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

<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#V6" target="_self">join-inheriting</a>  <a href="yellow_0.html#M1" target="_self">SubRelStr</a> of <font color="Maroon">L</font>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="93_1_1_1"><b>now </b></a><div class="add"><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>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font>, <font color="Maroon">b</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i><a class="ref" href="yellow_0.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E2:93_1_1_1"/><i><font color="Green">E24</font></i>: 
 <a href="yellow_0.html#R1" target="_self">ex_sup_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="E3:93_1_1_1"/><b>then </b>
 <a href="yellow_0.html#K1" target="_self">"\/"</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> <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#T8" target="_self">Th8</a></i>;<br/><b>hence </b><a NAME="E4:93_1_1_1"/>
 <a href="yellow_0.html#R1" target="_self">ex_sup_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>
 <b>by </b><i><a class="ref" href="yellow_0.html#T11" target="_self">Th11</a>, <a class="ref" href="yellow_0.html#T10" target="_self">Th10</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:93_1_1"/>
<font color="Maroon">S</font> is <a href="lattice3.html#V1">with_suprema</a>
 <b>by </b><i/>;<br/>


</div>
