<?xml version="1.0"?>
<div class="add">

<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">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H2</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H3</font> be  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:74"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">H1</font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">H3</font>
 <b>and </b><br/><a NAME="E2:74"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">H2</font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">H3</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>assume </b><a NAME="E1:74_1"/>
<font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H1</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H2</font>
 ;<br/><b>then consider </b><font color="Maroon">F</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>, <font color="Maroon">I</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E3:74_1"/><i><font color="Green">E34</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">I</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H1</font></span>)</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">H2</font></span>)</span> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="group_4.html#K3" target="_self">Product</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="group_4.html#K4" target="_self">|^</a> <font color="Maroon">I</font></span>)</span> )
 <b>by </b><i/>;<br/><a NAME="E4:74_1"/>
( 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">H3</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H3</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H1</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H2</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H3</font> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H3</font> )
 <b>by </b><i>, , <a class="ref" href="group_2.html#D5">GROUP_2:def 5</a></i>;<br/><a NAME="E5:74_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H1</font></span>)</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">H2</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H3</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/><a NAME="E6:74_1"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">H3</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E7:74_1"/><b>then </b>
<font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5" target="_self">gr</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">H3</font></span>)</span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E8:74_1"/>
<font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H3</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:74"/>
<font color="Maroon">H1</font> <a href="group_4.html#K8" target="_self">"\/"</a> <font color="Maroon">H2</font> is    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">H3</font>
 <b>by </b><i><a class="ref" href="group_2.html#T67">GROUP_2:67</a></i>;<br/>


</div>
