<?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#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&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#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&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/>
<a NAME="E1:14_1_1"/><i><font color="Green" title="E13">A1</font></i>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q1</font>, <font color="Olive" title="b3">q2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q1</font>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b3">q2</font>] holds <br/><font color="Olive" title="b2">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c13">p</font>, <font color="Maroon" title="c14">q1</font>, <font color="Maroon" title="c15">q2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>given </b><font color="Maroon" title="c16">x1</font>, <font color="Maroon" title="c17">y1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><a NAME="E2:14_1_1_1"/><i><font color="Green" title="E14">A2</font></i>: 
( <font color="Maroon" title="c16">x1</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="Maroon" title="c17">y1</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="Maroon" title="c13">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> <font color="Maroon" title="c16">x1</font>,<font color="Maroon" title="c17">y1</font> &amp; <font color="Maroon" title="c14">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">x1</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c17">y1</font></span>)</span> )
 ;<br/>

<b>given </b><font color="Maroon" title="c18">x2</font>, <font color="Maroon" title="c19">y2</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><a NAME="E4:14_1_1_1"/><i><font color="Green" title="E15">A3</font></i>: 
( <font color="Maroon" title="c18">x2</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="Maroon" title="c19">y2</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="Maroon" title="c13">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> <font color="Maroon" title="c18">x2</font>,<font color="Maroon" title="c19">y2</font> &amp; <font color="Maroon" title="c15">q2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">x2</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c19">y2</font></span>)</span> )
 ;<br/>

<i><font color="Green" title="E16">A4</font></i>: <font color="Maroon" title="c16">x1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> <font color="Maroon" title="c16">x1</font>,<font color="Maroon" title="c17">y1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="txt" href="ami_4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
<br/>.= 
<font color="Maroon" title="c18">x2</font>
<b>by </b><i><a class="txt" href="ami_4.html#E2:14_1_1_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="ami_4.html#E4:14_1_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="ami_4.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/>
<font color="Maroon" title="c17">y1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> <font color="Maroon" title="c16">x1</font>,<font color="Maroon" title="c17">y1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
<br/>.= 
<font color="Maroon" title="c19">y2</font>
<b>by </b><i><a class="txt" href="ami_4.html#E2:14_1_1_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="ami_4.html#E4:14_1_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/>
<b>hence </b><a NAME="E7:14_1_1_1"/>
<font color="Maroon" title="c14">q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">q2</font>
 <b>by </b><i><a class="txt" href="ami_4.html#E2:14_1_1_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="ami_4.html#E4:14_1_1_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="ami_4.html#E5:14_1_1_1"><i><font color="Green" title="E16">A4</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c13">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E3:14_1_1"/><i><font color="Green" title="E14">A5</font></i>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">f</font> iff ( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>] ) )
 <b>from </b><i><a class="ref" href="funct_1.html#S1" title="FUNCT_1:sch.1">FUNCT_1:sch 1</a>(<a class="txt" href="ami_4.html#E1:14_1_1"><i><font color="Green" title="E13">A1</font></i></a>);<br/></i>
<a NAME="E4:14_1_1"/><i><font color="Green" title="E15">A6</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c13">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:14_1_1_2"/>
<font color="Maroon" title="c14">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c13">f</font>
 ;<br/>

<a NAME="E2:14_1_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">e</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">e</font></span>)</span></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">f</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></i>;<br/>
<b>hence </b><a NAME="E3:14_1_1_2"/>
<font color="Maroon" title="c14">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>by </b><i><a class="txt" href="ami_4.html#E3:14_1_1"><i><font color="Green" title="E14">A5</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:14_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c13">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">q</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:14_1_1_3"/>
<font color="Maroon" title="c14">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c13">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c15">p</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:14_1_1_3"/><i><font color="Green" title="E16">A7</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c14">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">f</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D5" title="RELAT_1:def.5">RELAT_1:def 5</a></i>;<br/>
<a NAME="E4:14_1_1_3"/>
 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; <font color="Maroon" title="c15">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Maroon" title="c14">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&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> )
 
<b>by </b><i><a class="txt" href="ami_4.html#E3:14_1_1"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="ami_4.html#E3:14_1_1_3"><i><font color="Green" title="E16">A7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:14_1_1_3"/>
<font color="Maroon" title="c14">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c14">f</font> = <font color="Maroon" title="c13">f</font> as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> , <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <b>by </b><i><a class="txt" href="ami_4.html#E4:14_1_1"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c14">f</font>
;<br/>

<b>let </b><font color="Maroon" title="c15">p</font>, <font color="Maroon" title="c16">q</font> be   <a href="ami_1.html#NM7" title="AMI_1:NM.7">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>

<b>thus </b><a NAME="E7:14_1_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c16">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">f</font> implies  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; <font color="Maroon" title="c15">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Maroon" title="c16">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&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> ) )
 <b>by </b><i><a class="txt" href="ami_4.html#E3:14_1_1"><i><font color="Green" title="E14">A5</font></i></a></i>;<br/>

<b>given </b><font color="Maroon" title="c17">x</font>, <font color="Maroon" title="c18">y</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><b> such that </b><a NAME="E9:14_1_1"/><i><font color="Green" title="E16">A8</font></i>: 
( <font color="Maroon" title="c17">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="Maroon" title="c18">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; <font color="Maroon" title="c15">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">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#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> <font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font> &amp; <font color="Maroon" title="c16">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="ami_3.html#K13" title="AMI_3:func.13">.--&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">x</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c18">y</font></span>)</span> )
 ;<br/>

<a NAME="E10:14_1_1"/>
<font color="Maroon" title="c15">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_1.html#K14" title="AMI_1:func.14">FinPartSt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 
;<br/>
<b>hence </b><a NAME="E11:14_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">p</font>,<font color="Maroon" title="c16">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">f</font>
 <b>by </b><i><a class="txt" href="ami_4.html#E3:14_1_1"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="ami_4.html#E9:14_1_1"><i><font color="Green" title="E16">A8</font></i></a></i>;<br/>


</div>
