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

<span class="kw">take </span>
<a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1
; <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 <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  &amp; <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>  &amp; <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="counters.html#V4" title="COUNTERS:attr.4">with_cardinal_domain</a>  &amp; <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="valued_0.html#V4" title="VALUED_0:attr.4">natural-valued</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:122_3_1"/>
(  not <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  &amp; <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>  &amp; <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="counters.html#V4" title="COUNTERS:attr.4">with_cardinal_domain</a>  &amp; <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> 1 is  <a href="valued_0.html#V4" title="VALUED_0:attr.4">natural-valued</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"> verum</span><br/>


</div>
