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<b>let </b><font color="Maroon">L</font> be  <a href="yellow_0.html#V2">upper-bounded</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span>)</span>;<br/><b>let </b><font color="Maroon">p</font> be  <a href="waybel_6.html#V5" target="_self">prime</a> <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:52"/>
 <a href="funct_3.html#K5">chi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="funct_2.html#R1">=</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E2:52"/><b>then </b>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  iff <font color="Olive">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">p</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:52"/>
( <font color="Maroon">f</font> is <a href="waybel_0.html#V19">meet-preserving</a> &amp; <font color="Maroon">f</font> is <a href="waybel_0.html#V20">join-preserving</a> )
 <b>by </b><i/>;<br/>


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