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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">F</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="monoid_0.html#M2" title="MONOID_0:mode.2">SubStr</a> of <font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K9" title="MONOID_0:func.9">*+^</a> ;<br/><b>let </b><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">F</font>;<br/>





<a NAME="E1:127"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">F</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K9" title="MONOID_0:func.9">*+^</a> )
 
<b>by </b><i><a class="ref" href="monoid_0.html#T25" target="_self" title="MONOID_0:th.25">Th25</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">p'</font> = <font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c6">q'</font> = <font color="Maroon" title="c4">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">D</font> <a href="monoid_0.html#K9" title="MONOID_0:func.9">*+^</a> </span>)</span> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c3">p</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c4">q</font> = 
<font color="Maroon" title="c5">p'</font> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c6">q'</font>
<b>by </b><i><a class="ref" href="monoid_0.html#T27" target="_self" title="MONOID_0:th.27">Th27</a></i>
<br/>.= 
<font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c4">q</font>
<b>by </b><i><a class="ref" href="monoid_0.html#D34" target="_self" title="MONOID_0:def.34">Def34</a></i>
;<br/>


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