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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a>  <a href="vectsp_1.html#L1">multLoopStr</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>, <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="E1:15"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:15"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:15"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="gcd_1.html#E1:15"><i><font color="Green">E8</font></i></a>, <a class="ref" href="gcd_1.html#D1" target="_self">Def1</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="gcd_1.html#E5:15"><i><font color="Green">E10</font></i></a>, <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gcd_1.html#E3:15"><i><font color="Green">E9</font></i></a>, <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
;<br/>
<b>hence </b><a NAME="E7:15"/>
<font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="gcd_1.html#R1" target="_self">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="gcd_1.html#D1" target="_self">Def1</a></i>;<br/>


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