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

<span class="kw">let </span><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> &amp; 1 is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> &amp; 2 is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> )</span><br/>

<span class="kw">thus </span><a NAME="E1:47"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="classes2.html#T62" title="CLASSES2:th.62">CLASSES2:62</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( 1 is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> &amp; 2 is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> )</span><br/>

<a NAME="E2:47"/>
(  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> &amp; 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes2.html#T62" title="CLASSES2:th.62">CLASSES2:62</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:47"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
1 is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mod_2.html#T29" target="_self" title="MOD_2:th.29">Th29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 2 is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font></span><br/>

<a NAME="E4:47"/>
2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> 1
 
;<br/>
<span class="kw">hence </span><a NAME="E5:47"/>
2 is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="mod_2.html#T29" target="_self" title="MOD_2:th.29">Th29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
