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<b>set </b><font color="Maroon">S</font> = <span class="p1">{<span class="default"> <font color="Olive">R</font> where <font color="Olive">R</font> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> </span>)</span> : <font color="Olive">R</font> is <a href="comput_1.html#V8" target="_self">primitive-recursively_closed</a> </span>}</span> ;<br/>
<b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> </span>)</span>;<br/>

<b>assume </b><a NAME="E1:124"/>
<font color="Maroon">X</font> is <a href="comput_1.html#V8" target="_self">primitive-recursively_closed</a>
 ;<br/>

<a NAME="E2:124"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">R</font> where <font color="Olive">R</font> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="comput_1.html#K5" target="_self">HFuncs</a> <a href="numbers.html#K5">NAT</a> </span>)</span> : <font color="Olive">R</font> is <a href="comput_1.html#V8" target="_self">primitive-recursively_closed</a> </span>}</span> 
 
;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:124"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="comput_1.html#K11" target="_self">PrimRec</a> 
 ;<br/>

<b>hence </b><a NAME="E4:124"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="comput_1.html#T17" target="_self">Th17</a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>


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