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<b>let </b><font color="Maroon">p</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> 2</span>)</span>;<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> 2</span>)</span>;<br/><b>let </b><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> 2</span>)</span>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:35"/><i><font color="Green">E42</font></i>: 
not <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 <b>and </b><br/><a NAME="E2:35"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">p1</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">p2</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:35_1"/>
( <font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a>  or <font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1"><b>suppose </b></a><a NAME="E1:35_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:35_1_1_1_1"/>
( <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a>  or <font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  )
 </span><b>by </b><i>, , <a class="ref" href="goboard7.html#T8">GOBOARD7:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:35_1_1_1_1_1"/>
<font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:35_1_1_1_1_1"/>
( <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="goboard7.html#T8">GOBOARD7:8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:35_1_1_1_1_2"/>
<font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:35_1_1_1_1_2"/>
( <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="goboard7.html#T8">GOBOARD7:8</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:35_1_1"/>
( <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p1</font> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_2"><b>suppose </b></a><a NAME="E1:35_1_2"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:35_1_2_1_1"/>
( <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a>  or <font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  )
 </span><b>by </b><i>, , <a class="ref" href="goboard7.html#T8">GOBOARD7:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:35_1_2_1_1_1"/>
<font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p2</font> <a href="euclid.html#K22">`2</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:35_1_2_1_1_1"/>
( <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="goboard7.html#T8">GOBOARD7:8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="35_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:35_1_2_1_1_2"/>
<font color="Maroon">p1</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:35_1_2_1_1_2"/>
( <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p1</font> )
 <b>by </b><i>, , <a class="ref" href="goboard7.html#T8">GOBOARD7:8</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:35_1_2"/>
( <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p2</font> or <font color="Maroon">p2</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p1</font> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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