diff --git a/examples/Chapter2.ipynb b/examples/Chapter2.ipynb
index 9566aa1..f1b3997 100644
--- a/examples/Chapter2.ipynb
+++ b/examples/Chapter2.ipynb
@@ -840,6 +840,375 @@
    "source": [
     "(cat:check-rdct-no-wait)"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2.4.1 Useful functions related to the perturbation lemma\n",
+    "#### Example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K66 Homotopy-Equivalence K30 <= K30 => K30]"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def hmeq (cat:trivial-hmeq (cdelta 4)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K74 Homotopy-Equivalence K69 <= K69 => K69]"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(setf hmeq (cat:add hmeq (cat:opps (cat:dffr (cdelta 4)))))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 2}\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:gnrt-? (cat:dffr (cat:rbcc hmeq)) 3 '(0 1 2 3))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2.5.1 Representation of a combination in a bicone"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<2 * <BcnB B1>>\n",
+       "<4 * <BcnB B1>>\n",
+       "<6 * <BcnB B3>>\n",
+       "<3 * <BcnB C1>>\n",
+       "<5 * <BcnB C1>>\n",
+       "<7 * <BcnB D1>>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def comb-bic (cat:cmbn 3 2 (cat:bcnb 'b1) 4 (cat:bcnb 'b1) 6 (cat:bcnb 'b3)\n",
+    "                              3 (cat:bcnb 'c1) 5 (cat:bcnb 'c1) 7 (cat:bcnb 'd1)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((2 . <BcnB B1>) (4 . <BcnB B1>) (6 . <BcnB B3>) (3 . <BcnB C1>) (5 . <BcnB C1>) (7 . <BcnB D1>))"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:cmbn-list comb-bic)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2.5.2 Useful functions and macros for bicones\n",
+    "#### Examples"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<2 * B1>\n",
+       "<4 * B2>\n",
+       "<6 * B3>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def comb-b (cat:cmbn 3 2 'b1 4 'b2 6 'b3))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 4}\n",
+       "<3 * C1>\n",
+       "<5 * C2>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def comb-c (cat:cmbn 4 3 'c1 5 'c2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<7 * D1>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def comb-d (cat:cmbn 3 7 'd1))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<2 * <BcnB B1>>\n",
+       "<4 * <BcnB B2>>\n",
+       "<6 * <BcnB B3>>\n",
+       "<3 * <BcnC C1>>\n",
+       "<5 * <BcnC C2>>\n",
+       "<7 * <BcnD D1>>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def comb-bic (cat:make-bicn-cmbn comb-b comb-c comb-d))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<2 * B1>\n",
+       "<4 * B2>\n",
+       "<6 * B3>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:bicn-cmbn-cmbnb comb-bic)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 4}\n",
+       "<3 * C1>\n",
+       "<5 * C2>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 33,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:bicn-cmbn-cmbnc comb-bic)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<7 * D1>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:bicn-cmbn-cmbnd comb-bic)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<2 * B1>\n",
+       "<4 * B2>\n",
+       "<6 * B3>\n",
+       "------------------------------------------------------------------------------\n",
+       " \n",
+       "----------------------------------------------------------------------{CMBN 4}\n",
+       "<3 * C1>\n",
+       "<5 * C2>\n",
+       "------------------------------------------------------------------------------\n",
+       " \n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<7 * D1>\n",
+       "------------------------------------------------------------------------------\n",
+       ")"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(multiple-value-bind (b c d)\n",
+    "    (cat:dispatch-bicn-cmbn comb-bic)\n",
+    "    (list b c d))"
+   ]
   }
  ],
  "metadata": {