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<span class="kw">let </span><font color="Maroon" title="c3">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  st <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">i</font></span><br/>

<a NAME="E1:1"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#D2" title="SCMPDS_2:def.2">SCMPDS_2:def 2</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:1"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">and </span><br/><a NAME="E4:1"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <span class="kw">and </span><br/><a NAME="E5:1"/><span class="lab"><font color="Green" title="E4">A3</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T103" title="ZFMISC_1:th.103">ZFMISC_1:103</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">k</font> = <font color="Maroon" title="c5">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:1"><span class="lab"><font color="Green" title="E3">A2</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c6">k</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c6">k</font></span><br/>

<span class="kw">thus </span> <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c6">k</font> = 
 <a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Maroon" title="c6">k</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#D1" title="SCMP_GCD:def.1">SCMP_GCD:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:1"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="#E5:1"><span class="lab"><font color="Green" title="E4">A3</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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