<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">M</font> = <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> : <font color="Olive">a</font> <a href="ideal_1.html#K10" target="_self">*</a> <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font> </span>}</span> ;<br/>
<a NAME="E1:137_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> : <font color="Olive">a</font> <a href="ideal_1.html#K10" target="_self">*</a> <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font> </span>}</span>  is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:137_1_1_1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> : <font color="Olive">a</font> <a href="ideal_1.html#K10" target="_self">*</a> <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font> </span>}</span>  holds <br/><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">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="137_1_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> ;<br/>

<b>assume </b><a NAME="E1:137_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> : <font color="Olive">a</font> <a href="ideal_1.html#K10" target="_self">*</a> <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:137_1_1_1_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="ideal_1.html#K10" target="_self">*</a> <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font> )
 ;<br/>
<b>thus </b><a NAME="E4:137_1_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">R</font>
 <b>by </b><i><a class="ref" href="ideal_1.html#D5" target="_self">Def5</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:137_1_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> : <font color="Olive">a</font> <a href="ideal_1.html#K10" target="_self">*</a> <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font> </span>}</span>  is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:137_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> : <font color="Olive">a</font> <a href="ideal_1.html#K10" target="_self">*</a> <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font> </span>}</span>  is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>
 ;<br/>


</div>
