diff --git a/src/Quox/Syntax/Term.idr b/src/Quox/Syntax/Term.idr
index c9461ae..334aedf 100644
--- a/src/Quox/Syntax/Term.idr
+++ b/src/Quox/Syntax/Term.idr
@@ -305,47 +305,57 @@ ncloE e = Element e %search
 mutual
   ||| if the input term has any top-level closures, push them under one layer of
   ||| syntax
-  export
+  export %inline
   pushSubstsT : Term d n -> NotCloTerm d n
-  pushSubstsT s = pushSubstsT' id id s
+  pushSubstsT s = pushSubstsTWith id id s
 
   ||| if the input elimination has any top-level closures, push them under one
   ||| layer of syntax
-  export
+  export %inline
   pushSubstsE : Elim d n -> NotCloElim d n
-  pushSubstsE e = pushSubstsE' id id e
+  pushSubstsE e = pushSubstsEWith id id e
 
   private
-  pushSubstsT' : DSubst dfrom dto -> TSubst dto from to ->
-                 Term dfrom from -> NotCloTerm dto to
-  pushSubstsT' th ph (TYPE l) =
+  pushSubstsTWith : DSubst dfrom dto -> TSubst dto from to ->
+                    Term dfrom from -> NotCloTerm dto to
+  pushSubstsTWith th ph (TYPE l) =
     ncloT $ TYPE l
-  pushSubstsT' th ph (Pi qty qtm x a b) =
+  pushSubstsTWith th ph (Pi qty qtm x a b) =
     ncloT $ Pi qty qtm x (subs a th ph) (subs b th (push ph))
-  pushSubstsT' th ph (Lam x t) =
+  pushSubstsTWith th ph (Lam x t) =
     ncloT $ Lam x $ subs t th $ push ph
-  pushSubstsT' th ph (E e) =
-    let Element e _ = pushSubstsE' th ph e in ncloT $ E e
-  pushSubstsT' th ph (CloT  s ps) =
-    pushSubstsT' th (comp' th ps ph) s
-  pushSubstsT' th ph (DCloT s ps) =
-    pushSubstsT' (ps . th) ph s
+  pushSubstsTWith th ph (E e) =
+    let Element e _ = pushSubstsEWith th ph e in ncloT $ E e
+  pushSubstsTWith th ph (CloT  s ps) =
+    pushSubstsTWith th (comp' th ps ph) s
+  pushSubstsTWith th ph (DCloT s ps) =
+    pushSubstsTWith (ps . th) ph s
 
   private
-  pushSubstsE' : DSubst dfrom dto -> TSubst dto from to ->
-                 Elim dfrom from -> NotCloElim dto to
-  pushSubstsE' th ph (F x) =
+  pushSubstsEWith : DSubst dfrom dto -> TSubst dto from to ->
+                    Elim dfrom from -> NotCloElim dto to
+  pushSubstsEWith th ph (F x) =
     ncloE $ F x
-  pushSubstsE' th ph (B i) =
+  pushSubstsEWith th ph (B i) =
     assert_total pushSubstsE $ ph !! i
-  pushSubstsE' th ph (f :@ s) =
+  pushSubstsEWith th ph (f :@ s) =
     ncloE $ subs f th ph :@ subs s th ph
-  pushSubstsE' th ph (s :# a) =
+  pushSubstsEWith th ph (s :# a) =
     ncloE $ subs s th ph :# subs a th ph
-  pushSubstsE' th ph (CloE  e ps) =
-    pushSubstsE' th (comp' th ps ph) e
-  pushSubstsE' th ph (DCloE e ps) =
-    pushSubstsE' (ps . th) ph e
+  pushSubstsEWith th ph (CloE  e ps) =
+    pushSubstsEWith th (comp' th ps ph) e
+  pushSubstsEWith th ph (DCloE e ps) =
+    pushSubstsEWith (ps . th) ph e
+
+
+public export %inline
+pushSubstsT' : Term d n -> Term d n
+pushSubstsT' s = (pushSubstsT s).fst
+
+
+public export %inline
+pushSubstsE' : Elim d n -> Elim d n
+pushSubstsE' e = (pushSubstsE e).fst
 
 
 parameters {auto _ : Alternative f}