<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c6">I</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E18">A1</font></i>: 
 <a href="ami_1.html#K20" title="AMI_1:func.20">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 ;<br/>

<a NAME="E2:42"/>
( <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">k1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">k1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span>}</span>  or <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">d1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">d1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span>}</span>  or <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I1</font>,<span class="p3"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">d2</font>,<font color="Olive" title="b3">k2</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 14, <font color="Olive" title="b2">d2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">k2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I2</font>,<span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">d3</font>,<font color="Olive" title="b3">k3</font>,<font color="Olive" title="b4">k4</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 14, <font color="Olive" title="b2">d3</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">k3</font>, <font color="Olive" title="b4">k4</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span>  or <font color="Maroon" title="c6">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I3</font>,<span class="p3"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Olive" title="b2">d4</font>,<font color="Olive" title="b3">d5</font>,<font color="Olive" title="b4">k5</font>,<font color="Olive" title="b5">k6</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I3</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 14, <font color="Olive" title="b2">d4</font>, <font color="Olive" title="b3">d5</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b4">k5</font>, <font color="Olive" title="b5">k6</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span>  )
 
<b>by </b><i><a class="txt" href="scmpds_2.html#E16"><i><font color="Green" title="E5">Lm1</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">I1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 14, <font color="Maroon" title="c8">d1</font>, <font color="Maroon" title="c9">d2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Maroon" title="c10">k1</font>, <font color="Maroon" title="c11">k2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E4:42"/><i><font color="Green" title="E19">A2</font></i>: 
( <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">I1</font>,<span class="p2"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">d2</font>,<font color="Maroon" title="c10">k1</font>,<font color="Maroon" title="c11">k2</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> )
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:42"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="scmpds_2.html#E69"><i><font color="Green" title="E17">Lm8</font></i></a></i>;<br/>
<a NAME="E5:42"/>
( <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 )
 
<b>by </b><i><a class="txt" href="scmpds_2.html#E4:42"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c12">d1</font>, <font color="Maroon" title="c13">d2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Maroon" title="c14">k1</font>, <font color="Maroon" title="c15">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><br/><a NAME="E7:42"/><i><font color="Green" title="E20">A3</font></i>: 
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">12,<span class="p2"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c14">k1</font>,<font color="Maroon" title="c15">k2</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E1:42"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="scmpds_2.html#E4:42"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">a</font> = <font color="Maroon" title="c12">d1</font>, <font color="Maroon" title="c17">b</font> = <font color="Maroon" title="c13">d2</font> as    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  <b>by </b><i><a class="ref" href="scmpds_2.html#D2" target="_self" title="SCMPDS_2:def.2">Def2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c16">a</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c17">b</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c14">k1</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c15">k2</font>
;<br/>

<b>thus </b><a NAME="E9:42"/>
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c14">k1</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">k2</font>
 <b>by </b><i><a class="txt" href="scmpds_2.html#E7:42"><i><font color="Green" title="E20">A3</font></i></a></i>;<br/>


</div>
