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<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:41"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>, <font color="Maroon">y</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">x</font>,<font color="Maroon">y</font>, <font color="Maroon">Q</font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">x</font>,<font color="Maroon">y</font>;<br/>



<a NAME="E2:41"/>
 <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> is <a href="topalg_2.html#V3" target="_self">convex</a>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:41"/>
<font color="Maroon">P</font>,<font color="Maroon">Q</font> <a href="borsuk_2.html#R3">are_homotopic</a> 
 <b>by </b><i/>;<br/>


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