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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">p1</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>, <font color="Maroon">p2</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>, <font color="Maroon">q1</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>, <font color="Maroon">q2</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><a NAME="E1:16"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> &amp; <font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> )
 ;<br/>

<a NAME="E2:16"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">q1</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q1</font>,<font color="Maroon">p2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_1_1"/>
( <font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">q1</font> or <font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q1</font>,<font color="Maroon">p2</font> )
 </span><b>by </b><i>, , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_1"><b>suppose </b></a><a NAME="E1:16_1_1_1"/>
<font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">q1</font>
 ;<br/><div class="add"><a NAME="E2:16_1_1_1"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q2</font>,<font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">q1</font>
 <b>by </b><i/>;<br/><a NAME="E3:16_1_1_1"/>
 <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">q1</font> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:16_1_1_1"/>
 <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_2"><b>suppose </b></a><a NAME="E1:16_1_1_2"/>
<font color="Maroon">q2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q1</font>,<font color="Maroon">p2</font>
 ;<br/><div class="add"><a NAME="E2:16_1_1_2"/><b>then </b><i><font color="Green">E50</font></i>: 
 <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q1</font>,<font color="Maroon">p2</font>
 <b>by </b><i/>;<br/><a NAME="E3:16_1_1_2"/>
 <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q1</font>,<font color="Maroon">p2</font> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:16_1_1_2"/>
 <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:16"/>
 <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K3" target="_self">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 ;<br/>


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