diff --git a/src/num/theories/cv_compute/selftest.sml b/src/num/theories/cv_compute/selftest.sml
index 66e3a29f66..2db5065e25 100644
--- a/src/num/theories/cv_compute/selftest.sml
+++ b/src/num/theories/cv_compute/selftest.sml
@@ -1,5 +1,5 @@
 open testutils HolKernel Parse boolLib cv_computeLib cvSyntax cvTheory;
-open arithmeticTheory
+open arithmeticTheory tailrecLib
 
 fun simp ths = simpLib.ASM_SIMP_TAC (BasicProvers.srw_ss()) ths
 
@@ -57,3 +57,21 @@ fun test n =
 
 val _ = List.app test [0, 1, 5, 10, 13, 74, 157, 180];
 
+(* tail-recursion *)
+val base_t = “fib A N x = if x = 0 then A else fib (N + A) A (x -1) ”
+val expected = “?fib. !A N x. ^base_t”
+val _ = tprint "tailrecursive fibonacci"
+val _ = require_msg (check_result (aconv expected o concl)) thm_to_string
+                    prove_tailrec_exists
+                    base_t
+
+val odd = “(odd n = if n = 0 then F else even (n - 1))”
+val even = “(even i = if i = 0 then T else odd (i - 1))”
+val base_t = mk_conj(odd,even)
+val expected = “?odd even. (!n. ^odd) /\ (!i. ^even) ”
+val _ = tprint "tailrecursive even/odd"
+val _ = require_msg (check_result (aconv expected o concl)) thm_to_string
+                    prove_tailrec_exists
+                    base_t
+
+val _ = require_msg
diff --git a/src/num/theories/cv_compute/tailrecLib.sml b/src/num/theories/cv_compute/tailrecLib.sml
index 06dcf7b2ac..a3dfdce2c2 100644
--- a/src/num/theories/cv_compute/tailrecLib.sml
+++ b/src/num/theories/cv_compute/tailrecLib.sml
@@ -1,24 +1,15 @@
 structure tailrecLib :> tailrecLib =
 struct
 
-open HolKernel Parse boolLib bossLib;
+open HolKernel Parse boolLib simpLib boolSimps
+
+val Cases = BasicProvers.Cases
+val PairCases = pairLib.PairCases
 
 (*----------------------------------------------------------------------*
     Miscellaneous helper functions
  *----------------------------------------------------------------------*)
 
-fun list_dest_conj tm =
-  if is_conj tm then let
-    val (x,y) = dest_conj tm
-    in list_dest_conj x @ list_dest_conj y end
-  else [tm];
-
-fun list_dest_exists tm = let
-  val (v,y) = dest_exists tm
-  val (vs,t) = list_dest_exists y
-  in (v::vs,t) end
-  handle HOL_ERR _ => ([],tm);
-
 fun list_mk_pair_case pat r =
   if not (pairSyntax.is_pair pat) then (pat,r) else let
     val v = genvar (type_of pat)
@@ -27,7 +18,7 @@ fun list_mk_pair_case pat r =
     val new_pat = pairSyntax.mk_pair(x1,y1)
     in (v,TypeBase.mk_case(v,[(new_pat,r1)])) end
 
-fun auto_prove goal_tm (tac:tactic) = snd (tac ([],goal_tm)) [];
+fun auto_prove goal_tm (tac:tactic) = TAC_PROOF (([],goal_tm), tac)
 
 (*----------------------------------------------------------------------*
     Function for proving that non-mutually recursive tail-recursive
@@ -89,7 +80,8 @@ fun prove_simple_tailrec_exists tm = let
       val vs = xs |> map (fn (x,y) => (y,genvar (type_of y)))
       val specs = foldl (fn (x,t) => SPEC_TAC x THEN t) ALL_TAC vs
       val gens = foldr (fn ((_,x),t) =>
-                    if can pairSyntax.dest_prod (type_of x) then PairCases THEN t
+                    if can pairSyntax.dest_prod (type_of x) then
+                      PairCases THEN t
                     else gen_tac THEN t) ALL_TAC vs
       fun expand_lets 0 = ALL_CONV
         | expand_lets 1 = (REWR_CONV LET_THM THENC PairRules.PBETA_CONV)
@@ -129,7 +121,7 @@ fun prove_simple_tailrec_exists tm = let
  *----------------------------------------------------------------------*)
 
 fun prove_tailrec_exists def_tm = let
-  val defs = list_dest_conj def_tm
+  val defs = strip_conj def_tm
   (* build the goal to prove *)
   fun extract_def def_tm = let
     val (l,r) = dest_eq def_tm
@@ -190,7 +182,7 @@ fun prove_tailrec_exists def_tm = let
 
 fun tailrec_define name def_tm = let
   val lemma = prove_tailrec_exists def_tm
-  val names = lemma |> concl |> list_dest_exists |> fst |> map (fst o dest_var)
+  val names = lemma |> concl |> strip_exists |> fst |> map (fst o dest_var)
   in new_specification(name,names,lemma) end
 
 end