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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="gcd_1.html#NM3">gcdDomain</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="gcd_1.html#M2" target="_self">AmpleSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:61"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:61"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E3:61"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E4:61"/><b>then </b><i><font color="Green">E46</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E2:61"><i><font color="Green">E45</font></i></a>, <a class="ref" href="gcd_1.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E5:61"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E6:61"/><b>then </b><i><font color="Green">E47</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E4:61"><i><font color="Green">E46</font></i></a>, <a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E7:61"/><i><font color="Green">E48</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#T30" target="_self">Th30</a></i>;<br/>
<a NAME="E8:61"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E1:61"><i><font color="Green">E44</font></i></a>, <a class="ref" href="gcd_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E9:61"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E10:61"/><b>then </b><i><font color="Green">E50</font></i>: 
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E8:61"><i><font color="Green">E49</font></i></a>, <a class="ref" href="gcd_1.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E11:61"/>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E12:61"/><b>then </b>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a>  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E10:61"><i><font color="Green">E50</font></i></a>, <a class="ref" href="gcd_1.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E13:61"/><b>then </b>
 <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></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<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E6:61"><i><font color="Green">E47</font></i></a>, <a class="ref" href="gcd_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E14:61"/>
(  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></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<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="gcd_1.html#K5" target="_self">gcd</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></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<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="gcd_1.html#E7:61"><i><font color="Green">E48</font></i></a>, <a class="ref" href="gcd_1.html#T30" target="_self">Th30</a></i>;<br/>


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