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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">l</font> being  <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font> st <br/>( <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp;  ex <font color="Olive" title="b2">s</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">A</font> ex <font color="Olive" title="b3">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Olive" title="b1">l</font> st  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b1">l</font>,<font color="Olive" title="b3">a</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Olive" title="b2">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Olive" title="b1">l</font>,<font color="Olive" title="b3">a</font> );<br/>
<b>consider </b><font color="Maroon" title="c4">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">A</font><b> such that </b><br/><a NAME="E2:18_2_1"/><i><font color="Green" title="E9">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] ) )
 <b>from </b><i><a class="ref" href="subset_1.html#S1" title="SUBSET_1:sch.1">SUBSET_1:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c4">X</font>
;<br/>

<b>let </b><font color="Maroon" title="c5">l</font> be   <a href="ami_1.html#NM1" title="AMI_1:NM.1">Object</a> of <font color="Maroon" title="c2">A</font>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:18_2_1_1"/>
<font color="Maroon" title="c5">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 ;<br/><a NAME="E2:18_2_1_1"/><b>then </b>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">l</font>]
 <b>by </b><i><a class="txt" href="ami_7.html#E2:18_2_1"><i><font color="Green" title="E9">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E3:18_2_1_1"/>
 ex <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">A</font> ex <font color="Olive" title="b2">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c5">l</font> st  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">l</font>,<font color="Olive" title="b2">a</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">l</font>,<font color="Olive" title="b2">a</font>
 ;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E4:18_2_1"/>
(  ex <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <font color="Maroon" title="c2">A</font> ex <font color="Olive" title="b2">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c5">l</font> st  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">s</font> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">l</font>,<font color="Olive" title="b2">a</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">I</font>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_7.html#K1" title="AMI_7:func.1">+*</a> <font color="Maroon" title="c5">l</font>,<font color="Olive" title="b2">a</font> implies <font color="Maroon" title="c5">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font> )
 <b>by </b><i><a class="txt" href="ami_7.html#E2:18_2_1"><i><font color="Green" title="E9">A2</font></i></a></i>;<br/>


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