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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>

<b>thus </b><a NAME="E1:56"/>
 <a href="amistd_1.html#K3">SUCC</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:56"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  ;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : verum </span>}</span> ;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="scmpds_2.html#K4">goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>;<br/>
 <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font> = 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p0">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="scmpds_9.html#T14" target="_self">Th14</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1"><a href="realset1.html#K5">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="realset1.html#K5">}</a></span>
<b>by </b><i><a class="ref" href="scmpds_9.html#T8" target="_self">Th8</a></i>
;<br/>
<a NAME="E5:56"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:56"/>
<span class="p1">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" target="_self">locnum</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : verum </span>}</span> 
 
;<br/>
<a NAME="E7:56"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K2">JUMP</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : verum </span>}</span> 
 
<b>by </b><i><a class="txt" href="scmpds_9.html#E5:56"><i><font color="Green">E43</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>hence </b><a NAME="E8:56"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K3">SUCC</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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