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<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</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>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>5</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> be    <a href="borsuk_2.html#M1">Path</a> of <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="borsuk_1.html#K7">]</a></span>,<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="borsuk_1.html#K7">]</a></span>;<br/><b>let </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</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>16</sub></font> be    <a href="borsuk_6.html#M1">Homotopy</a> of <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>17</sub></font> be    <a href="borsuk_6.html#M1">Homotopy</a> of <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>;<br/>























<b>assume </b><b>that </b><br/><a NAME="E1:32"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="funct_2.html#R2">=</a>  <a href="topalg_4.html#K4" target="_self">pr1</a> <font color="Maroon">c<sub>10</sub></font>
 <b>and </b><br/><a NAME="E2:32"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#R2">=</a>  <a href="topalg_4.html#K4" target="_self">pr1</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E3:32"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="funct_2.html#R2">=</a>  <a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">c<sub>10</sub></font>
 <b>and </b><br/><a NAME="E4:32"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#R2">=</a>  <a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E5:32"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 <b>and </b><br/><a NAME="E6:32"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 ;<br/>

<b>set </b><font color="Maroon">c<sub>18</sub></font> = <span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span>;<br/>
<a NAME="E7:32"/>
( <font color="Maroon">c<sub>16</sub></font> is <a href="pre_topc.html#V5">continuous</a> &amp; <font color="Maroon">c<sub>17</sub></font> is <a href="pre_topc.html#V5">continuous</a> )
 
<b>by </b><i><a class="txt" href="topalg_4.html#E5:32"><i><font color="Green">E28</font></i></a>, <a class="txt" href="topalg_4.html#E6:32"><i><font color="Green">E29</font></i></a>, <a class="ref" href="borsuk_6.html#D13">BORSUK_6:def 13</a></i>;<br/>
<b>hence </b><a NAME="E8:32"/>
<span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="yellow12.html#T41">YELLOW12:41</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>19</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="borsuk_1.html#K20">I[01]</a> ;<br/>

<a NAME="E9:32"/><i><font color="Green">E30</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><a href="borsuk_1.html#K20">I[01]</a> ,<a href="borsuk_1.html#K20">I[01]</a> </span><a href="borsuk_1.html#K5">:]</a></span> &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><a href="borsuk_1.html#K20">I[01]</a> ,<a href="borsuk_1.html#K20">I[01]</a> </span><a href="borsuk_1.html#K5">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E10:32"/><i><font color="Green">E31</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E11:32"/><i><font color="Green">E32</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="borsuk_1.html#K20">I[01]</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:32"/><i><font color="Green">E33</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D5">BORSUK_1:def 5</a></i>;<br/>
<b>thus </b><span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,0 = 
<span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span>

<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E9:32"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_3.html#T69">FUNCT_3:69</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topalg_4.html#K4" target="_self">pr1</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E1:32"><i><font color="Green">E24</font></i></a>, <a class="txt" href="topalg_4.html#E5:32"><i><font color="Green">E28</font></i></a>, <a class="ref" href="borsuk_6.html#D13">BORSUK_6:def 13</a></i>
<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topalg_4.html#K4" target="_self">pr1</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E3:32"><i><font color="Green">E26</font></i></a>, <a class="txt" href="topalg_4.html#E6:32"><i><font color="Green">E29</font></i></a>, <a class="ref" href="borsuk_6.html#D13">BORSUK_6:def 13</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E10:32"><i><font color="Green">E31</font></i></a>, <a class="ref" href="mcart_1.html#D12">MCART_1:def 12</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E10:32"><i><font color="Green">E31</font></i></a>, <a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="txt" href="topalg_4.html#E12:32"><i><font color="Green">E33</font></i></a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>
;<br/>

<b>thus </b><span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,1 = 
<span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="borsuk_1.html#K7">]</a></span>

<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E9:32"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_3.html#T69">FUNCT_3:69</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topalg_4.html#K4" target="_self">pr1</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E2:32"><i><font color="Green">E25</font></i></a>, <a class="txt" href="topalg_4.html#E5:32"><i><font color="Green">E28</font></i></a>, <a class="ref" href="borsuk_6.html#D13">BORSUK_6:def 13</a></i>
<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topalg_4.html#K4" target="_self">pr1</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E4:32"><i><font color="Green">E27</font></i></a>, <a class="txt" href="topalg_4.html#E6:32"><i><font color="Green">E29</font></i></a>, <a class="ref" href="borsuk_6.html#D13">BORSUK_6:def 13</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E11:32"><i><font color="Green">E32</font></i></a>, <a class="ref" href="mcart_1.html#D12">MCART_1:def 12</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E11:32"><i><font color="Green">E32</font></i></a>, <a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="txt" href="topalg_4.html#E12:32"><i><font color="Green">E33</font></i></a>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>
;<br/>

<b>let </b><font color="Maroon">c<sub>20</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="borsuk_1.html#K20">I[01]</a> ;<br/>

<b>thus </b><span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="binop_1.html#K1">.</a> 0,<font color="Maroon">c<sub>20</sub></font> = 
<span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="borsuk_1.html#K7">]</a></span>

<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E9:32"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_3.html#T69">FUNCT_3:69</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E5:32"><i><font color="Green">E28</font></i></a>, <a class="ref" href="borsuk_6.html#D13">BORSUK_6:def 13</a></i>
<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E6:32"><i><font color="Green">E29</font></i></a>, <a class="ref" href="borsuk_6.html#D13">BORSUK_6:def 13</a></i>
;<br/>

<b>thus </b><span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="binop_1.html#K1">.</a> 1,<font color="Maroon">c<sub>20</sub></font> = 
<span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="borsuk_1.html#K7">]</a></span>

<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E9:32"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_3.html#T69">FUNCT_3:69</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>20</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>

<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E5:32"><i><font color="Green">E28</font></i></a>, <a class="ref" href="borsuk_6.html#D13">BORSUK_6:def 13</a></i>
<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E6:32"><i><font color="Green">E29</font></i></a>, <a class="ref" href="borsuk_6.html#D13">BORSUK_6:def 13</a></i>
;<br/>


</div>
