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<b>set </b><font color="Maroon">c<sub>4</sub></font> = <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> <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>3</sub></font></span>)</span>;<br/>
<a NAME="E1:80_1_1"/>
(  <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> &amp;  <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>3</sub></font> )
 
<b>by </b><i><a class="ref" href="group_2.html#T55" target="_self">Th55</a></i>;<br/>
<a NAME="E2:80_1_1"/><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> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E3:80_1_1"/><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" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <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" target="_self">carr</a> <font color="Maroon">c<sub>3</sub></font> )
 
;<br/>
<a NAME="E4:80_1_1"/><b>then </b><i><font color="Green">E54</font></i>: 
<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> <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>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<div><i><font color="Green">E55</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:80_1_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</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> <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>3</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</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> <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>3</sub></font></span>)</span> )
 ;<br/><a NAME="E2:80_1_1_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:80_1_1_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="group_2.html#T89" target="_self">Th89</a></i>;<br/><b>hence </b><a NAME="E4:80_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</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> <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>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:80_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</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> <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>3</sub></font></span>)</span>
 ;<br/><a NAME="E2:80_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:80_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="group_2.html#T90" target="_self">Th90</a></i>;<br/><b>hence </b><a NAME="E4:80_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R2">in</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> <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>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:80_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being <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> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <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>2</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>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="group_2.html#E4:80_1_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="group_2.html#E5:80_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="group_2.html#T61" target="_self">Th61</a></i>;<br/>


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