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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: OPENLATT:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">H</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="lattice2.html#NM2" title="LATTICE2:NM.2">H_Lattice</a> holds   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" title="OPENLATT:func.6">Open_setLatt</a> <span class="p2">(<span class="default"><a href="openlatt.html#K17" title="OPENLATT:func.17">HTopSpace</a> <font color="Olive" title="b1">H</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">A</font></span>)</span> where <font color="Olive" title="b2">A</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K9" title="OPENLATT:func.9">StoneS</a> <font color="Olive" title="b1">H</font></span>)</span> : verum </span> } </span>  <span class="kw">by</span> <span class="lab"><a class="ref" href="openlatt.html#D12" target="_self" onmouseover="rs('openlatt/D12')" onmouseout="rh()">Def12</a></span>;<br/></div></div>
