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

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="valued_2.html#D4" onmouseover="rs('valued_2/D4')" onmouseout="rh()">VALUED_2:def 4</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="toprealc.html#K2" title="TOPREALC:func.2">(-)</a> <font color="Maroon" title="c1">X</font> or <font color="Maroon" title="c2">x</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:45_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="toprealc.html#K2" title="TOPREALC:func.2">(-)</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c2">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="toprealc.html#K2" title="TOPREALC:func.2">(-)</a> <font color="Maroon" title="c1">X</font> ;<br/>
<a NAME="E3:45_1_1"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
 <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="toprealc.html#T24" target="_self" onmouseover="rs('toprealc/T24')" onmouseout="rh()">Th24</a></span>;<br/>
<a NAME="E4:45_1_1"/>
(  <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <span class="p1">(<span class="default"><a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> &amp;  <a href="toprealc.html#K2" title="TOPREALC:func.2">(-)</a> <span class="p1">(<span class="default"><a href="toprealc.html#K2" title="TOPREALC:func.2">(-)</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E5:45_1_1"/>
<font color="Maroon" title="c2">x</font> is    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:45_1_1"><span class="lab"><font color="Green" title="E16">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
