<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">S</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">T</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">s1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">s2</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">t1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">t2</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>











<b>assume </b><a NAME="E1:18"/><i><font color="Green">E39</font></i>: 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s1</font>,<font color="Maroon">t1</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">s2</font>,<font color="Maroon">t2</font></span><a href="borsuk_1.html#K7">]</a></span> <a href="borsuk_6.html#R1">are_connected</a> 
 ;<br/>

<b>let </b><font color="Maroon">L</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">s1</font>,<font color="Maroon">t1</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">s2</font>,<font color="Maroon">t2</font></span><a href="borsuk_1.html#K7">]</a></span>;<br/>

<b>set </b><font color="Maroon">f</font> =  <a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">L</font>;<br/>
<a NAME="E2:18"/><i><font color="Green">E40</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">L</font></span>)</span> <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="E3:18"/>
<font color="Maroon">L</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i>, <a class="ref" href="borsuk_2.html#D2">BORSUK_2:def 2</a></i>;<br/>
<a NAME="E4:18"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">L</font> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i/>;<br/>
<a NAME="E5:18"/><i><font color="Green">E43</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>;<br/>
<a NAME="E6:18"/><b>then </b>
<font color="Maroon">j0</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<b>then </b><i><font color="Green">E44</font></i>: <span class="p1">(<span class="default"><a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> 0 = 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="funct_1.html#K1">.</a> 0</span>)</span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s1</font>,<font color="Maroon">t1</font></span><a href="borsuk_1.html#K7">]</a></span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i>, <a class="ref" href="borsuk_2.html#D2">BORSUK_2:def 2</a></i>
<br/>.= 
<font color="Maroon">t1</font>
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>
;<br/>
<a NAME="E8:18"/>
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">L</font>
 
<b>by </b><i>, </i>;<br/>
<b>then </b><i><font color="Green">E47</font></i>: <span class="p1">(<span class="default"><a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="funct_1.html#K1">.</a> 1</span>)</span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s2</font>,<font color="Maroon">t2</font></span><a href="borsuk_1.html#K7">]</a></span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i>, <a class="ref" href="borsuk_2.html#D2">BORSUK_2:def 2</a></i>
<br/>.= 
<font color="Maroon">t2</font>
<b>by </b><i><a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>
;<br/>
<a NAME="E10:18"/><b>then </b>
<font color="Maroon">t1</font>,<font color="Maroon">t2</font> <a href="borsuk_6.html#R1">are_connected</a> 
 
<b>by </b><i>, , <a class="ref" href="borsuk_2.html#D1">BORSUK_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E11:18"/>
 <a href="topalg_4.html#K5" target="_self">pr2</a> <font color="Maroon">L</font> is    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">t1</font>,<font color="Maroon">t2</font>
 <b>by </b><i>, , , <a class="ref" href="borsuk_2.html#D2">BORSUK_2:def 2</a></i>;<br/>


</div>
