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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="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> be  non <a href="struct_0.html#V3">empty</a>  <a href="monoid_0.html#M3" target="_self">MonoidalSubStr</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:78"/><i><font color="Green">E39</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="monoid_0.html#M2" target="_self">SubStr</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="monoid_0.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E3:78"/>
(  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>4</sub></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">c<sub>5</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>5</sub></font> #) &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>3</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) )
 
<b>by </b><i><a class="txt" href="monoid_0.html#E1:78"><i><font color="Green">E39</font></i></a>, <a class="ref" href="monoid_0.html#D25" target="_self">Def25</a>, <a class="ref" href="monoid_0.html#T28" target="_self">Th28</a></i>;<br/>
<b>hence </b><a NAME="E4:78"/>
 <a href="vectsp_1.html#G1">multLoopStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="vectsp_1.html#U1">unity</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G1">multLoopStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="vectsp_1.html#U1">unity</a> of <font color="Maroon">c<sub>3</sub></font> #)
 ;<br/>


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