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<b>let </b><font color="Maroon">s1</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> , <font color="Maroon">s2</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">m</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">k1</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:106"/><i><font color="Green">E30</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font>
 <b>and </b><br/><a NAME="E2:106"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">m</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>and </b><br/><a NAME="E3:106"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font>
 ;<br/>

<b>consider </b><font color="Maroon">n1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:106"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">n1</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s1</font> &amp;  <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">s1</font>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">n1</font> <a href="xcmplx_0.html#K6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">k1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20">SCMPDS_2:def 20</a></i>;<br/>
<b>consider </b><font color="Maroon">n2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E7:106"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">n2</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s2</font> &amp;  <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">s2</font>,<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">n2</font> <a href="xcmplx_0.html#K6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">k1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20">SCMPDS_2:def 20</a></i>;<br/>
<b>reconsider </b><font color="Maroon">mk</font> = <font color="Maroon">m</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k1</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<i><font color="Green">E41</font></i>: <font color="Maroon">n2</font> = 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="scmpds_3.html#D3">SCMPDS_3:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2

;<br/>
<b>consider </b><font color="Maroon">nk</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E11:106"/><i><font color="Green">E42</font></i>: 
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">nk</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">s1</font>,<font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T32">SCMPDS_3:32</a></i>;<br/>
<a NAME="E12:106"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">m</font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i>, </i>;<br/>
<a NAME="E13:106"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">nk</font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">n1</font> <a href="xcmplx_0.html#K6">-</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">k1</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i>, </i>;<br/>
<a NAME="E14:106"/><b>then </b><i><font color="Green">E44</font></i>: 
2 <a href="nat_1.html#K2">*</a> <font color="Maroon">nk</font> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <font color="Maroon">mk</font>
 
<b>by </b><i>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">s1</font>,<font color="Maroon">k1</font></span>)</span> <a href="scmpds_3.html#K3">+</a> <font color="Maroon">n</font> = 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><font color="Maroon">nk</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_3.html#D3">SCMPDS_3:def 3</a></i>
<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">s2</font>,<font color="Maroon">k1</font>
<b>by </b><i>, , , <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>


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