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<b>assume </b><a NAME="E1:66_1_1"/>
 <a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p1"><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> is <a href="lattice3.html#V4" title="LATTICE3:attr.4">complete</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c2">K</font> =  <a href="substlat.html#K5" title="SUBSTLAT:func.5">SubstLatt</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p1"><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> as  <a href="lattice3.html#V4" title="LATTICE3:attr.4">complete</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> ;<br/>
<a NAME="E3:66_1_1"/><i><font color="Green" title="E46">A1</font></i>: 
 <a href="lattice3.html#K3" title="LATTICE3:func.3">LattPOSet</a> <font color="Maroon" title="c2">K</font> is <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>
 
;<br/>
<a NAME="E4:66_1_1"/>
not  <a href="heyting3.html#K1" title="HEYTING3:func.1">SubstPoset</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p1"><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> is <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>
 
;<br/>
<b>hence </b><a NAME="E5:66_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="heyting3.html#E3:66_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>;<br/>


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