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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">g</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="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/>





<b>thus </b><a NAME="E1:26"/>
( <font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">g</font> implies <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="group_1.html#K3" target="_self">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E2:26"/><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="group_1.html#K3" target="_self">"</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span>
 ;<br/>

<a NAME="E3:26"/><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="group_1.html#K3" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2" target="_self">1.</a> <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="group_1.html#K3" target="_self">"</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" target="_self">1.</a> <font color="Maroon">G</font></span>)</span></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="group_1.html#K2" target="_self">1.</a> <font color="Maroon">G</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E5:26"/>
<font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">g</font>
 <b>by </b><i>, </i>;<br/>


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