty
-lub p q = Just $ if p == q then p else Any
+lub : Qty -> Qty -> Qty
+lub p q = if p == q then p else Any
 
 
 ||| to maintain subject reduction, only 0 or 1 can occur
diff --git a/lib/Quox/Typechecker.idr b/lib/Quox/Typechecker.idr
index bfe0208..0cc2e19 100644
--- a/lib/Quox/Typechecker.idr
+++ b/lib/Quox/Typechecker.idr
@@ -39,15 +39,15 @@ parameters (loc : Loc)
   popQ pi = popQs [< pi]
 
 export
-lubs1 : List1 (QOutput n) -> Maybe (QOutput n)
-lubs1 ([<] ::: _) = Just [<]
+lubs1 : List1 (QOutput n) -> QOutput n
+lubs1 ([<] ::: _) = [<]
 lubs1 ((qs :< p) ::: pqs) =
   let (qss, ps) = unzip $ map unsnoc pqs in
-  [|lubs1 (qs ::: qss) :< foldlM lub p ps|]
+  lubs1 (qs ::: qss) :< foldl lub p ps
 
 export
-lubs : TyContext d n -> List (QOutput n) -> Maybe (QOutput n)
-lubs ctx []        = Just $ zeroFor ctx
+lubs : TyContext d n -> List (QOutput n) -> QOutput n
+lubs ctx []        = zeroFor ctx
 lubs ctx (x :: xs) = lubs1 $ x ::: xs
 
 
@@ -397,12 +397,9 @@ mutual
     unless (ttags == armTags) $ throw $ BadCaseEnum loc ttags armTags
     armres <- for arms $ \(a, s) =>
       checkC ctx sg s $ sub1 ret $ Ann (Tag a s.loc) tres.type s.loc
-    let Just armout = lubs ctx armres
-          | _ => throw $ BadQtys loc "case arms" ctx $
-              zipWith (\qs, (t, rhs) => (qs, Tag t noLoc)) armres arms
     pure $ InfRes {
       type = sub1 ret t,
-      qout = pi * tres.qout + armout
+      qout = pi * tres.qout + lubs ctx armres
     }
 
   infer' ctx sg (CaseNat pi pi' n ret zer suc loc) = do
@@ -474,12 +471,8 @@ mutual
         val1  = val1.term
     qout1 <- check ctx1 sg val1 ty'
     lift $ equal loc (eqDim (B VZ p.loc) p' ctx1) ty' val1 val'
-    let qout0' = toMaybe $ map (, val0 // one p) qout0
-        qout1' = toMaybe $ map (, val1 // one p) qout1
-        qouts  = (qout, val) :: catMaybes [qout0', qout1']
-    let Just qout = lubs ctx $ map fst qouts
-      | Nothing => throw $ BadQtys loc "composition" ctx qouts
-    pure $ InfRes {type = ty, qout}
+    let qouts  = qout :: catMaybes [toMaybe qout0, toMaybe qout1]
+    pure $ InfRes {type = ty, qout = lubs ctx qouts}
 
   infer' ctx sg (TypeCase ty ret arms def loc) = do
     -- if σ = 0