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<b>let </b><font color="Maroon" title="c7">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c7">T</font>;<br/><b>let </b><font color="Maroon" title="c10">f</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>;<br/>





<b>assume </b><a NAME="E1:54"/><i><font color="Green" title="E35">A1</font></i>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 ;<br/>

<b>hence </b><a NAME="E2:54"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c10">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a> <font color="Maroon" title="c10">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan.html#E39"><i><font color="Green" title="E33">Lm9</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/>

<a NAME="E3:54"/>
<font color="Maroon" title="c10">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a> <span class="p1">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a> <font color="Maroon" title="c10">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan.html#E1:54"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="borsuk_6.html#T50" title="BORSUK_6:th.50">BORSUK_6:50</a></i>;<br/>
<b>hence </b><a NAME="E4:54"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c10">f</font>
 <b>by </b><i><a class="txt" href="jordan.html#E1:54"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="jordan.html#E39"><i><font color="Green" title="E33">Lm9</font></i></a></i>;<br/>


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