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<b>let </b><font color="Maroon" title="c1">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="nat_lat.html#K11" title="NAT_LAT:func.11">NatPlus_Lattice</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> &amp; not <font color="Maroon" title="c1">x</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/>

<a NAME="E1:31_1_1"/>
<font color="Maroon" title="c1">x</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a> 
 
;<br/>
<b>hence </b><a NAME="E2:31_1_1"/>
<font color="Maroon" title="c1">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c1">x</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a></span><br/>

<b>thus </b><a NAME="E3:31_1_1"/>
not <font color="Maroon" title="c1">x</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="nat_lat.html#D9" target="_self" title="NAT_LAT:def.9">Def9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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