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<span class="kw">let </span><font color="Maroon" title="c1">k</font> be    <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> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="heyting3.html#K4" title="HEYTING3:func.4">PFBrt</a> (1,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>

<a NAME="E1:44"/>
 <a href="heyting3.html#K2" title="HEYTING3:func.2">PFArt</a> (1,<font color="Maroon" title="c1">k</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="heyting3.html#K4" title="HEYTING3:func.4">PFBrt</a> (1,<font color="Maroon" title="c1">k</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="heyting3.html#D4" target="_self" onmouseover="rs('heyting3/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:44"/>
 <a href="heyting3.html#K4" title="HEYTING3:func.4">PFBrt</a> (1,<font color="Maroon" title="c1">k</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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