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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>given </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <a href="borsuk_1.html#K20">I[01]</a> ,<font color="Maroon">c<sub>4</sub></font><b> such that </b><a NAME="E1:19"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>10</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E3:19"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D1">BORSUK_2:def 1</a><br/>

<b>given </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <a href="borsuk_1.html#K20">I[01]</a> ,<font color="Maroon">c<sub>5</sub></font><b> such that </b><a NAME="E4:19"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>11</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 <b>and </b><br/><a NAME="E5:19"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>and </b><br/><a NAME="E6:19"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D1">BORSUK_2:def 1</a><br/>

<b>take </b>
<span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D1">BORSUK_2:def 1</a><br/>

<b>thus </b><a NAME="E7:19"/>
<span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</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="txt" href="topalg_4.html#E1:19"><i><font color="Green">E18</font></i></a>, <a class="txt" href="topalg_4.html#E4:19"><i><font color="Green">E21</font></i></a>, <a class="ref" href="yellow12.html#T41">YELLOW12:41</a></i>;<br/>

<a NAME="E8:19"/><i><font color="Green">E24</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>  &amp;  <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/>
<b>hence </b><span class="p1"><a href="topalg_4.html#K3" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="funct_1.html#K1">.</a> 0 = 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="ref" href="funct_3.html#T69">FUNCT_3:69</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#E2:19"><i><font color="Green">E19</font></i></a>, <a class="txt" href="topalg_4.html#E5:19"><i><font color="Green">E22</font></i></a></i>
;<br/><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>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="topalg_4.html#K3" target="_self">:&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 = 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="borsuk_1.html#K7">]</a></span>
<b>by </b><i><a class="txt" href="topalg_4.html#E8:19"><i><font color="Green">E24</font></i></a>, <a class="ref" href="funct_3.html#T69">FUNCT_3:69</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#E3:19"><i><font color="Green">E20</font></i></a>, <a class="txt" href="topalg_4.html#E6:19"><i><font color="Green">E23</font></i></a></i>
;<br/>


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