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<b>let </b><font color="Maroon">M</font> be  non <a href="struct_0.html#V3">empty</a> <a href="vectsp_2.html#V1">well-unital</a> <a href="monoid_0.html#V17" target="_self">uniquely-decomposable</a>  <a href="vectsp_1.html#L1">multLoopStr</a> ;<br/><b>let </b><font color="Maroon">N</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">M</font>;<br/>



<a NAME="E1:88"/>
( <font color="Maroon">N</font> is    <a href="monoid_0.html#M2" target="_self">SubStr</a> of <font color="Maroon">M</font> &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">M</font>) <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">M</font>) &amp; <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="Maroon">N</font>) )
 
<b>by </b><i>, <a class="ref" href="monoid_0.html#D2" target="_self">Def2</a>, </i>;<br/>
<b>hence </b><a NAME="E2:88"/>
<font color="Maroon">N</font> is <a href="monoid_0.html#V17" target="_self">uniquely-decomposable</a>
 <b>by </b><i><a class="ref" href="monoid_0.html#T3" target="_self">Th3</a></i>;<br/>


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