diff --git a/examples/algorithms/unification/triangular/first-order/compilation/tcallUnifScript.sml b/examples/algorithms/unification/triangular/first-order/compilation/tcallUnifScript.sml
index 507f3b0819..804623c8bb 100644
--- a/examples/algorithms/unification/triangular/first-order/compilation/tcallUnifScript.sml
+++ b/examples/algorithms/unification/triangular/first-order/compilation/tcallUnifScript.sml
@@ -454,49 +454,12 @@ Theorem kunifywl_thm =
         REWRITE_RULE [GSYM kunifywl_def] (CONJ unifywl0_NIL $ cj 3 unifywl0)
 
 (* now to do guard-elimination *)
-
-fun findin f t =
-  if aconv f t then SOME []
-  else
-    case total dest_comb t of
-      NONE => NONE
-    | SOME (t1,t2) =>
-        case findin f t1 of
-          NONE => NONE
-        | SOME pfx => SOME (pfx @ [t2])
-
-
-fun tcallify fn_t inty t =
-  if TypeBase.is_case t then
-    let val (f, ts) = strip_comb t
-        val {Thy,Name,Ty} = dest_thy_const f
-        val f0 = prim_mk_const{Name=Name,Thy=Thy}
-        val basety = type_of f0
-        val (argtys, rngty) = strip_fun basety
-        val rng_th = match_type rngty (sumSyntax.mk_sum(inty,type_of t))
-        val argty_th = match_type (hd argtys) (type_of (hd ts))
-        val ft = Term.inst (rng_th @ argty_th) f0
-        val ft1 = mk_comb(ft, hd ts)
-        val ts' = map (tcallify fn_t inty) (tl ts)
-    in
-      list_mk_comb(ft1, ts')
-    end
-  else
-    case dest_term t of
-      CONST _ => sumSyntax.mk_inr(t,inty)
-    | VAR _ => sumSyntax.mk_inr(t,inty)
-    | LAMB(vt,bt) => mk_abs(vt, tcallify fn_t inty bt)
-    | COMB _ =>
-      case findin fn_t t of
-        NONE => sumSyntax.mk_inr(t,inty)
-      | SOME args => sumSyntax.mk_inl(pairSyntax.list_mk_pair args, type_of t)
-
 fun tcallify_th th =
   let val (l,r) = dest_eq (concl th)
       val (lf, args) = strip_comb l
       val atup = pairSyntax.list_mk_pair args
       val inty = type_of atup
-      val body_t = tcallify lf inty r
+      val body_t = tailrecLib.mk_sum_term lf inty r
   in
       pairSyntax.mk_pabs(atup, body_t)
   end
diff --git a/src/num/theories/cv_compute/tailrecLib.sig b/src/num/theories/cv_compute/tailrecLib.sig
index 971d3e0b03..dd0a9a75bd 100644
--- a/src/num/theories/cv_compute/tailrecLib.sig
+++ b/src/num/theories/cv_compute/tailrecLib.sig
@@ -3,7 +3,17 @@ sig
 
     include Abbrev
 
+    val mk_sum_term : term -> hol_type -> term -> term
+
     val tailrec_define         : string -> term -> thm
     val prove_tailrec_exists   : term -> thm
 
 end
+
+(* [mk_sum_term fnt inty t] generates an abstraction term c that can be an
+   argument to TAILREC (or TAILCALL) such that ("roughly")
+
+     TAILCALL c fnt x = fnt x
+
+   The argument inty is type of the argument to fnt (x above)
+*)
diff --git a/src/num/theories/cv_compute/tailrecLib.sml b/src/num/theories/cv_compute/tailrecLib.sml
index a3dfdce2c2..60338e6a0c 100644
--- a/src/num/theories/cv_compute/tailrecLib.sml
+++ b/src/num/theories/cv_compute/tailrecLib.sml
@@ -3,6 +3,9 @@ struct
 
 open HolKernel Parse boolLib simpLib boolSimps
 
+fun mk_HOL_ERR f msg = HOL_ERR {origin_structure = "tailrecLib",
+                                origin_function = f, message = msg}
+
 val Cases = BasicProvers.Cases
 val PairCases = pairLib.PairCases
 
@@ -29,6 +32,36 @@ val TAILREC_def = whileTheory.TAILREC
                   |> CONV_RULE (DEPTH_CONV ETA_CONV)
                   |> REWRITE_RULE [GSYM combinTheory.I_EQ_IDABS];
 
+fun mk_sum_term fn_t inty tm =
+    let
+      fun build_sum t =
+          if TypeBase.is_case t then
+            let val (a,b,xs) = TypeBase.dest_case t
+                val ys = map (apsnd build_sum) xs
+            in
+              TypeBase.mk_case (b,ys)
+            end
+          else if can pairSyntax.dest_anylet t then
+            let val (xs,x) = pairSyntax.dest_anylet t
+            in pairSyntax.mk_anylet(xs,build_sum x) end
+          else if cvSyntax.is_cv_if tm then
+            let val (b,x,y) = cvSyntax.dest_cv_if tm
+            in mk_cond(cvSyntax.mk_c2b b,build_sum x,build_sum y) end
+          else
+            let val (f, xs) = strip_comb t
+            in
+              if aconv f fn_t then
+                if null xs then raise mk_HOL_ERR "mk_sum_term" "malformed term"
+                else
+                  sumSyntax.mk_inl (pairSyntax.list_mk_pair xs, type_of t)
+              else if is_abs t then
+                mk_abs (apsnd build_sum (dest_abs t))
+              else sumSyntax.mk_inr(t,inty)
+            end
+    in
+      build_sum tm
+    end
+
 fun prove_simple_tailrec_exists tm = let
   val (l,r) = dest_eq tm
   val (f_tm,arg_tm) = dest_comb l
@@ -39,26 +72,7 @@ fun prove_simple_tailrec_exists tm = let
   fun mk_inl x = sumSyntax.mk_inl(x,output_ty)
   fun mk_inr x = sumSyntax.mk_inr(x,input_ty)
   (* building the witness *)
-  fun build_sum tm =
-    if is_comb tm andalso aconv (rator tm) f_tm then
-      mk_inl (rand tm)
-    else if List.all (not o aconv f_tm) (free_vars tm) then
-      mk_inr tm
-    else if is_cond tm then let
-      val (b,x,y) = dest_cond tm
-      in mk_cond(b,build_sum x,build_sum y) end
-    else if cvSyntax.is_cv_if tm then let
-      val (b,x,y) = cvSyntax.dest_cv_if tm
-      in mk_cond(cvSyntax.mk_c2b b,build_sum x,build_sum y) end
-    else if can pairSyntax.dest_anylet tm then let
-      val (xs,x) = pairSyntax.dest_anylet tm
-      in pairSyntax.mk_anylet(xs,build_sum x) end
-    else if TypeBase.is_case tm then let
-      val (a,b,xs) = TypeBase.dest_case tm
-      val ys = map (fn (x,tm) => (x,build_sum tm)) xs
-      in TypeBase.mk_case(b,ys) end
-    else failwith ("Unsupported: " ^ term_to_string tm)
-  val sum_tm = build_sum r
+  val sum_tm = mk_sum_term f_tm input_ty r
   val abs_sum_tm = pairSyntax.mk_pabs(arg_tm,sum_tm)
   val witness = ISPEC abs_sum_tm whileTheory.TAILREC |> SPEC_ALL
                 |> concl |> dest_eq |> fst |> rator