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<span class="kw">let </span><font color="Maroon" title="c6">I</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 implies  ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Olive" title="b3">k2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:41"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  ex <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Olive" title="b3">k2</font></span><br/>

<a NAME="E2:41"/>
( <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#M2" title="SUBSET_1:mode.2">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#M2" title="SUBSET_1:mode.2">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#M2" title="SUBSET_1:mode.2">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>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="scmpds_2.html#E16"><span class="lab"><font color="Green" title="E5">Lm1</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">I1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 14, <font color="Maroon" title="c8">d1</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="c9">k1</font>, <font color="Maroon" title="c10">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> <span class="kw"> such that </span><br/><a NAME="E4:41"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<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_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c8">d1</font>,<font color="Maroon" title="c9">k1</font>,<font color="Maroon" title="c10">k2</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>
 <span class="kw">and </span><br/><a NAME="E5:41"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<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">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="scmpds_2.html#E63"><span class="lab"><font color="Green" title="E16">Lm7</font></span></a></span>;<br/>
<a NAME="E6:41"/>
( <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:41"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">d1</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="c12">k1</font>, <font color="Maroon" title="c13">k2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><span class="kw"> such that </span><br/><a NAME="E8:41"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<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">4,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c11">d1</font>,<font color="Maroon" title="c12">k1</font>,<font color="Maroon" title="c13">k2</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E4:41"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">a</font> = <font color="Maroon" title="c11">d1</font> as    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#D2" target="_self" title="SCMPDS_2:def.2">Def2</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c14">a</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">k1</font>, <font color="Olive" title="b2">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a</font>,<font color="Olive" title="b1">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Olive" title="b2">k2</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c12">k1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a</font>,<font color="Maroon" title="c12">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Olive" title="b1">k2</font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c13">k2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a</font>,<font color="Maroon" title="c12">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Maroon" title="c13">k2</font></span><br/>

<span class="kw">thus </span><a NAME="E10:41"/>
<font color="Maroon" title="c6">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a</font>,<font color="Maroon" title="c12">k1</font> <a href="scmpds_2.html#K8" title="SCMPDS_2:func.8">&lt;&gt;0_goto</a> <font color="Maroon" title="c13">k2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:41"><span class="lab"><font color="Green" title="E20">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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