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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>;<br/><b>let </b><font color="Maroon" title="c6">P</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>;<br/><b>let </b><font color="Maroon" title="c7">Q</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>;<br/><b>let </b><font color="Maroon" title="c8">R</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:99"/><i><font color="Green" title="E79">A1</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <b>and </b><br/><a NAME="E2:99"/><i><font color="Green" title="E80">A2</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <b>and </b><br/><a NAME="E3:99"/><i><font color="Green" title="E81">A3</font></i>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 ;<br/>

<a NAME="E4:99"/><i><font color="Green" title="E82">A4</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E1:99"><i><font color="Green" title="E79">A1</font></i></a>, <a class="txt" href="borsuk_6.html#E2:99"><i><font color="Green" title="E80">A2</font></i></a>, <a class="ref" href="borsuk_6.html#T46" target="_self" title="BORSUK_6:th.46">Th46</a></i>;<br/>
<a NAME="E5:99"/>
 <a href="borsuk_6.html#K2" title="BORSUK_6:func.2">RePar</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">P</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c7">Q</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c8">R</font></span>)</span>,<a href="borsuk_6.html#K5" title="BORSUK_6:func.5">3RP</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">P</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">Q</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c8">R</font></span>)</span>
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E1:99"><i><font color="Green" title="E79">A1</font></i></a>, <a class="txt" href="borsuk_6.html#E2:99"><i><font color="Green" title="E80">A2</font></i></a>, <a class="txt" href="borsuk_6.html#E3:99"><i><font color="Green" title="E81">A3</font></i></a>, <a class="ref" href="borsuk_6.html#T60" target="_self" title="BORSUK_6:th.60">Th60</a></i>;<br/>
<b>hence </b><a NAME="E6:99"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">P</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c7">Q</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c8">R</font>,<font color="Maroon" title="c6">P</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">Q</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c8">R</font></span>)</span> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 <b>by </b><i><a class="txt" href="borsuk_6.html#E3:99"><i><font color="Green" title="E81">A3</font></i></a>, <a class="txt" href="borsuk_6.html#E4:99"><i><font color="Green" title="E82">A4</font></i></a>, <a class="ref" href="borsuk_6.html#T46" target="_self" title="BORSUK_6:th.46">Th46</a>, <a class="ref" href="borsuk_6.html#T53" target="_self" title="BORSUK_6:th.53">Th53</a>, <a class="ref" href="borsuk_6.html#T57" target="_self" title="BORSUK_6:th.57">Th57</a></i>;<br/>


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