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<div><span class="kw">theorem </span><a NAME="T21"><span class="comment"><font color="firebrick">:: HEYTING3:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">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" title="b3">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="heyting3.html#K4" title="HEYTING3:func.4">PFBrt</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b2">k</font>) holds <br/> ex <font color="Olive" title="b4">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>( <font color="Olive" title="b4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="heyting3.html#K4" title="HEYTING3:func.4">PFBrt</a> (<font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">k</font>) &amp; <font color="Olive" title="b4">y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">x</font> )</div></div>
