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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th16</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: LATTICE8:16</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</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="b2">O</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive" title="b3">T</font> being   <a href="ordinal1.html#NM4" title="ORDINAL1:NM.4">Sequence</a>  st <font color="Olive" title="b2">O</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">O</font> is  <a href="ordinal1.html#V4" title="ORDINAL1:attr.4">limit_ordinal</a>  &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">O</font> &amp; (  for <font color="Olive" title="b4">O1</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b4">O1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">O</font> holds <br/><font color="Olive" title="b3">T</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">O1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice8.html#K3" title="LATTICE8:func.3">ConsecutiveSet2</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b4">O1</font>) ) holds <br/> <a href="lattice8.html#K3" title="LATTICE8:func.3">ConsecutiveSet2</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">O</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">T</font></span>)</span></div></div>
