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

<b>let </b><font color="Maroon">a</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/>

<b>set </b><font color="Maroon">i</font> =  <a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font>;<br/>
<b>set </b><font color="Maroon">A</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 </span>}</span> ;<br/>
<a NAME="E1:34"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:34"/>
 <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 </span>}</span> 
 <b>by </b><i/>; <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">x</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="E3:34"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 </span>}</span> 
 ;<br/>

<b>set </b><font color="Maroon">X</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : verum </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><a NAME="E1:34_1"/>
 <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 0</span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : verum </span>}</span> 
 ;<br/><b>hence </b><a NAME="E2:34_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : verum </span>}</span>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E3:34_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : verum </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <b> such that </b><br/><a NAME="E5:34_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K1">NIC</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">l</font>
 ;<br/><a NAME="E6:34_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="scmpds_2.html#D2">SCMPDS_2:def 2</a></i>;<br/><b>then consider </b><font color="Maroon">j</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E8:34_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="ami_2.html#D2">AMI_2:def 2</a></i>;<br/><b>consider </b><font color="Maroon">s</font> being   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>reconsider </b><font color="Maroon">il1</font> = <font color="Maroon">l</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <b>by </b><i><a class="ref" href="ami_1.html#D11">AMI_1:def 11</a></i>;<br/><b>reconsider </b><font color="Maroon">I</font> =  <a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">l</font> <b>by </b><i><a class="ref" href="ami_1.html#D14">AMI_1:def 14</a></i>;<br/><b>set </b><font color="Maroon">u</font> = <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span>;<br/><b>consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E13:34_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E14:34_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="ref" href="scmpds_9.html#T1" target="_self">Th1</a></i>;<br/><b>set </b><font color="Maroon">t</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2;<br/><a NAME="E15:34_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E16:34_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 <b>by </b><i><a class="ref" href="ami_2.html#D2">AMI_2:def 2</a></i>;<br/><b>then reconsider </b><font color="Maroon">t1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2 as    <a href="scmpds_2.html#M1">Int_position</a>  <b>by </b><i><a class="ref" href="scmpds_2.html#T9">SCMPDS_2:9</a></i>;<br/><b>reconsider </b><font color="Maroon">k2</font> = <font color="Maroon">k</font> <a href="xcmplx_0.html#K6">-</a> 2 as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="scmpds_9.html#T3" target="_self">Th3</a>, </i>;<br/><b>set </b><font color="Maroon">g</font> = <font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span>;<br/><b>set </b><font color="Maroon">v</font> = <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span>;<br/><a NAME="E19:34_1"/><i><font color="Green">E78</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="funct_4.html#T65">FUNCT_4:65</a></i>;<br/><a NAME="E20:34_1"/><i><font color="Green">E79</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="ami_6.html#T6">AMI_6:6</a></i>;<br/><i><font color="Green">E80</font></i>: <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">l</font>
<b>by </b><i><a class="ref" href="ami_6.html#T6">AMI_6:6</a></i>
;<br/><a NAME="E22:34_1"/>
( <font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a</font> &amp; <font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t1</font> )
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/><a NAME="E23:34_1"/><b>then </b>
not <font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_9.html#T4" target="_self">Th4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E24:34_1"/><b>then </b><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><a NAME="E25:34_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  &amp; <font color="Maroon">t1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  )
 <b>by </b><i><a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a></i>;<br/><a NAME="E26:34_1"/><b>then </b><i><font color="Green">E82</font></i>: 
not  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_9.html#T4" target="_self">Th4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><i><font color="Green">E83</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon">l</font>
<b>by </b><i>, <a class="txt" href="scmpds_9.html#E13:34_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><a NAME="E28:34_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 0
 <b>by </b><i><a class="txt" href="scmpds_9.html#E5:34_1"><i><font color="Green">E31</font></i></a></i>;<br/><a NAME="E29:34_1"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t1</font>
 ;<br/><a NAME="E30:34_1"/><b>then </b><i><font color="Green">E85</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 <b>by </b><i/>;<br/><a NAME="E31:34_1"/><i><font color="Green">E86</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">t1</font> <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font>
 <b>by </b><i>, </i>;<br/><i><font color="Green">E92</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">j</font>,1 = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmpds_2.html#D4">SCMPDS_2:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2

;<br/><b>reconsider </b><font color="Maroon">r</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, </i>;<br/><font color="Maroon">x</font> = 
2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">k2</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_9.html#T2" target="_self">Th2</a></i>
<br/>.= 
2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span> <a href="nat_1.html#K5">div</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="nat_1.html#T68">NAT_1:68</a></i>
<br/>.= 
2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <font color="Maroon">r</font></span>)</span> <a href="nat_1.html#K5">div</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">j</font>,1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K5">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 2</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_1.html#D23">SCMPDS_1:def 23</a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<font color="Maroon">l</font> <a href="ami_1.html#K16">--&gt;</a> <font color="Maroon">il1</font>,<font color="Maroon">I</font></span>)</span></span>)</span> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">t1</font> <a href="scmpds_9.html#K1" target="_self">--&gt;</a> <font color="Maroon">j</font>,<span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">k2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E8:34_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="scmpds_9.html#T5" target="_self">Th5</a>, </i>
;<br/><b>hence </b><a NAME="E35:34_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="scmpds_9.html#E3:34"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmpds_9.html#E8:34_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="scmpds_9.html#T5" target="_self">Th5</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:34"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K1">NIC</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>,<font color="Olive">l</font></span>)</span> where <font color="Olive">l</font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:34"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="amistd_1.html#K2">JUMP</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <font color="Maroon">a</font></span>)</span>
 ;<br/>


</div>
