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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a> <a href="waybel_0.html#NM6" title="WAYBEL_0:NM.6">Semilattice</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be    <a href="waybel21.html#M1" title="WAYBEL21:mode.1">SemilatticeHomomorphism</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>;<br/>



<a NAME="E1:4"/>
( <font color="Maroon" title="c3">f</font> <a href="waybel_0.html#R3" title="WAYBEL_0:pred.3">preserves_inf_of</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">S</font> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font> )
 
<b>by </b><i><a class="ref" href="waybel21.html#D1" target="_self" title="WAYBEL21:def.1">Def1</a>, <a class="ref" href="yellow_0.html#T43" title="YELLOW_0:th.43">YELLOW_0:43</a></i>;<br/>
<a NAME="E2:4"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p2">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p2">(<span class="default"><a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_0.html#D30" title="WAYBEL_0:def.30">WAYBEL_0:def 30</a></i>;<br/>
<b>hence </b><a NAME="E3:4"/>
<font color="Maroon" title="c3">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T149" title="RELAT_1:th.149">RELAT_1:149</a></i>;<br/>


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