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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:23"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<a NAME="E2:23"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="catalan1.html#K1" target="_self">Catalan</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="catalan1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E3:23"/><i><font color="Green">E22</font></i>: 
 <a href="catalan1.html#K1" target="_self">Catalan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">3 <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="catalan1.html#K1" target="_self">Catalan</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="catalan1.html#E1:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="catalan1.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E4:23"/>
2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default">3 <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> 4
 
<b>by </b><i><a class="ref" href="catalan1.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E5:23"/>
 <a href="catalan1.html#K1" target="_self">Catalan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;</a> 4 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="catalan1.html#K1" target="_self">Catalan</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="catalan1.html#E2:23"><i><font color="Green">E21</font></i></a>, <a class="txt" href="catalan1.html#E3:23"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>


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