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<b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K5">:]</a></span>, <font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K5">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D3">BORSUK_2:def 3</a><br/>

<b>consider </b><font color="Maroon">a1</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>, <font color="Maroon">a2</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E2:23_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="ref" href="borsuk_1.html#T50">BORSUK_1:50</a></i>;<br/>
<b>consider </b><font color="Maroon">b1</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>, <font color="Maroon">b2</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E4:23_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="ref" href="borsuk_1.html#T50">BORSUK_1:50</a></i>;<br/>
<a NAME="E5:23_1_1"/>
( <font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="borsuk_6.html#R1">are_connected</a>  &amp; <font color="Maroon">a2</font>,<font color="Maroon">b2</font> <a href="borsuk_6.html#R1">are_connected</a>  )
 
<b>by </b><i><a class="ref" href="borsuk_2.html#D3">BORSUK_2:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:23_1_1"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="borsuk_2.html#R1">are_connected</a> 
 <b>by </b><i>, , </i>;<br/>


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