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

<b>let </b><font color="Maroon">S</font> be  <a href="yellow_0.html#V2">upper-bounded</a> <a href="waybel_0.html#NM6">Semilattice</a>, <font color="Maroon">T</font> be  <a href="yellow_0.html#V2">upper-bounded</a> <a href="waybel_0.html#NM6">Semilattice</a>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="waybel21.html#M1" target="_self">SemilatticeHomomorphism</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/>



<a NAME="E1:4"/>
( <font color="Maroon">f</font> <a href="waybel_0.html#R3">preserves_inf_of</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">S</font> &amp;  <a href="yellow_0.html#R2">ex_inf_of</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">S</font>,<font color="Maroon">S</font> )
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T43">YELLOW_0:43</a></i>;<br/>
<a NAME="E2:4"/><b>then </b>
<font color="Maroon">f</font> <a href="yellow_6.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">S</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">S</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_0.html#D30">WAYBEL_0:def 30</a></i>;<br/>
<b>hence </b><a NAME="E3:4"/>
<font color="Maroon">f</font> <a href="yellow_6.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K4">Top</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T149">RELAT_1:149</a></i>;<br/>


</div>
