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<b>let </b><font color="Maroon" title="c1">X</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> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:24"/><i><font color="Green" title="E19">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="E2:24"/><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 ;<br/>

<b>let </b><font color="Maroon" title="c5">A1</font>, <font color="Maroon" title="c6">A2</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">B</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="c2">a</font>;<br/>



<b>consider </b><font color="Maroon" title="c8">X</font> being  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  <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="c2">a</font>;<br/>
<b>assume </b><a NAME="E4:24"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c5">A1</font>,<font color="Maroon" title="c6">A2</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 ;<br/>

<a NAME="E5:24"/>
<span class="p1">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c8">X</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_1.html#E2:24"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="borsuk_6.html#T94" title="BORSUK_6:th.94">BORSUK_6:94</a></i>;<br/>
<a NAME="E6:24"/><b>then </b><i><font color="Green" title="E22">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c6">A2</font>,<font color="Maroon" title="c8">X</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c5">A1</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_1.html#E1:24"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="topalg_1.html#E4:24"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="borsuk_6.html#T83" title="BORSUK_6:th.83">BORSUK_6:83</a></i>;<br/>
<a NAME="E7:24"/>
<font color="Maroon" title="c5">A1</font>,<font color="Maroon" title="c8">X</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c5">A1</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<b>by </b><i><a class="txt" href="topalg_1.html#E1:24"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="borsuk_6.html#T90" title="BORSUK_6:th.90">BORSUK_6:90</a></i>;<br/>
<b>hence </b><a NAME="E8:24"/>
<font color="Maroon" title="c5">A1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c6">A2</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 <b>by </b><i><a class="txt" href="topalg_1.html#E6:24"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="borsuk_6.html#T87" title="BORSUK_6:th.87">BORSUK_6:87</a></i>;<br/>


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