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<b>consider </b><font color="Maroon">X</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>
<a NAME="E2:3_1_1"/><i><font color="Green">E59</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">X</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">X</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T56">FINSEQ_1:56</a></i>;<br/>
<a NAME="E3:3_1_1"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">X</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i><a class="ref" href="funct_7.html#T20">FUNCT_7:20</a></i>;<br/>
<a NAME="E4:3_1_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">X</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a> 
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">F</font> = <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">X</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="finseq_1.html#K9">*&gt;</a></span> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon">F</font>
;<br/>

<b>thus </b><a NAME="E6:3_1_1"/>
not <font color="Maroon">F</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>assume </b><a NAME="E7:3_1_1"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_1.html#D9">RELAT_1:def 9</a><br/>

<b>hence </b><a NAME="E8:3_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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