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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">A</font> being   <a href="kurato_2.html#M1" target="_self">subsequence</a> of <font color="Maroon">S</font> st <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="kurato_2.html#K8" target="_self">Lim_inf</a> <font color="Olive">A</font>;<br/>
<b>consider </b><font color="Maroon">X</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:85_1_1"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<a NAME="E3:85_1_1"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:85_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>hence </b><a NAME="E2:85_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="kurato_2.html#T4" target="_self">Th4</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">X</font> = <font color="Maroon">X</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> ;<br/>
<b>take </b>
<font color="Maroon">X</font>
;<br/>

<b>thus </b><a NAME="E5:85_1_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff  ex <font color="Olive">A</font> being   <a href="kurato_2.html#M1" target="_self">subsequence</a> of <font color="Maroon">S</font> st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="kurato_2.html#K8" target="_self">Lim_inf</a> <font color="Olive">A</font> )
 <b>by </b><i><a class="ref" href="kurato_2.html#T4" target="_self">Th4</a></i>;<br/>


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