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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>assume </b><a NAME="E1:56"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">g</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>  st <font color="Olive">g</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H1</font> holds <br/><font color="Olive">g</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H2</font>
 ;<br/>

<a NAME="E2:56"/>
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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:56_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H1</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">g</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H1</font> ;<br/>
<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">g</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> <b>by </b><i/>;<br/>
<a NAME="E4:56_1"/>
<font color="Maroon">g</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H1</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E5:56_1"/><b>then </b>
<font color="Maroon">g</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H2</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:56_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H2</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:56"/>
<font color="Maroon">H1</font> is    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">H2</font>
 <b>by </b><i/>;<br/>


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