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<div><span class="kw">theorem </span><a NAME="T21"><span class="comment"><font color="firebrick">:: WAYBEL_5:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</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> holds <br/> ( <font color="Olive" title="b1">L</font> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  iff  for <font color="Olive" title="b2">J</font>, <font color="Olive" title="b3">K</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b2">J</font>,<font color="Olive" title="b3">K</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">L</font>  st (  for <font color="Olive" title="b5">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">J</font> holds   <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_5.html#K6" title="WAYBEL_5:func.6">curry</a> <font color="Olive" title="b4">F</font></span>)</span> <a href="waybel_5.html#K1" title="WAYBEL_5:func.1">.</a> <font color="Olive" title="b5">j</font></span>)</span> is  <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  ) holds <br/> <a href="yellow_2.html#NK7" title="YELLOW_2:NK.7">Inf</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_2.html#NK6" title="YELLOW_2:NK.6">Sup</a>  ) <span class="kw">by</span> <span class="lab"><a class="txt" href="waybel_5.html#E27"><span class="lab"><font color="Green" title="E21">Lm8</font></span></a>, <a class="txt" href="waybel_5.html#E32"><span class="lab"><font color="Green" title="E25">Lm10</font></span></a></span>;<br/></div></div>
