<?xml version="1.0"?>
<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> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<i><font color="Green">E51</font></i>:  <a href="group_2.html#K7">carr</a> <span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<br/>.= 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="group_2.html#D7">GROUP_2:def 7</a></i>
;<br/>
<a NAME="E2:69"/>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="group_2.html#T55">GROUP_2:55</a></i>;<br/>
<a NAME="E3:69"/><b>then </b>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E4:69"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E5:69"/><b>then </b><i><font color="Green">E52</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font> = 
 <a href="group_4.html#K5" target="_self">gr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_2.html#K7">carr</a> <span class="p3">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="group_4.html#E1:69"><i><font color="Green">E51</font></i></a>, <a class="txt" href="group_4.html#E5:69"><i><font color="Green">E52</font></i></a>, <a class="ref" href="group_4.html#T40" target="_self">Th40</a></i>
;<br/>

<b>hence </b><a NAME="E7:69"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K8" target="_self">"\/"</a> <span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_2.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div>
