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<b>let </b><font color="Maroon" title="c1">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="heyting3.html#K1" title="HEYTING3:func.1">SubstPoset</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">m</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>;<br/>



<b>assume </b><a NAME="E1:63"/><i><font color="Green" title="E45">A1</font></i>: 
 <a href="heyting3.html#K5" title="HEYTING3:func.5">PFDrt</a> <font color="Maroon" title="c1">m</font> <a href="lattice3.html#NR3" title="LATTICE3:NR.3">is_&gt;=_than</a> <font color="Maroon" title="c2">a</font>
 ;<br/>

<b>assume </b><a NAME="E2:63"/><i><font color="Green" title="E46">A2</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>
 ;<br/>

<a NAME="E3:63"/><i><font color="Green" title="E47">A3</font></i>: 
 <a href="heyting3.html#K4" title="HEYTING3:func.4">PFBrt</a> 1,<font color="Maroon" title="c1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="heyting3.html#K5" title="HEYTING3:func.5">PFDrt</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="ref" href="heyting3.html#D5" target="_self" title="HEYTING3:def.5">Def5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">P1</font> =  <a href="heyting3.html#K4" title="HEYTING3:func.4">PFBrt</a> 1,<font color="Maroon" title="c1">m</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="heyting3.html#K1" title="HEYTING3:func.1">SubstPoset</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">m</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="heyting3.html#T28" target="_self" title="HEYTING3:th.28">Th28</a></i>;<br/>
<a NAME="E5:63"/><i><font color="Green" title="E48">A4</font></i>: 
 <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <span class="p1">(<span class="default"><a href="heyting3.html#K1" title="HEYTING3:func.1">SubstPoset</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c1">m</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>
 
<b>by </b><i><a class="ref" href="heyting3.html#T39" target="_self" title="HEYTING3:th.39">Th39</a></i>;<br/>
<a NAME="E6:63"/>
<font color="Maroon" title="c3">P1</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="heyting3.html#E1:63"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="heyting3.html#E3:63"><i><font color="Green" title="E47">A3</font></i></a>, <a class="ref" href="lattice3.html#D8" title="LATTICE3:def.8">LATTICE3:def 8</a></i>;<br/>
<a NAME="E7:63"/><b>then </b>
<font color="Maroon" title="c3">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>
 
<b>by </b><i><a class="txt" href="heyting3.html#E2:63"><i><font color="Green" title="E46">A2</font></i></a>, <a class="txt" href="heyting3.html#E5:63"><i><font color="Green" title="E48">A4</font></i></a>, <a class="ref" href="waybel15.html#T5" title="WAYBEL15:th.5">WAYBEL15:5</a></i>;<br/>
<b>hence </b><a NAME="E8:63"/>
contradiction
 <b>by </b><i><a class="ref" href="heyting3.html#T30" target="_self" title="HEYTING3:th.30">Th30</a></i>;<br/>


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