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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> : ( <font color="Olive">b<sub>1</sub></font> is <a href="funct_2.html#V2">onto</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="stirl2_1.html#V1" target="_self">"increasing</a> ) </span>}</span> ;<br/>
<a NAME="E1:31"/>
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> : ( <font color="Olive">b<sub>1</sub></font> is <a href="funct_2.html#V2">onto</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="stirl2_1.html#V1" target="_self">"increasing</a> ) </span>}</span>  is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="stirl2_1.html#T24" target="_self">Th24</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:31"/><i><font color="Green">E19</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> : ( <font color="Olive">b<sub>1</sub></font> is <a href="funct_2.html#V2">onto</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="stirl2_1.html#V1" target="_self">"increasing</a> ) </span>}</span> ,<font color="Maroon">c<sub>4</sub></font> <a href="wellord2.html#R2">are_equipotent</a> 
 <b>by </b><i><a class="ref" href="card_1.html#T74">CARD_1:74</a></i>;<br/>
<a NAME="E4:31"/>
(  <a href="card_1.html#K1">Card</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> : ( <font color="Olive">b<sub>1</sub></font> is <a href="funct_2.html#V2">onto</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="stirl2_1.html#V1" target="_self">"increasing</a> ) </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="stirl2_1.html#E3:31"><i><font color="Green">E19</font></i></a>, <a class="ref" href="card_1.html#T21">CARD_1:21</a>, <a class="ref" href="card_1.html#T66">CARD_1:66</a></i>;<br/>
<b>hence </b><a NAME="E5:31"/>
 <a href="card_1.html#K1">Card</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> : ( <font color="Olive">b<sub>1</sub></font> is <a href="funct_2.html#V2">onto</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="stirl2_1.html#V1" target="_self">"increasing</a> ) </span>}</span>  is   <a href="nat_1.html#NM1">Nat</a>
 ;<br/>


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