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<b>let </b><font color="Maroon" title="c1">k1</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/><b>let </b><font color="Maroon" title="c2">s1</font>, <font color="Maroon" title="c3">s2</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>



<b>assume </b><a NAME="E1:1"/><i><font color="Green" title="E2">A1</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s2</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:1"/><i><font color="Green" title="E3">A2</font></i>: 
( <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c2">s1</font> &amp;  <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c1">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">k1</font></span>)</span> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20" title="SCMPDS_2:def.20">SCMPDS_2:def 20</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">j</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E5:1"/><i><font color="Green" title="E4">A3</font></i>: 
( <font color="Maroon" title="c5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c3">s2</font> &amp;  <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c1">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">k1</font></span>)</span> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20" title="SCMPDS_2:def.20">SCMPDS_2:def 20</a></i>;<br/>
<b>thus </b><a NAME="E6:1"/>
 <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c1">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K19" title="SCMPDS_2:func.19">ICplusConst</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c1">k1</font>
 <b>by </b><i><a class="txt" href="scmpds_3.html#E1:1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="scmpds_3.html#E3:1"><i><font color="Green" title="E3">A2</font></i></a>, <a class="txt" href="scmpds_3.html#E5:1"><i><font color="Green" title="E4">A3</font></i></a></i>;<br/>


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