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<b>let </b><font color="Maroon" title="c1">R</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">multLoopStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1_1_1"/><i><font color="Green" title="E1">A1</font></i>: 
<font color="Maroon" title="c1">R</font> is <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a>
 <b>and </b><br/><a NAME="E2:1_1_1"/><i><font color="Green" title="E2">A2</font></i>: 
<font color="Maroon" title="c1">R</font> is <a href="vectsp_1.html#V6" title="VECTSP_1:attr.6">right_unital</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">x</font> = 
<font color="Maroon" title="c2">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">R</font></span>)</span>
<b>by </b><i><a class="txt" href="gcd_1.html#E1:1_1_1"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="group_1.html#D16" title="GROUP_1:def.16">GROUP_1:def 16</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="txt" href="gcd_1.html#E2:1_1_1"><i><font color="Green" title="E2">A2</font></i></a>, <a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">VECTSP_1:def 13</a></i>
;<br/>


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