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<span class="kw">take </span>
 <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">thus </span><a NAME="E1:87_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:87_1_1"/>
(  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  is  <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">limit_ordinal</a>  &amp;  <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" target="_self" title="ORDINAL1:def.12">Def12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:87_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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#T41" target="_self" title="ORDINAL1:th.41">Th41</a></span>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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