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<b>let </b><font color="Maroon">f1</font> be   <a href="card_3.html#NM1">Cardinal-Function</a>, <font color="Maroon">f2</font> be   <a href="card_3.html#NM1">Cardinal-Function</a>;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> &amp; <font color="Maroon">a<sub>1</sub></font> is   <a href="card_1.html#NM1">Cardinal</a> );<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:22_3_2"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] )
 <b>and </b><br/><a NAME="E2:22_3_2"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">K</font> being  <a href="card_1.html#NM1">Cardinal</a>  st <font color="Olive">K</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">K</font> <a href="hidden.html#R1">=</a>  <a href="card_2.html#K3">exp</a> <font color="Olive">K</font>,<font color="Maroon">N</font>
 <b>and </b><br/><a NAME="E3:22_3_2"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] )
 <b>and </b><br/><a NAME="E4:22_3_2"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">K</font> being  <a href="card_1.html#NM1">Cardinal</a>  st <font color="Olive">K</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> holds <br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">K</font> <a href="hidden.html#R1">=</a>  <a href="card_2.html#K3">exp</a> <font color="Olive">K</font>,<font color="Maroon">N</font>
 ;<br/>

<a NAME="E5:22_3_2"/><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font>
 
<b>from </b><i><a class="ref" href="xboole_0.html#S2">XBOOLE_0:sch 2</a>(, );<br/></i>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_3_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_3_2_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font>
 ;<br/><b>then reconsider </b><font color="Maroon">K</font> = <font color="Maroon">x</font> as   <a href="card_1.html#NM1">Cardinal</a> <b>by </b><i/>;<br/><a NAME="E3:22_3_2_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">K</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="card_2.html#K3">exp</a> <font color="Maroon">K</font>,<font color="Maroon">N</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="txt" href="card_5.html#E1"><i><font color="Green">Lemma22</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:22_3_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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