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<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c</font> be  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:59"/>
 <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c</font> is <a href="waybel_0.html#V4">directed-sups-inheriting</a>
 ;<br/>

<a NAME="E2:59"/><b>then </b>
(  <a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c</font> is <a href="waybel_0.html#V22">directed-sups-preserving</a> &amp;  <a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c</font> is <a href="waybel_0.html#V17">infs-preserving</a> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:59"/><b>then </b>
 <a href="waybel34.html#K1" target="_self">LowerAdj</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c</font></span>)</span> is <a href="waybel34.html#V1" target="_self">waybelow-preserving</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:59"/>
 <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c</font> is <a href="waybel34.html#V1" target="_self">waybelow-preserving</a>
 <b>by </b><i/>;<br/>


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