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<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] means ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="ami_3.html#K18">--&gt;</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="ami_3.html#K17">.--&gt;</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="int_2.html#K3">gcd</a> <font color="Olive">b<sub>2</sub></font></span>)</span> );<br/>
<b>let </b><font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="ami_1.html#K14">FinPartSt</a> <a href="ami_3.html#K1">SCM</a> , <a href="ami_1.html#K14">FinPartSt</a> <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:16_1_2"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_1.html#M1">FinPartState</a> of  <a href="ami_3.html#K1">SCM</a>  holds <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> iff <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] )
 <b>and </b><br/><a NAME="E2:16_1_2"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_1.html#M1">FinPartState</a> of  <a href="ami_3.html#K1">SCM</a>  holds <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>14</sub></font> iff <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] )
 ;<br/>

<b>thus </b><a NAME="E3:16_1_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>from </b><i><a class="ref" href="ami_3.html#S2">AMI_3:sch 2</a>(<a class="txt" href="ami_4.html#E1:16_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ami_4.html#E2:16_1_2"><i><font color="Green">E15</font></i></a>);</i><br/>


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