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<b>let </b><font color="Maroon" title="c2">H</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="monoid_0.html#M2" title="MONOID_0:mode.2">SubStr</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">H</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D1" target="_self" title="MONOID_0:def.1">MONOID_0:def 1</a><br/>



<a NAME="E1:89_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">H</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">G</font>)
 
<b>by </b><i><a class="ref" href="monoid_0.html#T25" target="_self" title="MONOID_0:th.25">Th25</a></i>;<br/>
<a NAME="E2:89_1_1"/><b>then </b>
<font color="Maroon" title="c3">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:89_1_1"/>
<font color="Maroon" title="c3">a</font> is   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>
 ;<br/>


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