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<span class="kw">assume </span><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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><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"/>
(  <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>  &amp; 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/>
<span class="kw">hence </span><a NAME="E4:66_1_1"/>
contradiction
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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