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<b>set </b><font color="Maroon" title="c2">M</font> =  <a href="algstr_0.html#G4" title="ALGSTR_0:aggr.4">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>)</span>)</span> #);<br/>
<a NAME="E1:54_1_1"/>
 <a href="algstr_0.html#G4" title="ALGSTR_0:aggr.4">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>)</span>)</span> #) is    <a href="monoid_0.html#M1" title="MONOID_0:mode.1">MonoidalExtension</a> of <font color="Maroon" title="c1">G</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:54_1_1_1"/>
 <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="algstr_0.html#G4" title="ALGSTR_0:aggr.4">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>)</span>)</span> #),the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <a href="algstr_0.html#G4" title="ALGSTR_0:aggr.4">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>)</span>)</span> #) #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> #)
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D22" target="_self" title="MONOID_0:def.22">MONOID_0:def 22</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c3">M</font> =  <a href="algstr_0.html#G4" title="ALGSTR_0:aggr.4">multLoopStr</a>(# <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>),<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>),<span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>)</span>)</span> #) as    <a href="monoid_0.html#M1" title="MONOID_0:mode.1">MonoidalExtension</a> of <font color="Maroon" title="c1">G</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c3">M</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">M</font> is <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a> &amp; <font color="Maroon" title="c3">M</font> is <a href="algstr_0.html#V22" title="ALGSTR_0:attr.22">strict</a> )</span><br/>

<b>thus </b><a NAME="E3:54_1_1"/>
<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c3">M</font>) <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c3">M</font>)
 <b>by </b><i><a class="ref" href="monoid_0.html#T4" target="_self" title="MONOID_0:th.4">Th4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D21" target="_self" title="MONOID_0:def.21">MONOID_0:def 21</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">M</font> is <a href="algstr_0.html#V22" title="ALGSTR_0:attr.22">strict</a></span><br/>

<b>thus </b><a NAME="E4:54_1_1"/>
<font color="Maroon" title="c3">M</font> is <a href="algstr_0.html#V22" title="ALGSTR_0:attr.22">strict</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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