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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="E1:61"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">B</font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Maroon">C</font>
 ;<br/>

<a NAME="E2:61"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">B</font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">C</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:61"/>
 <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/>
<a NAME="E4:61"/><b>then </b><i><font color="Green">E25</font></i>: 
 <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">C</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T4" target="_self">Th4</a>, </i>;<br/>
<a NAME="E5:61"/>
 <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/>
<a NAME="E6:61"/><b>then </b><i><font color="Green">E26</font></i>: 
 <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>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">C</font>,<font color="Maroon">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T5" target="_self">Th5</a>, <a class="ref" href="gcd_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E7:61"/><i><font color="Green">E53</font></i>: 
 <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="hidden.html#R1">=</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">B</font>,<font color="Maroon">A</font>,<font color="Maroon">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E8:61"/><i><font color="Green">E54</font></i>: 
<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/>
<a NAME="E9:61"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">C</font>,<font color="Maroon">Amp</font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E10:61"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">C</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#T8" target="_self">Th8</a>, </i>;<br/>
<a NAME="E11:61"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">C</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/>
<a NAME="E12:61"/><b>then </b>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">C</font>,<font color="Maroon">Amp</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>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T9" target="_self">Th9</a>, <a class="ref" href="gcd_1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E13:61"/><b>then </b>
 <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#R4" target="_self">is_associated_to</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">C</font>,<font color="Maroon">Amp</font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T6" target="_self">Th6</a>, </i>;<br/>
<b>hence </b><a NAME="E14:61"/>
(  <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#R4" target="_self">is_associated_to</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">A</font>,<font color="Maroon">C</font>,<font color="Maroon">Amp</font> &amp;  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">B</font>,<font color="Maroon">A</font>,<font color="Maroon">Amp</font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">C</font>,<font color="Maroon">A</font>,<font color="Maroon">Amp</font> )
 <b>by </b><i><a class="ref" href="gcd_1.html#T7" target="_self">Th7</a>, <a class="ref" href="gcd_1.html#D4" target="_self">Def4</a></i>;<br/>


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