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<b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmpds_2.html#K1" target="_self">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:55"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k1</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k1</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d1</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I1</font>,<span class="p3"><a href="scmpds_1.html#K9">&lt;*</a><span class="default"><font color="Olive">d2</font>,<font color="Olive">k2</font></span><a href="scmpds_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k2</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span> </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I2</font>,<span class="p3"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Olive">d3</font>,<font color="Olive">k3</font>,<font color="Olive">k4</font></span><a href="finseq_1.html#K11">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k3</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">k4</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3">}</a></span> </span>}</span>  )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:55_1"/>
( <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k1</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k1</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d1</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I1</font>,<span class="p3"><a href="scmpds_1.html#K9">&lt;*</a><span class="default"><font color="Olive">d2</font>,<font color="Olive">k2</font></span><a href="scmpds_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k2</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span> </span>}</span>  or <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I2</font>,<span class="p3"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Olive">d3</font>,<font color="Olive">k3</font>,<font color="Olive">k4</font></span><a href="finseq_1.html#K11">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k3</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">k4</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3">}</a></span> </span>}</span>  )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1"><b>suppose </b></a><a NAME="E1:55_1_1"/>
<font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k1</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k1</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:55_1_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 8 )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_2"><b>suppose </b></a><a NAME="E1:55_1_2"/>
<font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d1</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:55_1_2"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 8 )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_3"><b>suppose </b></a><a NAME="E1:55_1_3"/>
<font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I1</font>,<span class="p3"><a href="scmpds_1.html#K9">&lt;*</a><span class="default"><font color="Olive">d2</font>,<font color="Olive">k2</font></span><a href="scmpds_1.html#K9">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k2</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:55_1_3"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 8 )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_4"><b>suppose </b></a><a NAME="E1:55_1_4"/>
<font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I2</font>,<span class="p3"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Olive">d3</font>,<font color="Olive">k3</font>,<font color="Olive">k4</font></span><a href="finseq_1.html#K11">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k3</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">k4</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:55_1_4"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 0 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 1 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 4 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 5 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 6 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a> 8 )
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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