diff --git a/src/sat/Solver.ml b/src/sat/Solver.ml
index 84f23ded..10be61c4 100644
--- a/src/sat/Solver.ml
+++ b/src/sat/Solver.ml
@@ -42,7 +42,13 @@ module Make(Plugin : PLUGIN)
   (* ### types ### *)
 
   (* a boolean variable (positive int) *)
-  module Var0 : INT_ID = Mk_int_id()
+  module Var0 : sig
+    include INT_ID
+    module Set : Set.S with type elt = t
+  end = struct
+    include Mk_int_id()
+    module Set = Util.Int_set
+  end
   type var = Var0.t
 
   (* a signed atom. +v is (v << 1), -v is (v<<1 | 1) *)
diff --git a/src/util/Vec.ml b/src/util/Vec.ml
index 782a8b6a..89759a51 100644
--- a/src/util/Vec.ml
+++ b/src/util/Vec.ml
@@ -31,6 +31,12 @@ let[@inline] copy t : _ t =
   let data = Array.copy t.data in
   {t with data}
 
+let resize_ t x size =
+  let arr' = Array.make size x in
+  Array.blit t.data 0 arr' 0 t.sz;
+  t.data <- arr';
+  ()
+
 (* grow the array *)
 let[@inline never] grow_to_double_size t x : unit =
   if Array.length t.data = Sys.max_array_length then (
@@ -39,9 +45,7 @@ let[@inline never] grow_to_double_size t x : unit =
   let size =
     min Sys.max_array_length (max 4 (2 * Array.length t.data))
   in
-  let arr' = Array.make size x in
-  Array.blit t.data 0 arr' 0 (Array.length t.data);
-  t.data <- arr';
+  resize_ t x size;
   assert (Array.length t.data > t.sz);
   ()
 
@@ -67,6 +71,17 @@ let[@inline] fast_remove t i =
   Array.unsafe_set t.data i @@ Array.unsafe_get t.data (t.sz - 1);
   t.sz <- t.sz - 1
 
+let prepend v ~into : unit =
+  if v.sz = 0 then ()
+  else (
+    if v.sz + into.sz > Array.length into.data then (
+      resize_ into v.data.(0) (v.sz + into.sz);
+    );
+    Array.blit into.data 0 into.data v.sz into.sz; (* shift elements *)
+    Array.blit v.data 0 into.data 0 v.sz;
+  )
+
+
 let filter_in_place f vec =
   let i = ref 0 in
   while !i < size vec do
diff --git a/src/util/Vec.mli b/src/util/Vec.mli
index b4994de4..d00f060f 100644
--- a/src/util/Vec.mli
+++ b/src/util/Vec.mli
@@ -62,6 +62,10 @@ val fast_remove : 'a t -> int -> unit
 (** Remove element at index [i] without preserving order
     (swap with last element) *)
 
+val prepend : 'a t -> into:'a t -> unit
+(** [prepend v ~into] pushes all elements of [v] into [into],
+    at the beginning. consumes [v]. *)
+
 val filter_in_place : ('a -> bool) -> 'a t -> unit
 (** [filter_in_place f v] removes from [v] the elements that do
     not satisfy [f] *)