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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E38">Th39</font></span>: <a NAME="T39"><span class="comment"><font color="firebrick">:: CATALAN2:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">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>  holds <br/> ex <font color="Olive" title="b2">Catal</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 <br/>(  <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Olive" title="b2">Catal</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalan1.html#K1" title="CATALAN1:func.1">Catalan</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b2">Catal</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n</font> &amp; (  for <font color="Olive" title="b3">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> holds <br/><font color="Olive" title="b2">Catal</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="catalan1.html#K1" title="CATALAN1:func.1">Catalan</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="catalan1.html#K1" title="CATALAN1:func.1">Catalan</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Olive" title="b3">j</font></span>)</span></span>)</span> ) )</div></div>
