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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="E1:21"/><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/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means  <a href="catalan1.html#K1" target="_self">Catalan</a> <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0;<br/>
<a NAME="E2:21"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[1]
 
<b>by </b><i><a class="ref" href="catalan1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E3:21"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1]
 
<b>by </b><i><a class="ref" href="catalan1.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E4:21"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="binarith.html#S1">BINARITH:sch 1</a>(<a class="txt" href="catalan1.html#E2:21"><i><font color="Green">E21</font></i></a>, <a class="txt" href="catalan1.html#E3:21"><i><font color="Green">E22</font></i></a>);<br/></i>
<a NAME="E5:21"/>
<font color="Maroon">c<sub>1</sub></font> is  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a>
 
<b>by </b><i><a class="txt" href="catalan1.html#E1:21"><i><font color="Green">E20</font></i></a>, <a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E6:21"/>
 <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="txt" href="catalan1.html#E4:21"><i><font color="Green">E23</font></i></a></i>;<br/>


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