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<b>let </b><font color="Maroon">c<sub>7</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>7</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>16</sub></font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>17</sub></font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>18</sub></font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>;<br/>













<b>assume </b><b>that </b><br/><a NAME="E1:66"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="borsuk_6.html#R1">are_connected</a> 
 <b>and </b><br/><a NAME="E2:66"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="borsuk_6.html#R1">are_connected</a> 
 <b>and </b><br/><a NAME="E3:66"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="borsuk_6.html#R1">are_connected</a> 
 <b>and </b><br/><a NAME="E4:66"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="borsuk_6.html#R1">are_connected</a> 
 <b>and </b><br/><a NAME="E5:66"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="borsuk_6.html#R1">are_connected</a> 
 ;<br/>

<a NAME="E6:66"/>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="borsuk_6.html#R1">are_connected</a> 
 
<b>by </b><i><a class="txt" href="jordan.html#E1:66"><i><font color="Green">E44</font></i></a>, <a class="txt" href="jordan.html#E2:66"><i><font color="Green">E45</font></i></a>, <a class="ref" href="borsuk_6.html#T46">BORSUK_6:46</a></i>;<br/>
<a NAME="E7:66"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="borsuk_6.html#R1">are_connected</a> 
 
<b>by </b><i><a class="txt" href="jordan.html#E3:66"><i><font color="Green">E46</font></i></a>, <a class="ref" href="borsuk_6.html#T46">BORSUK_6:46</a></i>;<br/>
<a NAME="E8:66"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="borsuk_6.html#R1">are_connected</a> 
 
<b>by </b><i><a class="txt" href="jordan.html#E4:66"><i><font color="Green">E47</font></i></a>, <a class="ref" href="borsuk_6.html#T46">BORSUK_6:46</a></i>;<br/>
<b>hence </b> <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E5:66"><i><font color="Green">E48</font></i></a>, <a class="ref" href="jordan.html#T37" target="_self">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p4">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E1:66"><i><font color="Green">E44</font></i></a>, <a class="txt" href="jordan.html#E2:66"><i><font color="Green">E45</font></i></a>, <a class="txt" href="jordan.html#E3:66"><i><font color="Green">E46</font></i></a>, <a class="txt" href="jordan.html#E4:66"><i><font color="Green">E47</font></i></a>, <a class="txt" href="jordan.html#E50"><i><font color="Green">Lemma41</font></i></a></i>
;<br/><br/>


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