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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: CATALAN2:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b1">p</font> is  <a href="catalan2.html#V1" title="CATALAN2:attr.1">dominated_by_0</a>  holds <br/>( <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="catalan2.html#K1" title="CATALAN2:func.1">^</a> <font color="Olive" title="b1">p</font> is  <a href="catalan2.html#V1" title="CATALAN2:attr.1">dominated_by_0</a>  &amp; <span class="p1"> { <span class="default"> <font color="Olive" title="b2">N</font> where <font color="Olive" title="b2">N</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : ( 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="catalan2.html#K1" title="CATALAN2:func.1">^</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b2">N</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b2">N</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</div></div>
