diff --git a/lib/Quox/Equal.idr b/lib/Quox/Equal.idr
index fb15c82..780a121 100644
--- a/lib/Quox/Equal.idr
+++ b/lib/Quox/Equal.idr
@@ -165,13 +165,14 @@ parameters {0 isGlobal : _} (defs : Definitions' q isGlobal)
       compare0 : CanEqual q m => Eq q => Elim q 0 n -> Elim q 0 n -> m ()
       compare0 e f = compareN (whnf defs e) (whnf defs f)
 
-    namespace ScopeTerm
+    namespace ScopeTermN
       export covering %inline
-      compare0 : CanEqual q m => Eq q =>
-                 ScopeTerm q 0 n -> ScopeTerm q 0 n -> m ()
+      compare0 : {s : Nat} -> CanEqual q m => Eq q =>
+                 ScopeTermN s q 0 n -> ScopeTermN s q 0 n -> m ()
       compare0 (TUnused body0) (TUnused body1) = compare0 body0 body1
       compare0 body0 body1 = compare0 body0.term body1.term
 
+    -- [todo] extend to multi-var scopes
     namespace DScopeTerm
       export covering %inline
       compare0 : CanEqual q m => Eq q =>
diff --git a/lib/Quox/Syntax/Subst.idr b/lib/Quox/Syntax/Subst.idr
index 7b6e53f..5057a59 100644
--- a/lib/Quox/Syntax/Subst.idr
+++ b/lib/Quox/Syntax/Subst.idr
@@ -5,6 +5,7 @@ import Quox.Syntax.Var
 import Quox.Name
 import Quox.Pretty
 
+import Data.Nat
 import Data.List
 
 %default total
@@ -84,6 +85,16 @@ public export %inline
 push : CanSubst1 f => Subst f from to -> Subst f (S from) (S to)
 push th = fromVar VZ ::: (th . shift 1)
 
+-- [fixme] a better way to do this?
+public export
+pushN : CanSubst1 f => (s : Nat) ->
+        Subst f from to -> Subst f (s + from) (s + to)
+pushN 0     th = th
+pushN (S s) th =
+  rewrite plusSuccRightSucc s from in
+  rewrite plusSuccRightSucc s to in
+  pushN s $ fromVar VZ ::: (th . shift 1)
+
 public export
 drop1 : Subst f (S from) to -> Subst f from to
 drop1 (Shift by) = Shift $ ssDown by
diff --git a/lib/Quox/Syntax/Term/Base.idr b/lib/Quox/Syntax/Term/Base.idr
index afff7e2..1e0e77a 100644
--- a/lib/Quox/Syntax/Term/Base.idr
+++ b/lib/Quox/Syntax/Term/Base.idr
@@ -92,26 +92,34 @@ mutual
     DCloE : (el : Elim q dfrom n) -> (th : Lazy (DSubst dfrom dto)) ->
             Elim q dto n
 
-  ||| a scope with one more bound variable
+  ||| a scope with some more bound term variables
   public export
-  data ScopeTerm : TermLike where
-    ||| variable is used
-    TUsed : (body : Term q d (S n)) -> ScopeTerm q d n
-    ||| variable is unused
-    TUnused : (body : Term q d n) -> ScopeTerm q d n
+  data ScopeTermN : Nat -> TermLike where
+    ||| at least some variables are used
+    TUsed : (body : Term q d (s + n)) -> ScopeTermN s q d n
+    ||| all variables are unused
+    TUnused : (body : Term q d n) -> ScopeTermN s q d n
 
-  ||| a scope with one more bound dimension variable
   public export
-  data DScopeTerm : TermLike where
-    ||| variable is used
-    DUsed : (body : Term q (S d) n) -> DScopeTerm q d n
-    ||| variable is unused
-    DUnused : (body : Term q d n) -> DScopeTerm q d n
+  0 ScopeTerm : TermLike
+  ScopeTerm = ScopeTermN 1
+
+  ||| a scope with some more bound dimension variable
+  public export
+  data DScopeTermN : Nat -> TermLike where
+    ||| at least some variables are used
+    DUsed : (body : Term q (s + d) n) -> DScopeTermN s q d n
+    ||| all variables are unused
+    DUnused : (body : Term q d n) -> DScopeTermN s q d n
+
+  public export
+  0 DScopeTerm : TermLike
+  DScopeTerm = DScopeTermN 1
 
 %name Term s, t, r
 %name Elim e, f
-%name ScopeTerm body
-%name DScopeTerm body
+%name ScopeTermN body
+%name DScopeTermN body
 
 ||| non dependent function type
 public export %inline
diff --git a/lib/Quox/Syntax/Term/Pretty.idr b/lib/Quox/Syntax/Term/Pretty.idr
index 3c9cf08..f140bb0 100644
--- a/lib/Quox/Syntax/Term/Pretty.idr
+++ b/lib/Quox/Syntax/Term/Pretty.idr
@@ -82,7 +82,7 @@ mutual
         [|withPrec SApp (prettyM e) </> prettyDSubst th|]
 
   export covering
-  PrettyHL q => PrettyHL (ScopeTerm q d n) where
+  {s : Nat} -> PrettyHL q => PrettyHL (ScopeTermN s q d n) where
     prettyM body = prettyM body.term
 
   export covering
diff --git a/lib/Quox/Syntax/Term/Subst.idr b/lib/Quox/Syntax/Term/Subst.idr
index 100bfc1..8d0bbc3 100644
--- a/lib/Quox/Syntax/Term/Subst.idr
+++ b/lib/Quox/Syntax/Term/Subst.idr
@@ -42,16 +42,18 @@ mutual
     DCloE e ph /// th       = DCloE e $ ph . th
     e          /// th       = DCloE e th
 
-  namespace ScopeTerm
+  namespace ScopeTermN
     export
-    (///) : ScopeTerm q dfrom n -> DSubst dfrom dto -> ScopeTerm q dto n
+    (///) : ScopeTermN s q dfrom n -> DSubst dfrom dto -> ScopeTermN s q dto n
     TUsed   body /// th = TUsed   $ body /// th
     TUnused body /// th = TUnused $ body /// th
 
-  namespace DScopeTerm
+  namespace DScopeTermN
     export
-    (///) : DScopeTerm q dfrom n -> DSubst dfrom dto -> DScopeTerm q dto n
-    DUsed   body /// th = DUsed   $ body /// push th
+    (///) : {s : Nat} ->
+            DScopeTermN s q dfrom n -> DSubst dfrom dto ->
+            DScopeTermN s q dto n
+    DUsed   body /// th = DUsed   $ body /// pushN s th
     DUnused body /// th = DUnused $ body /// th
 
 
@@ -89,19 +91,25 @@ CanSubst (Elim q d) (Term q d) where
                          th       => CloT s th
 
 export %inline
-CanSubst (Elim q d) (ScopeTerm q d) where
-  TUsed   body // th = TUsed   $ body // push th
+{s : Nat} -> CanSubst (Elim q d) (ScopeTermN s q d) where
+  TUsed   body // th = TUsed   $ body // pushN s th
   TUnused body // th = TUnused $ body // th
 
 export %inline
-CanSubst (Elim q d) (DScopeTerm q d) where
-  DUsed   body // th = DUsed   $ body // map (/// shift 1) th
+{s : Nat} -> CanSubst (Elim q d) (DScopeTermN s q d) where
+  DUsed   body // th = DUsed   $ body // map (/// shift s) th
   DUnused body // th = DUnused $ body // th
 
-export %inline CanSubst Var (Term       q d) where s // th = s // map (B {q, d}) th
-export %inline CanSubst Var (Elim       q d) where e // th = e // map (B {q, d}) th
-export %inline CanSubst Var (ScopeTerm  q d) where s // th = s // map (B {q, d}) th
-export %inline CanSubst Var (DScopeTerm q d) where s // th = s // map (B {q, d}) th
+export %inline CanSubst Var (Term q d) where s // th = s // map (B {q, d}) th
+export %inline CanSubst Var (Elim q d) where e // th = e // map (B {q, d}) th
+
+export %inline
+{s : Nat} -> CanSubst Var (ScopeTermN s q d) where
+  b // th = b // map (B {q, d}) th
+
+export %inline
+{s : Nat} -> CanSubst Var (DScopeTermN s q d) where
+  b // th = b // map (B {q, d}) th
 
 
 infixl 8 //., ///
@@ -130,33 +138,43 @@ mutual
            Elim q dto to
     subs e th ph = e /// th // ph
 
-  namespace ScopeTerm
+  namespace ScopeTermN
     ||| applies a term substitution with a less ambiguous type
     export %inline
-    (//.) : ScopeTerm q d from -> TSubst q d from to -> ScopeTerm q d to
+    (//.) : {s : Nat} ->
+            ScopeTermN s q d from -> TSubst q d from to ->
+            ScopeTermN s q d to
     body //. th = body // th
 
     ||| applies a term and dimension substitution
     public export %inline
-    subs : ScopeTerm q dfrom from -> DSubst dfrom dto -> TSubst q dto from to ->
-           ScopeTerm q dto to
+    subs : {s : Nat} ->
+           ScopeTermN s q dfrom from ->
+           DSubst dfrom dto -> TSubst q dto from to ->
+           ScopeTermN s q dto to
     subs body th ph = body /// th // ph
 
-  namespace DScopeTerm
+  namespace DScopeTermN
     ||| applies a term substitution with a less ambiguous type
     export %inline
-    (//.) : DScopeTerm q d from -> TSubst q d from to -> DScopeTerm q d to
+    (//.) : {s : Nat} -> DScopeTermN s q d from -> TSubst q d from to ->
+            DScopeTermN s q d to
     body //. th = body // th
 
     ||| applies a term and dimension substitution
     public export %inline
-    subs : DScopeTerm q dfrom from -> DSubst dfrom dto -> TSubst q dto from to ->
-           DScopeTerm q dto to
+    subs : {s : Nat} ->
+           DScopeTermN s q dfrom from ->
+           DSubst dfrom dto -> TSubst q dto from to ->
+           DScopeTermN s q dto to
     subs body th ph = body /// th // ph
 
-export %inline CanShift (Term      q d) where s // by = s //. Shift by
-export %inline CanShift (Elim      q d) where e // by = e //. Shift by
-export %inline CanShift (ScopeTerm q d) where s // by = s //. Shift by
+export %inline CanShift (Term q d) where s // by = s //. Shift by
+export %inline CanShift (Elim q d) where e // by = e //. Shift by
+
+export %inline
+{s : Nat} -> CanShift (ScopeTermN s q d) where
+  b // by = b //. Shift by
 
 
 export %inline
@@ -165,17 +183,17 @@ comp : DSubst dfrom dto -> TSubst q dfrom from mid -> TSubst q dto mid to ->
 comp th ps ph = map (/// th) ps . ph
 
 
-namespace ScopeTerm
+namespace ScopeTermN
   export %inline
-  (.term) : ScopeTerm q d n -> Term q d (S n)
+  (.term) : {s : Nat} -> ScopeTermN s q d n -> Term q d (s + n)
   (TUsed   body).term = body
-  (TUnused body).term = body //. shift 1
+  (TUnused body).term = body //. shift s
 
-namespace DScopeTerm
+namespace DScopeTermN
   export %inline
-  (.term) : DScopeTerm q d n -> Term q (S d) n
+  (.term) : {s : Nat} -> DScopeTermN s q d n -> Term q (s + d) n
   (DUsed   body).term = body
-  (DUnused body).term = body /// shift 1
+  (DUnused body).term = body /// shift s
 
 export %inline
 sub1 : ScopeTerm q d n -> Elim q d n -> Term q d n