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<b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/><b>let </b><font color="Maroon">H1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="monoid_0.html#M2" target="_self">SubStr</a> of <font color="Maroon">G</font>, <font color="Maroon">H2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="monoid_0.html#M2" target="_self">SubStr</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:79"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H1</font>) <a href="tarski.html#R1">c=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H2</font>)
 ;<br/>

<a NAME="E2:79"/><b>then </b>
( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H1</font>) <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">G</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H2</font>) <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">G</font>) &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H1</font>) <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H1</font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H1</font>)</span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H1</font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H1</font>)</span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H2</font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H2</font>)</span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H2</font>) <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H2</font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H2</font>)</span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E3:79"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">G</font>) <a href="realset1.html#K1">||</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H2</font>)</span>)</span> <a href="realset1.html#K1">||</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H1</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">G</font>) <a href="realset1.html#K1">||</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H1</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H1</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">G</font>) <a href="realset1.html#K1">||</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H1</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H2</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">G</font>) <a href="realset1.html#K1">||</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H2</font>) )
 
<b>by </b><i><a class="ref" href="funct_1.html#T82">FUNCT_1:82</a>, <a class="ref" href="grfunc_1.html#T64">GRFUNC_1:64</a></i>;<br/>
<b>hence </b><a NAME="E4:79"/>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H1</font>) <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H2</font>)
 <b>by </b><i><a class="ref" href="relat_1.html#T88">RELAT_1:88</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D23" target="_self">MONOID_0:def 23</a><br/>


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