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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() ) or ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Olive">m</font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Olive">m</font>) ) or ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Olive">m</font>,0 &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">m</font>) ) );<br/>
<b>set </b><font color="Maroon">S1</font> = <span class="p1"><a href="tarski.html#K1">{</a><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></span><a href="tarski.html#K1">}</a></span>;<br/>
<b>set </b><font color="Maroon">S2</font> =  <a href="ami_2.html#K2">SCM-Data-Loc</a> ;<br/>
<b>set </b><font color="Maroon">S3</font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>
<a NAME="E1:22_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  holds <br/> ex <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">e</font>,<font color="Olive">u</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:22_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/>

<a NAME="E2:22_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><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></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  or <font color="Maroon">e</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>  )
 
<b>by </b><i><a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_1_1_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><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></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  or <font color="Maroon">e</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>  )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1_1_1"><b>case </b></a><a NAME="E1:22_1_1_1_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><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></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:22_1_1_1_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R1">=</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="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1_1_2"><b>case </b></a><a NAME="E1:22_1_1_1_1_2"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_1_1_1_2"/><b>then </b>
<font color="Maroon">e</font> is    <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>hence </b><a NAME="E3:22_1_1_1_1_2"/>
 ex <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Olive">m</font>,0
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_1_1_3"><b>case </b></a><a NAME="E1:22_1_1_1_1_3"/>
<font color="Maroon">e</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/><div class="add"><b>hence </b><a NAME="E2:22_1_1_1_1_3"/>
 ex <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Olive">m</font>
 <b>by </b><i><a class="ref" href="scmpds_3.html#T32">SCMPDS_3:32</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>then consider </b><font color="Maroon">m</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="E5:22_1_1"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  or <font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font> or <font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,0 )
 ;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_1_2"/>
( <font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  or <font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font> or <font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,0 )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_2_1"><b>suppose </b></a><a NAME="E1:22_1_1_2_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/><div class="add"><b>take </b><font color="Maroon">u</font> = <font color="Maroon">F<sub>3</sub></font>();<br/><b>thus </b><a NAME="E2:22_1_1_2_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">e</font>,<font color="Maroon">u</font>]
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_2_2"><b>suppose </b></a><a NAME="E1:22_1_1_2_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font>
 ;<br/><div class="add"><b>take </b><font color="Maroon">u</font> = <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">m</font>);<br/><b>thus </b><a NAME="E2:22_1_1_2_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">e</font>,<font color="Maroon">u</font>]
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_1_2_3"><b>suppose </b></a><a NAME="E1:22_1_1_2_3"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,0
 ;<br/><div class="add"><b>take </b><font color="Maroon">u</font> = <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">m</font>);<br/><b>thus </b><a NAME="E2:22_1_1_2_3"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">e</font>,<font color="Maroon">u</font>]
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:22_1"/><i><font color="Green">E42</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 <b>and </b><br/><a NAME="E4:22_1"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">e</font>,<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">e</font>]
 <b>from </b><i><a class="ref" href="zfrefle1.html#S1">ZFREFLE1:sch 1</a>();<br/></i>
<a NAME="E5:22_1"/><i><font color="Green">E44</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_2"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
 ;<br/><a NAME="E2:22_1_2"/><b>then </b><i><font color="Green">E58</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><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></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  or <font color="Maroon">x</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>  )
 <b>by </b><i>, <a class="ref" href="scmpds_3.html#T5">SCMPDS_3:5</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>consider </b><font color="Maroon">m</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="E4:22_1_2"/><i><font color="Green">E59</font></i>: 
( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">m</font>) ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,0 &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">m</font>) ) )
 <b>by </b><i>, , </i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:22_1_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a>  or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><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></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">x</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>  )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2_1_1"><b>suppose </b></a><a NAME="E1:22_1_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/><div class="add"><a NAME="E2:22_1_2_1_1"/><b>then </b><i><font color="Green">E60</font></i>: 
<font color="Maroon">x</font> is    <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>then </b>the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,0</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a>, <a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>
<br/>.= 
 <a href="numbers.html#K4">INT</a> 
<b>by </b><i><a class="ref" href="scmpds_2.html#T13">SCMPDS_2:13</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_2_1_1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="ref" href="int_1.html#D2">INT_1:def 2</a>, <a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a>, <a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2_1_2"><b>suppose </b></a><a NAME="E1:22_1_2_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><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></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:22_1_2_1_2"/><b>then </b><i><font color="Green">E61</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</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="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>then </b>the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <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>

<br/>.= 
the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="ref" href="ami_1.html#D11">AMI_1:def 11</a></i>
;<br/><b>hence </b><a NAME="E4:22_1_2_1_2"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="ref" href="ami_1.html#T48">AMI_1:48</a>, <a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="22_1_2_1_3"><b>suppose </b></a><a NAME="E1:22_1_2_1_3"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">x</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/><div class="add"><b>then </b>the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
 <a href="ami_1.html#K3">ObjectKind</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ami_1.html#T48">AMI_1:48</a>, <a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>
<br/>.= 
the <a href="ami_1.html#U4">Instructions</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="ref" href="ami_1.html#D14">AMI_1:def 14</a></i>
;<br/><b>hence </b><a NAME="E3:22_1_2_1_3"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U5">Object-Kind</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="ref" href="ami_1.html#T48">AMI_1:48</a>, <a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  <b>by </b><i>, , <a class="ref" href="card_3.html#T18">CARD_3:18</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>consider </b><font color="Maroon">m</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="E9:22_1"/><i><font color="Green">E63</font></i>: 
( (  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  &amp; <font color="Maroon">f</font> <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="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() ) or (  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font> &amp; <font color="Maroon">f</font> <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="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">m</font>) ) or (  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,0 &amp; <font color="Maroon">f</font> <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="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">m</font>) ) )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E10:22_1"/>
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>()
 <b>by </b><i>, <a class="ref" href="ami_1.html#T48">AMI_1:48</a>, <a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a></i>;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>consider </b><font color="Maroon">m</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="E12:22_1"/><i><font color="Green">E64</font></i>: 
( (  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  &amp; <font color="Maroon">f</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() ) or (  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font> &amp; <font color="Maroon">f</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">m</font>) ) or (  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,0 &amp; <font color="Maroon">f</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">m</font>) ) )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E13:22_1"/>
<font color="Maroon">f</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">i</font>)
 <b>by </b><i>, <a class="ref" href="ami_1.html#T48">AMI_1:48</a>, <a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/>

<b>consider </b><font color="Maroon">m</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="E15:22_1"/><i><font color="Green">E82</font></i>: 
( (  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">i</font>,0 <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a>  &amp; <font color="Maroon">f</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">i</font>,0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() ) or (  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">i</font>,0 <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">m</font> &amp; <font color="Maroon">f</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">i</font>,0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">m</font>) ) or (  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">i</font>,0 <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">m</font>,0 &amp; <font color="Maroon">f</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">i</font>,0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">m</font>) ) )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E16:22_1"/>
<font color="Maroon">f</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">i</font>,0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">i</font>)
 <b>by </b><i>, , <a class="ref" href="scmpds_2.html#T52">SCMPDS_2:52</a>, <a class="ref" href="scmpds_2.html#T53">SCMPDS_2:53</a></i>;<br/>


</div>
