<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E25">Def5</font></span>   defines <a href="heyting3.html#K5" title="HEYTING3:func.5">PFDrt</a> <a onclick="hs(this)" href="javascript:()">HEYTING3:def 5 : <br/></a><span> for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive">b<sub>2</sub></font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="heyting3.html#K1" title="HEYTING3:func.1">SubstPoset</a> (<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">k</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>)</span>)</span> holds <br/> ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="heyting3.html#K5" title="HEYTING3:func.5">PFDrt</a> <font color="Olive" title="b1">k</font> iff  for <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>2</sub></font> iff  ex <font color="Olive" title="b4">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="heyting3.html#K4" title="HEYTING3:func.4">PFBrt</a> (<font color="Olive" title="b4">n</font>,<font color="Olive" title="b1">k</font>) ) );<br/></span></div>
