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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="E1:80"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="tarski.html#R1">c=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>3</sub></font>)
 ;<br/>

<a NAME="E2:80"/>
( <font color="Maroon">c<sub>2</sub></font> is    <a href="monoid_0.html#M2" target="_self">SubStr</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> is    <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="E3:80"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is    <a href="monoid_0.html#M6" target="_self">SubStr</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="monoid_0.html#E1:80"><i><font color="Green">E40</font></i></a>, <a class="ref" href="monoid_0.html#T30" target="_self">Th30</a></i>;<br/>
<b>hence </b><a NAME="E4:80"/>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="funct_4.html#NR1" target="_self">&lt;=</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#D23" target="_self">Def23</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D25" target="_self">MONOID_0:def 25</a><br/>

<a NAME="E5:80"/>
( <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="ref" href="monoid_0.html#D25" target="_self">Def25</a></i>;<br/>
<b>hence </b><a NAME="E6:80"/>
the <a href="vectsp_1.html#U1">unity</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


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