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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#V3">Group-like</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/><b>let </b><font color="Maroon">g1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">g2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H</font> be    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">h1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>;<br/><b>let </b><font color="Maroon">h2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>;<br/>











<b>assume </b><a NAME="E1:38"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">h1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g1</font> &amp; <font color="Maroon">h2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> )
 ;<br/>

<a NAME="E2:38"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">h1</font> <a href="group_1.html#K1">*</a> <font color="Maroon">h2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">h1</font>,<font color="Maroon">h2</font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="txt" href="group_2.html#E1"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<b>thus </b><a NAME="E3:38"/>
<font color="Maroon">h1</font> <a href="group_1.html#K1">*</a> <font color="Maroon">h2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g1</font> <a href="group_1.html#K1">*</a> <font color="Maroon">g2</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>


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