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<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="vectsp_1.html#G1">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span> #);<br/>
<a NAME="E1:57_1_1"/>
 <a href="vectsp_1.html#G1">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span> #) is    <a href="monoid_0.html#M1" target="_self">MonoidalExtension</a> of <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:57_1_1_1"/>
 <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <a href="vectsp_1.html#G1">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span> #),the <a href="group_1.html#U1">mult</a> of <a href="vectsp_1.html#G1">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span> #) #) <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>1</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> #)
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D22" target="_self">MONOID_0:def 22</a><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="vectsp_1.html#G1">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span> #) as    <a href="monoid_0.html#M1" target="_self">MonoidalExtension</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E3:57_1_1"/>
<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>3</sub></font>) <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>3</sub></font>)
 <b>by </b><i><a class="ref" href="monoid_0.html#T4" target="_self">Th4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D21" target="_self">MONOID_0:def 21</a><br/>

<b>thus </b><a NAME="E4:57_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="vectsp_1.html#V1">strict</a>
 ;<br/>


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