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+(* Split a list at a given index [i] (the first list contains all the elements
+   up to element of index [i], not included, the second one contains the remaining
+   elements. Note that the first returned list has length [i].
+*)
+let rec list_split_at (ls : 'a list) (i : int) =
+  if i < 0 then raise (Invalid_argument "list_split_at take positive integers")
+  else if i = 0 then ([], ls)
+  else
+    match ls with
+    | [] ->
+        raise
+          (Failure
+             "The int given to list_split_at should be <= the list's length")
+    | x :: ls' ->
+        let ls1, ls2 = list_split_at ls' (i - 1) in
+        (x :: ls1, ls2)
+
+exception Found
+(** Utility exception
+
+    When looking for something while exploring a term, it can be easier to
+    just throw an exception to signal we found what we were looking for.
+ *)