diff --git a/packages/@ot-doc/document/src/lib/array-document.spec.ts b/packages/@ot-doc/document/src/lib/array-document.spec.ts
index 669c027..7d020b0 100644
--- a/packages/@ot-doc/document/src/lib/array-document.spec.ts
+++ b/packages/@ot-doc/document/src/lib/array-document.spec.ts
@@ -1,56 +1,42 @@
 import { describeDocumentMeta, DocumentTestCases } from "../util/test-utility";
-import { arrayDocument, Oplet } from "./array-document";
+import { arrayDocument, deleteAt, insertAt, Oplet } from "./array-document";
 
 const arrNum = arrayDocument<number>();
 
 describeDocumentMeta('arrayDocument<number>', arrNum, {
   singleton: [
     [],
-    [{ typ: 'ins', idx: 0, val: 1 }],
-    [{ typ: 'del', idx: 0, val: 1 }],
-    [
-      { typ: 'del', idx: 0, val: 1 },
-      { typ: 'ins', idx: 1, val: 2 },
-    ],
-    [
-      { typ: 'ins', idx: 1, val: 2 },
-      { typ: 'del', idx: 0, val: 1 },
-    ],
+    insertAt(0, 1),
+    deleteAt(0, 1),
+    [...deleteAt(0, 1), ...insertAt(1, 2)],
+    [...insertAt(1, 2), ...deleteAt(0, 1)],
   ],
   composable3: [
     [
       [],
-      [
-        { typ: 'ins', idx: 1, val: 2 },
-        { typ: 'del', idx: 0, val: 1 },
-      ],
-      [
-        { typ: 'del', idx: 0, val: 2 },
-        { typ: 'ins', idx: 1, val: 2 },
-      ],
+      [...insertAt(1, 2), ...deleteAt(0, 1)],
+      [...deleteAt(0, 2), ...insertAt(1, 2)],
     ],
     [
-      [
-        { typ: 'ins', idx: 1, val: 2 },
-        { typ: 'del', idx: 0, val: 1 },
-      ],
+      [...insertAt(1, 2), ...deleteAt(0, 1)],
       [],
-      [
-        { typ: 'del', idx: 0, val: 2 },
-        { typ: 'ins', idx: 1, val: 2 },
-      ],
+      [...deleteAt(0, 2), ...insertAt(1, 2)],
     ],
     [
-      [
-        { typ: 'ins', idx: 1, val: 2 },
-        { typ: 'del', idx: 0, val: 1 },
-      ],
-      [
-        { typ: 'del', idx: 0, val: 2 },
-        { typ: 'ins', idx: 1, val: 2 },
-      ],
+      [...insertAt(1, 2), ...deleteAt(0, 1)],
+      [...deleteAt(0, 2), ...insertAt(1, 2)],
       [],
     ],
+    [
+      insertAt(0, 1, 2, 3),
+      insertAt(1, 4, 5),
+      insertAt(3, 6),
+    ],
+    [
+      insertAt(0, 0, 1, 2, 3),
+      deleteAt(2, 2, 3),
+      deleteAt(0, 0),
+    ],
   ],
   others({ comp, inv }) {
     // const a: Oplet<number>[] = [{ typ: 'ins', idx: 1, val: 2}, { typ: 'del', idx: 0, val: 1 }];
diff --git a/packages/@ot-doc/document/src/lib/array-document.ts b/packages/@ot-doc/document/src/lib/array-document.ts
index a8ad7d4..d2a8373 100644
--- a/packages/@ot-doc/document/src/lib/array-document.ts
+++ b/packages/@ot-doc/document/src/lib/array-document.ts
@@ -75,7 +75,7 @@ export const arrayDocument = <T>({
     const update = (...ops: Oplet<T>[]): void => {
       if (r === a) r = [...a];
       r.splice(i, 2, ...ops);
-      i = i + ops.length - 1;
+      i = Math.max(i + ops.length - 1, 0);
       updated = true;
     };
 
@@ -83,7 +83,8 @@ export const arrayDocument = <T>({
       updated = false;
       i = 0;
       while (i < r.length - 1) {
-        const [eA, eB] = r.slice(i, i + 2);
+        const eA = r[i];
+        const eB = r[i + 1];
         if (eA.typ === 'ins') {
           if (eB.typ === 'ins') {
             if (eA.idx >= eB.idx) {
@@ -142,4 +143,10 @@ export const arrayDocument = <T>({
       return true;
     },
   };
-};
\ No newline at end of file
+};
+
+export const insertAt = <T>(i: number, ...arr: T[]): Oplet<T>[] =>
+  arr.map((val, j) => ({ typ: 'ins', val, idx: i + j }));
+
+export const deleteAt = <T>(i: number, ...arr: T[]): Oplet<T>[] =>
+  arr.map((val, j): Oplet<T> => ({ typ: 'del', val, idx: i + j })).reverse();
\ No newline at end of file