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<b>assume </b><a NAME="E1:3_1_1"/><i><font color="Green">E36</font></i>: 
 <a href="finseq_5.html#K3">Rev</a> <font color="Maroon">p</font> is <a href="realset1.html#V1">trivial</a>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_1_1_1"/>
(  <a href="finseq_5.html#K3">Rev</a> <font color="Maroon">p</font> is <a href="xboole_0.html#V1">empty</a> or  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st  <a href="finseq_5.html#K3">Rev</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Olive">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span> )
 </span><b>by </b><i>, </i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1"><b>suppose </b></a><a NAME="E1:3_1_1_1_1"/>
 <a href="finseq_5.html#K3">Rev</a> <font color="Maroon">p</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:3_1_1_1_1"/>
contradiction
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_2"><b>suppose </b></a><a NAME="E1:3_1_1_1_2"/>
 ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st  <a href="finseq_5.html#K3">Rev</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Olive">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:3_1_1_1_2"/><i><font color="Green">E39</font></i>: 
 <a href="finseq_5.html#K3">Rev</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
 ;<br/><font color="Maroon">p</font> = 
 <a href="finseq_5.html#K3">Rev</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="finseq_6.html#T29">FINSEQ_6:29</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">x</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_5.html#T63">FINSEQ_5:63</a></i>
;<br/><b>hence </b><a NAME="E5:3_1_1_1_2"/>
contradiction
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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