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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>set </b><font color="Maroon">A</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>;<br/>
<b>set </b><font color="Maroon">B</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>;<br/>
<b>set </b><font color="Maroon">h</font> = the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G</font>;<br/>
<b>assume </b><a NAME="E1:55"/><i><font color="Green">E35</font></i>: 
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>
 ;<br/>

<b>hence </b><a NAME="E2:55"/>
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>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_2.html#D5" target="_self">GROUP_2:def 5</a><br/>

<a NAME="E3:55"/>
( the <a href="group_1.html#U1">mult</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> &amp; the <a href="group_1.html#U1">mult</a> of <font color="Maroon">H2</font> <a href="hidden.html#R1">=</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">G</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> &amp; <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">H1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</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">H2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i>, <a class="txt" href="group_2.html#E1"><i><font color="Green">Lemma22</font></i></a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<b>hence </b><a NAME="E4:55"/>
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">H2</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T82">FUNCT_1:82</a></i>;<br/>


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