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<b>let </b><font color="Maroon">R</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V4">associative</a>  <a href="vectsp_1.html#L1">multLoopStr</a> ;<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="E1:19"/>
<font color="Maroon">a</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">b</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="E3:19"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i/>;<br/>
<a NAME="E4:19"/>
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:19"/>
<font color="Maroon">a</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font>
 <b>by </b><i/>;<br/>


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