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

<b>let </b><font color="Maroon" title="c1">W</font> be  <a href="setfam_1.html#NV3" title="SETFAM_1:NV.3">with_non-empty_element</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<a NAME="E1:50"/><i><font color="Green" title="E20">A1</font></i>: 
 ex <font color="Olive" title="b1">w</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Olive" title="b1">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#D11" title="SETFAM_1:def.11">SETFAM_1:def 11</a></i>;<br/>
<b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:50"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font> <a href="yellow21.html#K6" title="YELLOW21:func.6">-UPS_category</a> </span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c2">x</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">W</font> <a href="yellow21.html#K6" title="YELLOW21:func.6">-UPS_category</a> </span>)</span> ;<br/>
<a NAME="E4:50"/>
 <a href="yellow21.html#K4" title="YELLOW21:func.4">latt</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font>
 
;<br/>
<a NAME="E5:50"/><b>then </b>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow21.html#K4" title="YELLOW21:func.4">latt</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> &amp; <font color="Maroon" title="c3">x</font> is  <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> )
 
<b>by </b><i><a class="txt" href="yellow21.html#E1:50"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="yellow21.html#D10" target="_self" title="YELLOW21:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E6:50"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow21.html#K2" title="YELLOW21:func.2">POSETS</a> <font color="Maroon" title="c1">W</font>
 <b>by </b><i><a class="ref" href="yellow21.html#D2" target="_self" title="YELLOW21:def.2">Def2</a></i>;<br/>


</div>
