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<b>let </b><font color="Maroon" title="c1">M</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a> <a href="monoid_0.html#V17" title="MONOID_0:attr.17">uniquely-decomposable</a>  <a href="algstr_0.html#L4" title="ALGSTR_0:struct.4">multLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">N</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="monoid_0.html#M3" title="MONOID_0:mode.3">MonoidalSubStr</a> of <font color="Maroon" title="c1">M</font>;<br/>



<a NAME="E1:85"/>
( <font color="Maroon" title="c2">N</font> is    <a href="monoid_0.html#M2" title="MONOID_0:mode.2">SubStr</a> of <font color="Maroon" title="c1">M</font> &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">M</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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">M</font>) &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">M</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">N</font>) )
 
<b>by </b><i><a class="ref" href="monoid_0.html#D25" target="_self" title="MONOID_0:def.25">Def25</a>, <a class="ref" href="monoid_0.html#T19" target="_self" title="MONOID_0:th.19">Th19</a>, <a class="ref" href="monoid_0.html#T23" target="_self" title="MONOID_0:th.23">Th23</a></i>;<br/>
<b>hence </b><a NAME="E2:85"/>
<font color="Maroon" title="c2">N</font> is <a href="monoid_0.html#V17" title="MONOID_0:attr.17">uniquely-decomposable</a>
 <b>by </b><i><a class="ref" href="monoid_0.html#T38" target="_self" title="MONOID_0:th.38">Th38</a></i>;<br/>


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