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<b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="heyting3.html#K1" target="_self">SubstPoset</a> <a href="numbers.html#K5">NAT</a> ,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">m</font></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/>



<b>assume </b><a NAME="E1:63"/><i><font color="Green">E30</font></i>: 
 <a href="heyting3.html#K5" target="_self">PFDrt</a> <font color="Maroon">m</font> <a href="lattice3.html#NR3" target="_self">is_&gt;=_than</a> <font color="Maroon">a</font>
 ;<br/>

<b>assume </b><a NAME="E2:63"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E3:63"/><i><font color="Green">E46</font></i>: 
 <a href="heyting3.html#K4" target="_self">PFBrt</a> 1,<font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="heyting3.html#K5" target="_self">PFDrt</a> <font color="Maroon">m</font>
 
<b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">P1</font> =  <a href="heyting3.html#K4" target="_self">PFBrt</a> 1,<font color="Maroon">m</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="heyting3.html#K1" target="_self">SubstPoset</a> <a href="numbers.html#K5">NAT</a> ,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">m</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E5:63"/><i><font color="Green">E48</font></i>: 
 <a href="yellow_0.html#K4">Top</a> <span class="p1">(<span class="default"><a href="heyting3.html#K1" target="_self">SubstPoset</a> <a href="numbers.html#K5">NAT</a> ,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">m</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="heyting3.html#E3"><i><font color="Green">Lemma40</font></i></a></i>;<br/>
<a NAME="E6:63"/>
<font color="Maroon">P1</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">a</font>
 
<b>by </b><i>, , <a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/>
<a NAME="E7:63"/><b>then </b>
<font color="Maroon">P1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="heyting3.html#E3:63"><i><font color="Green">E46</font></i></a>, <a class="txt" href="heyting3.html#E5:63"><i><font color="Green">E48</font></i></a>, <a class="ref" href="waybel15.html#T5">WAYBEL15:5</a></i>;<br/>
<b>hence </b><a NAME="E8:63"/>
contradiction
 <b>by </b><i><a class="txt" href="heyting3.html#E1:63"><i><font color="Green">E30</font></i></a></i>;<br/>


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