<?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_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>thus </b><a NAME="E1:87"/>
( <font color="Maroon">c<sub>3</sub></font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="group_2.html#K9" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="group_2.html#R1" target="_self">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="87_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:87_1"/>
<font color="Maroon">c<sub>3</sub></font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:87_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="group_2.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E3:87_1"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="group_2.html#K9" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="group_2.html#D10" target="_self">Def10</a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<b>hence </b><a NAME="E4:87_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="group_2.html#K9" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="group_2.html#R1" target="_self">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="group_2.html#T68" target="_self">Th68</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:87"/>
<font color="Maroon">c<sub>3</sub></font> <a href="group_2.html#K9" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="group_2.html#R1" target="_self">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then </b>the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_2.html#D10" target="_self">Def10</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>

;<br/>
<a NAME="E4:87"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E5:87"/>
<font color="Maroon">c<sub>3</sub></font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="group_2.html#T66" target="_self">Th66</a></i>;<br/>


</div>
