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

<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <br/>( <font color="Olive" title="b1">x</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b2">y</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> 1</span>)</span> <a href="ami_3.html#K15" title="AMI_3:func.15">--&gt;</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">.--&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Olive" title="b2">y</font></span>)</span> );<br/>
<b>let </b><font color="Maroon" title="c13">IT1</font>, <font color="Maroon" title="c14">IT2</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="ami_1.html#K13" title="AMI_1:func.13">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> , <a href="ami_1.html#K13" title="AMI_1:func.13">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:14_1_2"/><i><font color="Green" title="E13">A9</font></i>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">IT1</font> iff <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>] )
 <b>and </b><br/><a NAME="E2:14_1_2"/><i><font color="Green" title="E14">A10</font></i>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">IT2</font> iff <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>] )
 ;<br/>

<b>thus </b><a NAME="E3:14_1_2"/>
<font color="Maroon" title="c13">IT1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">IT2</font>
 <b>from </b><i><a class="ref" href="relset_1.html#S4" title="RELSET_1:sch.4">RELSET_1:sch 4</a>(<a class="txt" href="ami_4.html#E1:14_1_2"><i><font color="Green" title="E13">A9</font></i></a>, <a class="txt" href="ami_4.html#E2:14_1_2"><i><font color="Green" title="E14">A10</font></i></a>);</i><br/>


</div>
