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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<a NAME="E1:46"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">n</font></span>)</span> <a href="binop_2.html#K23">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> 2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">n</font></span>)</span> <a href="binop_2.html#K23">+</a> 2</span>)</span> <a href="binop_2.html#K10">-</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K10">-</a> 1 )
 
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E2:46"/><b>then </b>
( <span class="p1">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 2 <a href="hidden.html#R1">=</a> 2 <a href="binop_2.html#K24">*</a> <font color="Maroon">n</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="catalan1.html#K1">Catalan</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 2</span>)</span> <a href="newton.html#K9">choose</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> )
 
<b>by </b><i><a class="ref" href="catalan1.html#D1">CATALAN1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:46"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="catalan2.html#K2" target="_self">Domin_0</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="catalan1.html#K1">Catalan</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="binop_2.html#K23">+</a> 1</span>)</span>
 <b>by </b><i/>;<br/>


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