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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:52"/>
<font color="Maroon">X</font>,<font color="Maroon">Y</font> <a href="wellord2.html#R2">are_equipotent</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:52"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> )
 <b>by </b><i><a class="ref" href="wellord2.html#D4">WELLORD2:def 4</a></i>;<br/>
<b>given </b><font color="Maroon">p</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><a NAME="E4:52"/><i><font color="Green">E34</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 <b>and </b><br/><a NAME="E5:52"/><i><font color="Green">E42</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="finset_1.html#D1">FINSET_1:def 1</a><br/>

<b>take </b>
<font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="finset_1.html#D1">FINSET_1:def 1</a><br/>

<b>thus </b><a NAME="E6:52"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="card_1.html#D1" target="_self">Def1</a>, , <a class="ref" href="relat_1.html#T47">RELAT_1:47</a></i>;<br/>

<b>thus </b><a NAME="E7:52"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a> 
 <b>by </b><i><a class="ref" href="card_1.html#D1" target="_self">Def1</a>, , , <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>


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