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<b>let </b><font color="Maroon">f</font> be  <a href="finset_1.html#V1">finite</a> <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:1"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<a NAME="E2:1"/><b>then </b>
 <a href="card_3.html#K3">Union</a> <font color="Maroon">f</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="card_4.html#T63">CARD_4:63</a></i>;<br/>
<a NAME="E3:1"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">f</font></span>)</span> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="fraenkel.html#T16">FRAENKEL:16</a></i>;<br/>
<a NAME="E4:1"/>
 <a href="card_3.html#K4">product</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_3.html#K3">Union</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_6.html#T10">FUNCT_6:10</a></i>;<br/>
<b>hence </b><a NAME="E5:1"/>
 <a href="card_3.html#K4">product</a> <font color="Maroon">f</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i>, <a class="ref" href="finset_1.html#T13">FINSET_1:13</a></i>;<br/>


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