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

<b>set </b><font color="Maroon">c<sub>1</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>() : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) </span>}</span> ;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being  <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E2:2_1"/><i><font color="Green">E2</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>]
 <b>by </b><i><a class="txt" href="group_4.html#E1:2"><i><font color="Green">E1</font></i></a></i>;<br/>
<a NAME="E3:2_1"/><i><font color="Green">E3</font></i>: 
 <a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>() : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="group_4.html#E2:2_1"><i><font color="Green">E2</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>() : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>() <b>by </b><i><a class="ref" href="setfam_1.html#T8">SETFAM_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:2_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>() : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E3:2_1_1"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E4:2_1_1"/><i><font color="Green">E5</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 ;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E6:2_1_1"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>6</sub></font>] )
 <b>by </b><i><a class="txt" href="group_4.html#E4:2_1_1"><i><font color="Green">E5</font></i></a></i>;<br/><a NAME="E7:2_1_1"/>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">F<sub>1</sub></font>() <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="group_2.html#T55">GROUP_2:55</a></i>;<br/><b>hence </b><a NAME="E8:2_1_1"/>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="group_4.html#E3:2_1_1"><i><font color="Green">E4</font></i></a>, <a class="txt" href="group_4.html#E6:2_1_1"><i><font color="Green">E6</font></i></a>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:2_1"/><b>then </b><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="group_4.html#E3:2_1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<div><i><font color="Green">E5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>assume </b><a NAME="E1:2_1_2"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:2_1_2_1"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>() : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E3:2_1_2_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E4:2_1_2_1"/><i><font color="Green">E9</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 ;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E6:2_1_2_1"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>8</sub></font>] )
 <b>by </b><i><a class="txt" href="group_4.html#E4:2_1_2_1"><i><font color="Green">E9</font></i></a></i>;<br/><a NAME="E7:2_1_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="group_4.html#E1:2_1_2"><i><font color="Green">E6</font></i></a>, <a class="txt" href="group_4.html#E1:2_1_2_1"><i><font color="Green">E7</font></i></a>, <a class="txt" href="group_4.html#E3:2_1_2_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="group_4.html#E6:2_1_2_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/><a NAME="E8:2_1_2_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/><a NAME="E9:2_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="group_2.html#T59">GROUP_2:59</a></i>;<br/><b>hence </b><a NAME="E10:2_1_2_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="group_4.html#E3:2_1_2_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="group_4.html#E6:2_1_2_1"><i><font color="Green">E10</font></i></a>, <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="E3:2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="group_4.html#E3:2_1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>assume </b><a NAME="E1:2_1_3"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:2_1_3_1"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>() : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>2</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E3:2_1_3_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E4:2_1_3_1"/><i><font color="Green">E9</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 ;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E6:2_1_3_1"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>7</sub></font>] )
 <b>by </b><i><a class="txt" href="group_4.html#E4:2_1_3_1"><i><font color="Green">E9</font></i></a></i>;<br/><a NAME="E7:2_1_3_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="group_4.html#E1:2_1_3"><i><font color="Green">E6</font></i></a>, <a class="txt" href="group_4.html#E1:2_1_3_1"><i><font color="Green">E7</font></i></a>, <a class="txt" href="group_4.html#E3:2_1_3_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="group_4.html#E6:2_1_3_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/><a NAME="E8:2_1_3_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/><a NAME="E9:2_1_3_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K3">"</a>  <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="group_2.html#T60">GROUP_2:60</a></i>;<br/><b>hence </b><a NAME="E10:2_1_3_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="group_4.html#E3:2_1_3_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="group_4.html#E6:2_1_3_1"><i><font color="Green">E10</font></i></a>, <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="E3:2_1_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="group_4.html#E3:2_1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:2_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">Subgroup</a> of <font color="Maroon">F<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>  <a href="setfam_1.html#K1">meet</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">F<sub>1</sub></font>() : ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">F<sub>1</sub></font>() st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>3</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>3</sub></font>] ) </span>}</span> 
 <b>by </b><i><a class="txt" href="group_4.html#E6:2_1"><i><font color="Green">E4</font></i></a>, <a class="txt" href="group_4.html#E7:2_1"><i><font color="Green">E5</font></i></a>, <a class="ref" href="group_2.html#T61">GROUP_2:61</a></i>;<br/>


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