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

<b>take </b>
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> )</span><br/>

<b>thus </b><a NAME="E1:76_1_1"/>
not  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a></span><br/>

<a NAME="E2:76_1_1"/><i><font color="Green" title="E36">A1</font></i>: 
 <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal1.html#NR2" title="ORDINAL1:NR.2">is_limit_ordinal</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D12" target="_self" title="ORDINAL1:def.12">Def12</a></i>;<br/>
<a NAME="E3:76_1_1"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" target="_self" title="ORDINAL1:def.13">Def13</a></i>;<br/>
<b>hence </b><a NAME="E4:76_1_1"/>
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a> 
 <b>by </b><i><a class="txt" href="ordinal1.html#E2:76_1_1"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="ordinal1.html#T41" target="_self" title="ORDINAL1:th.41">Th41</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ordinal1.html#D13" target="_self" title="ORDINAL1:def.13">ORDINAL1:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
