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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/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:14_1"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">A</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">B</font> &amp; <font color="Maroon">B</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">C</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="E3:14_1"/><i><font color="Green">E21</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/><b>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="E5:14_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">B</font> <a href="group_1.html#K1">*</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>by </b><i>, </i>;<br/><a NAME="E6:14_1"/>
<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">E</font></span>)</span> <a href="hidden.html#R1">=</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="E7:14_1"/>
( <font color="Maroon">A</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">B</font> &amp; <font color="Maroon">B</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">C</font> implies <font color="Maroon">A</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">C</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:14"/>
( <font color="Maroon">A</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">B</font> &amp; <font color="Maroon">B</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">C</font> implies <font color="Maroon">A</font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">C</font> )
 ;<br/>


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