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<b>consider </b><font color="Maroon">M</font> being    <a href="monoid_0.html#M1" target="_self">MonoidalExtension</a> of <font color="Maroon">G</font>;<br/>
<a NAME="E2:63_1_1"/><i><font color="Green">E28</font></i>: 
 <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">M</font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">M</font> #) <a href="hidden.html#R1">=</a>  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G</font> #)
 
<b>by </b><i/>;<br/>
<div><i><font color="Green">E39</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">M</font> being    <a href="vectsp_1.html#L1">multLoopStr</a> <b> such that </b><a NAME="E1:63_1_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font>
 ;<br/><b>take </b><font color="Maroon">M</font> = <font color="Maroon">M</font>;<br/><b>thus </b><a NAME="E2:63_1_1_1"/>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">M</font>) <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">G</font>)
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E3:63_1_1_1"/>
for <font color="Olive">N</font> being   <a href="vectsp_1.html#L1">multLoopStr</a>   st <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Olive">N</font> holds <br/><font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">M</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">N</font>)
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E4:63_1_1"/>
(  ex <font color="Olive">M</font> being   <a href="vectsp_1.html#L1">multLoopStr</a>  st <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Olive">M</font> or for <font color="Olive">N</font> being   <a href="vectsp_1.html#L1">multLoopStr</a>   st <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Olive">N</font> holds <br/><font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">M</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">N</font>) )
 
;<br/>
<b>hence </b><a NAME="E5:63_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="vectsp_1.html#L1">multLoopStr</a>  st <br/>( the <a href="group_1.html#U1">mult</a> of <font color="Olive">b<sub>1</sub></font> <a href="funct_4.html#NR1" target="_self">&lt;=</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G</font> &amp; ( for <font color="Olive">M</font> being   <a href="vectsp_1.html#L1">multLoopStr</a>   st <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Olive">M</font> holds <br/>the <a href="vectsp_1.html#U1">unity</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <font color="Olive">M</font> ) )
 <b>by </b><i>, </i>;<br/>


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