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<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">p0</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">f</font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="mesfunc1.html#K2">INT</a> ;<br/>





<b>assume </b><a NAME="E1:11"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">p0</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 &amp; <font color="Maroon">f</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">s</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 ;<br/>

<b>hence </b><a NAME="E2:11"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K1" target="_self">sum</a> <font color="Maroon">n</font>,<font color="Maroon">p0</font></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K6">Sum</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>consider </b><font color="Maroon">g</font> being    <a href="trees_4.html#M1">FinSequence</a> of  <a href="mesfunc1.html#K2">INT</a> <b> such that </b><br/><a NAME="E2:11_1"/><i><font color="Green">E46</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">g</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">t</font>,<font color="Maroon">p0</font> )
 <b>by </b><i><a class="ref" href="scpisort.html#T3">SCPISORT:3</a></i>;<br/><b>thus </b><a NAME="E3:11_1"/>
 <a href="scpinvar.html#K1" target="_self">sum</a> <font color="Maroon">n</font>,<font color="Maroon">p0</font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">t</font>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:11"/>
 <a href="scpinvar.html#K1" target="_self">sum</a> <font color="Maroon">n</font>,<font color="Maroon">p0</font> is <a href="scmpds_4.html#V2">parahalting</a>
 <b>by </b><i><a class="ref" href="scmpds_6.html#T35">SCMPDS_6:35</a></i>;<br/>


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