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<b>let </b><font color="Maroon" title="c1">F</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><a NAME="E1:18_1_1"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c1">F</font> is <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a> &amp; <font color="Maroon" title="c1">F</font> is <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">left_unital</a> )
 ;<br/>

<b>take </b>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">F</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D2" title="GROUP_1:def.2">GROUP_1:def 2</a><br/>

<b>let </b><font color="Maroon" title="c2">x</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Scalar</a> of <font color="Maroon" title="c1">F</font>;<br/>

<a NAME="E2:18_1_1"/>
for <font color="Olive" title="b1">F</font> being non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a> <br/> for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">F</font> holds  <font color="Olive" title="b2">x</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Olive" title="b2">x</font>
 
;<br/>
<a NAME="E3:18_1_1"/><b>then </b>
<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">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.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">F</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="txt" href="vectsp_2.html#E1:18_1_1"><i><font color="Green" title="E5">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:18_1_1"/>
( <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">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> )
 <b>by </b><i><a class="txt" href="vectsp_2.html#E1:18_1_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>;<br/>


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