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<b>let </b><font color="Maroon">N</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">r1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">r2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">w1</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">N</font></span>)</span>;<br/><b>let </b><font color="Maroon">w2</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">N</font></span>)</span>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:42"/><i><font color="Green">E44</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r1</font>
 <b>and </b><br/><a NAME="E2:42"/><i><font color="Green">E45</font></i>: 
<span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w1</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w2</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span>
 <b>and </b><br/><a NAME="E3:42"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">r1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">r2</font>
 ;<br/>

<a NAME="E4:42"/><i><font color="Green">E50</font></i>: 
<span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w1</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="real_1.html#K4">*</a> <font color="Maroon">r2</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w2</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="real_1.html#K4">*</a> <font color="Maroon">r2</font>
 
<b>by </b><i>, , , <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E5:42"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w1</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E6:42"/><b>then </b>
<span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w1</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w1</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="real_1.html#K4">*</a> <font color="Maroon">r2</font>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<b>hence </b><a NAME="E7:42"/>
<span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w1</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="real_1.html#K4">*</a> <font color="Maroon">r1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1"><a href="toprns_1.html#K5" target="_self">|.</a><span class="default"><font color="Maroon">w2</font></span><a href="toprns_1.html#K5" target="_self">.|</a></span> <a href="real_1.html#K4">*</a> <font color="Maroon">r2</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>


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