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<b>let </b><font color="Maroon">G1</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">G2</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">G3</font> be   <a href="group_1.html#NM1">Group</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:54"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">G1</font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">G2</font>
 <b>and </b><br/><a NAME="E2:54"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">G2</font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">G3</font>
 ;<br/>

<b>set </b><font color="Maroon">A</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font>;<br/>
<b>set </b><font color="Maroon">B</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font>;<br/>
<b>set </b><font color="Maroon">C</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G3</font>;<br/>
<b>set </b><font color="Maroon">h</font> = the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G3</font>;<br/>
<a NAME="E3:54"/><i><font color="Green">E47</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G3</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="E4:54"/><b>then </b><i><font color="Green">E49</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G3</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:54"/><i><font color="Green">E50</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G1</font> = 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G2</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font>
<b>by </b><i>, <a class="txt" href="group_2.html#E1"><i><font color="Green">Lemma22</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G3</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font></span>)</span> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font>
<b>by </b><i>, <a class="txt" href="group_2.html#E1"><i><font color="Green">Lemma22</font></i></a></i>
<br/>.= 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G3</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T82">FUNCT_1:82</a></i>
;<br/>
<b>hence </b><a NAME="E7:54"/>
<font color="Maroon">G1</font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">G3</font>
 <b>by </b><i>, <a class="txt" href="group_2.html#E1"><i><font color="Green">Lemma22</font></i></a></i>;<br/>


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