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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>thus </b><a NAME="E1:22"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" target="_self">Def4</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" target="_self">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="group_1.html#D5" target="_self">Def5</a></i>
;<br/>
<b>hence </b><a NAME="E2:22_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="group_1.html#T14" target="_self">Th14</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:22"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span>
 ;<br/>

<b>hence </b><font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K3" target="_self">"</a> </span>)</span> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" target="_self">Def4</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" target="_self">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="group_1.html#D5" target="_self">Def5</a></i>
;<br/><br/>


</div>
