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<span class="kw">let </span><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="heyting3.html#K3" title="HEYTING3:func.3">PFCrt</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="heyting3.html#K3" title="HEYTING3:func.3">PFCrt</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">k</font>)</span><br/>

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 <a href="heyting3.html#K3" title="HEYTING3:func.3">PFCrt</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">k</font>) <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="heyting3.html#K3" title="HEYTING3:func.3">PFCrt</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="heyting3.html#T17" target="_self" title="HEYTING3:th.17">Th20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:31"/>
 <a href="heyting3.html#K3" title="HEYTING3:func.3">PFCrt</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">k</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="heyting3.html#K3" title="HEYTING3:func.3">PFCrt</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>,<font color="Maroon" title="c2">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D8" title="XBOOLE_0:def.8">XBOOLE_0:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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