<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: OPENLATT:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font><br/>  for <font color="Olive" title="b4">Z</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">Z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b4">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" title="OPENLATT:func.10">SF_have</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" title="OPENLATT:func.10">SF_have</a> <font color="Olive" title="b2">a</font></span>)</span> &amp; <font color="Olive" title="b4">Z</font> is  <a href="ordinal1.html#V6" title="ORDINAL1:attr.6">c=-linear</a>  holds <br/> ex <font color="Olive" title="b5">Y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>( <font color="Olive" title="b5">Y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" title="OPENLATT:func.10">SF_have</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="openlatt.html#K10" title="OPENLATT:func.10">SF_have</a> <font color="Olive" title="b2">a</font></span>)</span> &amp; (  for <font color="Olive" title="b6">X1</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b6">X1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">Z</font> holds <br/><font color="Olive" title="b6">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">Y</font> ) )</div></div>
