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<b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L1" target="_self">multLoopStr</a> ;<br/>

<b>assume </b><a NAME="E1:27_1_1"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="group_1.html#V2">unital</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:27_1_1"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="group_1.html#D2">GROUP_1:def 2</a></i>;<br/>
<a NAME="E4:27_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="vectsp_1.html#E1:27_1_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="vectsp_1.html#E3:27_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:27_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="vectsp_1.html#E3:27_1_1"><i><font color="Green">E12</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D19" target="_self">VECTSP_1:def 19</a><br/>

<b>thus </b><a NAME="E6:27_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="vectsp_1.html#E3:27_1_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="vectsp_1.html#E4:27_1_1"><i><font color="Green">E13</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D13" target="_self">VECTSP_1:def 13</a><br/>


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