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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="funct_1.html#NM1">Function</a>) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  =  <a href="relat_1.html#K2">rng</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">A</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">f</font>) where <font color="Olive">f</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a>  : <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font> </span>}</span> ;<br/>
<a NAME="E1:7_1_1"/><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font> is <a href="finset_1.html#V1">finite</a>
 
;<br/>
<a NAME="E2:7_1_1"/><i><font color="Green">E58</font></i>: 
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">f</font>) where <font color="Olive">f</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a>  : <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font> </span>}</span>  is <a href="finset_1.html#V1">finite</a>
 
<b>from </b><i><a class="ref" href="fraenkel.html#S21">FRAENKEL:sch 21</a>();<br/></i>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1_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="E1:7_1_1_1"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">f</font>) where <font color="Olive">f</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a>  : <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font> </span>}</span> 
 ;<br/><a NAME="E2:7_1_1_1"/><b>then </b>
 ex <font color="Olive">f</font> being   <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a>  st <br/>( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Olive">f</font> &amp; <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font> )
 ;<br/><b>hence </b><a NAME="E3:7_1_1_1"/>
<font color="Maroon">X</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/></div><b>end;</b></div>
<a NAME="E4:7_1_1"/><b>then </b>
 <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">f</font>) where <font color="Olive">f</font> is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">D</font> <a href="finseq_2.html#K3">*</a>  : <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font> </span>}</span>  is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, <a class="ref" href="finset_1.html#T25">FINSET_1:25</a></i>;<br/>
<b>hence </b><a NAME="E5:7_1_1"/>
 <a href="gobrd13.html#K2" target="_self">Values</a> <font color="Maroon">M</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i/>;<br/>


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