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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="group_1.html#V7">commutative</a> <a href="vectsp_2.html#V2">domRing-like</a> <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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="E1:31"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:31"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <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> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="gcd_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E3:31"/><b>then </b><i><font color="Green">E23</font></i>: 
<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="txt" href="gcd_1.html#E1:31"><i><font color="Green">E22</font></i></a>, <a class="ref" href="gcd_1.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E4:31"/>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E1:31"><i><font color="Green">E22</font></i></a>, <a class="ref" href="gcd_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E5:31"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="gcd_1.html#R2" target="_self">divides</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="gcd_1.html#E1:31"><i><font color="Green">E22</font></i></a>, <a class="ref" href="gcd_1.html#T15" target="_self">Th15</a></i>;<br/>
<b>hence </b><a NAME="E6:31"/>
<font color="Maroon">c<sub>2</sub></font> <a href="gcd_1.html#R4" target="_self">is_associated_to</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E3:31"><i><font color="Green">E23</font></i></a>, <a class="ref" href="gcd_1.html#D3" target="_self">Def3</a></i>;<br/>


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