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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" target="_self">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H2</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">H3</font> be    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">G</font>;<br/>







<b>assume </b><a NAME="E1:92"/>
<font color="Maroon">H1</font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">H2</font>
 ;<br/>

<a NAME="E2:92"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 
<b>by </b><i><a class="txt" href="group_2.html#E1"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<a NAME="E3:92"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H3</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H3</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T26">XBOOLE_1:26</a></i>;<br/>
<a NAME="E4:92"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="group_2.html#K9" target="_self">/\</a> <font color="Maroon">H3</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H3</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:92"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="group_2.html#K9" target="_self">/\</a> <font color="Maroon">H3</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">H2</font> <a href="group_2.html#K9" target="_self">/\</a> <font color="Maroon">H3</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:92"/>
<font color="Maroon">H1</font> <a href="group_2.html#K9" target="_self">/\</a> <font color="Maroon">H3</font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">H2</font> <a href="group_2.html#K9" target="_self">/\</a> <font color="Maroon">H3</font>
 <b>by </b><i/>;<br/>


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