<?xml version="1.0"?>
<div class="add">

<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="algstr_0.html#L4" title="ALGSTR_0:struct.4">multLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">H2</font> being 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>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">H2</font> holds <br/><font color="Olive" title="b1">H1</font> is    <a href="monoid_0.html#M7" title="MONOID_0:mode.7">MonoidalSubStr</a> of <font color="Olive" title="b2">H2</font></span><br/><b>let </b><font color="Maroon" title="c2">H1</font>, <font color="Maroon" title="c3">H2</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">H1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">H2</font> implies <font color="Maroon" title="c2">H1</font> is    <a href="monoid_0.html#M7" title="MONOID_0:mode.7">MonoidalSubStr</a> of <font color="Maroon" title="c3">H2</font> )</span><br/>



<b>assume </b><a NAME="E1:77"/><i><font color="Green" title="E39">A1</font></i>: 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">H1</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">H2</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">H1</font> is    <a href="monoid_0.html#M7" title="MONOID_0:mode.7">MonoidalSubStr</a> of <font color="Maroon" title="c3">H2</font></span><br/>

<a NAME="E2:77"/>
( <font color="Maroon" title="c2">H1</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" title="c3">H2</font> is    <a href="monoid_0.html#M2" title="MONOID_0:mode.2">SubStr</a> of <font color="Maroon" title="c1">M</font> )
 
<b>by </b><i><a class="ref" href="monoid_0.html#T23" target="_self" title="MONOID_0:th.23">Th23</a></i>;<br/>
<a NAME="E3:77"/><b>then </b>
<font color="Maroon" title="c2">H1</font> is    <a href="monoid_0.html#M6" title="MONOID_0:mode.6">SubStr</a> of <font color="Maroon" title="c3">H2</font>
 
<b>by </b><i><a class="txt" href="monoid_0.html#E1:77"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="monoid_0.html#T30" target="_self" title="MONOID_0:th.30">Th30</a></i>;<br/>
<b>hence </b><a NAME="E4:77"/>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">H1</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c3">H2</font>)
 <b>by </b><i><a class="ref" href="monoid_0.html#D23" target="_self" title="MONOID_0:def.23">Def23</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D25" target="_self" title="MONOID_0:def.25">MONOID_0:def 25</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c3">H2</font></span><br/>

<a NAME="E5:77"/>
( <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">H1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">M</font>) &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c3">H2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">M</font>) )
 
<b>by </b><i><a class="ref" href="monoid_0.html#D25" target="_self" title="MONOID_0:def.25">Def25</a></i>;<br/>
<b>hence </b><a NAME="E6:77"/>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c2">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c3">H2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
