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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>;<br/>
<div><i><font color="Green">E14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="71_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="E1:71_1_1_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><b>then reconsider </b><font color="Maroon">A'</font> = <font color="Maroon">A</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/><b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A'</font> <b>by </b><i/>;<br/><a NAME="E4:71_1_1_1"/>
<span class="p1"><a href="setwiseo.html#K2" target="_self">{.</a><span class="default"><font color="Maroon">x'</font></span><a href="setwiseo.html#K2" target="_self">.}</a></span> <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A'</font>
 ;<br/><b>hence </b><a NAME="E5:71_1_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">x</font>) <a href="hidden.html#R2">in</a>  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font>
 ;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E2:71_1_1"/>
 ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>, <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font> st <br/>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> <font color="Maroon">A</font> holds <br/><font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S2">FUNCT_2:sch 2</a>();</i><br/>


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