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

<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V2">with_infima</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V4" target="_self">full</a> <a href="yellow_0.html#V5" target="_self">meet-inheriting</a>  <a href="yellow_0.html#M1" target="_self">SubRelStr</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>







<b>assume </b><a NAME="E1:96"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 ;<br/>

<a NAME="E2:96"/><i><font color="Green">E29</font></i>: 
 <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:96"/><b>then </b>
 <a href="yellow_0.html#K2" target="_self">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T11" target="_self">Th11</a>, </i>;<br/>
<a NAME="E4:96"/><b>then </b>
(  <a href="yellow_0.html#R2" target="_self">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">S</font> &amp;  <a href="yellow_0.html#K2" target="_self">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K2" target="_self">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> &amp; <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="domain_1.html#K7">}</a></span> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T11" target="_self">Th11</a>, <a class="ref" href="yellow_0.html#T12" target="_self">Th12</a>, , <a class="ref" href="yellow_0.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E5:96"/>
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T11" target="_self">Th11</a>, </i>;<br/>


</div>
