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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">H1</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H3</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>, <font color="Maroon">H2</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>





<b>assume </b><a NAME="E1:75"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">H1</font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">H2</font>
 ;<br/>

<span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">H2</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H1</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H2</font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">H3</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H2</font></span>)</span></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">H2</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font></span>)</span></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H1</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H2</font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">H2</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">H2</font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">H3</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">H2</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E3:75"/>
<font color="Maroon">H1</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">H2</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H3</font>
 <b>by </b><i/>;<br/>


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