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<b>let </b><font color="Maroon">R</font> be   <a href="gcd_1.html#NM3">gcdDomain</a>;<br/><b>let </b><font color="Maroon">Amp</font> be    <a href="gcd_1.html#M2" target="_self">AmpleSet</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>, <font color="Maroon">C</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>;<br/>





<b>assume </b><a NAME="E1:55"/>
<font color="Maroon">C</font> <a href="gcd_1.html#R2" target="_self">divides</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">Amp</font>
 ;<br/>

<b>then consider </b><font color="Maroon">D</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:55"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">C</font> <a href="group_1.html#K10">*</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">Amp</font>
 <b>by </b><i/>;<br/>
<a NAME="E4:55"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">Amp</font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>then consider </b><font color="Maroon">E</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E6:55"/><i><font color="Green">E21</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">Amp</font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>
<a NAME="E7:55"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">C</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="group_1.html#K10">*</a> <font color="Maroon">E</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D4" target="_self">Def4</a>, <a class="ref" href="gcd_1.html#T2" target="_self">Th2</a>, <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/>
<a NAME="E8:55"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">Amp</font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>then consider </b><font color="Maroon">E</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E10:55"/><i><font color="Green">E26</font></i>: 
<span class="p1">(<span class="default"><a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">Amp</font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>by </b><i/>;<br/>
<a NAME="E11:55"/>
<font color="Maroon">C</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="group_1.html#K10">*</a> <font color="Maroon">E</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D4" target="_self">Def4</a>, , <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E12:55"/>
( <font color="Maroon">C</font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">A</font> &amp; <font color="Maroon">C</font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">B</font> )
 <b>by </b><i>, </i>;<br/>


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