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<b>let </b><font color="Maroon" title="c3">M'</font> be    <a href="monoid_0.html#M3" title="MONOID_0:mode.3">MonoidalSubStr</a> of <font color="Maroon" title="c2">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="monoid_0.html#M3" title="MONOID_0:mode.3">MonoidalSubStr</a> of <font color="Maroon" title="c1">G</font></span><br/>

<a NAME="E1:69_1_1"/>
( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c3">M'</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">M</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">M</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>) &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c3">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">M</font>) &amp; ( for <font color="Olive" title="b1">N</font> being   <a href="algstr_0.html#L4" title="ALGSTR_0:struct.4">multLoopStr</a>   st <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">N</font> holds <br/><font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">M</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive" title="b1">N</font>) ) )
 
<b>by </b><i><a class="ref" href="monoid_0.html#D24" target="_self" title="MONOID_0:def.24">Def24</a></i>;<br/>
<b>hence </b><a NAME="E2:69_1_1"/>
( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c3">M'</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>) &amp; ( for <font color="Olive" title="b1">N</font> being   <a href="algstr_0.html#L4" title="ALGSTR_0:struct.4">multLoopStr</a>   st <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">N</font> holds <br/><font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c3">M'</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive" title="b1">N</font>) ) )
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D24" target="_self" title="MONOID_0:def.24">MONOID_0:def 24</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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