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<div><span class="kw">theorem </span><a NAME="T67"><span class="comment"><font color="firebrick">:: WAYBEL34:67</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>  st <font color="Olive" title="b2">T</font> is  <a href="waybel_8.html#V2" title="WAYBEL_8:attr.2">algebraic</a>  holds <br/> for <font color="Olive" title="b3">g</font> being   <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font> holds <br/> ( <font color="Olive" title="b3">g</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  iff <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Olive" title="b3">g</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Olive" title="b2">T</font></span>)</span> is   <a href="waybel34.html#V4" title="WAYBEL34:attr.4">finite-sups-preserving</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Olive" title="b2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <font color="Olive" title="b1">S</font></span>)</span> )</div></div>
