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<b>assume </b><a NAME="E1:54_1_1"/><i><font color="Green" title="E39">A1</font></i>: 
 <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  is <a href="amistd_1.html#V3" title="AMISTD_1:attr.3">InsLoc-antisymmetric</a>
 ;<br/>

<a NAME="E2:54_1_1"/>
(  <a href="amistd_1.html#K3" title="AMISTD_1:func.3">SUCC</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  &amp;  <a href="amistd_1.html#K3" title="AMISTD_1:func.3">SUCC</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="scmpds_9.html#T29" target="_self" title="SCMPDS_9:th.29">Th29</a></i>;<br/>
<a NAME="E3:54_1_1"/><b>then </b>
(  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 1 <a href="amistd_1.html#R1" title="AMISTD_1:pred.1">&lt;=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 2 &amp;  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 2 <a href="amistd_1.html#R1" title="AMISTD_1:pred.1">&lt;=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 1 )
 
<b>by </b><i><a class="ref" href="scmpds_9.html#T30" target="_self" title="SCMPDS_9:th.30">Th30</a></i>;<br/>
<b>hence </b><a NAME="E4:54_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmpds_9.html#E1:54_1_1"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="amistd_1.html#D9" title="AMISTD_1:def.9">AMISTD_1:def 9</a></i>;<br/>


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