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

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">c<sub>3</sub></font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="graph_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] means ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span>ex <font color="Olive">b<sub>2</sub></font> being  <a href="graph_1.html#NM1">Graph</a>ex <font color="Olive">b<sub>3</sub></font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ex <font color="Olive">b<sub>4</sub></font> being   <a href="hidden.html#M1">set</a> ex <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="mcart_1.html#K8">`1</a>  &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="mcart_1.html#K9">`2</a>  &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="mcart_1.html#K10">`3</a>  &amp; <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="mcart_1.html#K11">`4</a>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="graph_1.html#G1" target="_self">MultiGraphStruct</a>(# <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> #) &amp; <font color="Olive">b<sub>2</sub></font> is    <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">c<sub>3</sub></font> );<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:41_1_1"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] means ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span>ex <font color="Olive">b<sub>2</sub></font> being <a href="graph_1.html#V1" target="_self">strict</a> <a href="graph_1.html#NM1">Graph</a>ex <font color="Olive">b<sub>3</sub></font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ex <font color="Olive">b<sub>4</sub></font> being   <a href="hidden.html#M1">set</a> ex <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="mcart_1.html#K8">`1</a>  &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="mcart_1.html#K9">`2</a>  &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="mcart_1.html#K10">`3</a>  &amp; <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="mcart_1.html#K11">`4</a>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="graph_1.html#G1" target="_self">MultiGraphStruct</a>(# <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> #) &amp; <font color="Olive">b<sub>2</sub></font> is    <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> );<br/>
<a NAME="E4:41_1_1"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>] holds <br/><font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font>
 
;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:41_1_1"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> iff ex <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>] ) )
 <b>from </b><i><a class="ref" href="tarski.html#S1">TARSKI:sch 1</a>(<a class="txt" href="graph_1.html#E4:41_1_1"><i><font color="Green">E24</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon">c<sub>8</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E7:41_1_1"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> implies <font color="Maroon">c<sub>9</sub></font> is  <a href="graph_1.html#V1" target="_self">strict</a>  <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">c<sub>3</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:41_1_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:41_1_1_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>9</sub></font>] )
 
<b>by </b><i><a class="txt" href="graph_1.html#E6:41_1_1"><i><font color="Green">E25</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:41_1_1_1"/>
<font color="Maroon">c<sub>9</sub></font> is  <a href="graph_1.html#V1" target="_self">strict</a>  <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


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

<b>assume </b><a NAME="E8:41_1_1"/>
<font color="Maroon">c<sub>9</sub></font> is  <a href="graph_1.html#V1" target="_self">strict</a>  <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font> as  <a href="graph_1.html#V1" target="_self">strict</a>  <a href="graph_1.html#M3" target="_self">Subgraph</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<a NAME="E10:41_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>9</sub></font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_2"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default">the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">c<sub>10</sub></font>,the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>10</sub></font>,the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">c<sub>10</sub></font>,the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">c<sub>10</sub></font></span><a href="mcart_1.html#K4">]</a></span>;<br/>

<a NAME="E1:41_1_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:41_1_1_2_1"/><i><font color="Green">E26</font></i>: 
the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="graph_1.html#D17" target="_self">Def17</a></i>;<br/>
<a NAME="E2:41_1_1_2_1"/><i><font color="Green">E27</font></i>: 
the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="graph_1.html#D17" target="_self">Def17</a></i>;<br/>
<a NAME="E3:41_1_1_2_1"/>
( the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="graph_1.html#E33"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:41_1_1_2_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span>
 <b>by </b><i><a class="txt" href="graph_1.html#E1:41_1_1_2_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="graph_1.html#E2:41_1_1_2_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="mcart_1.html#T84">MCART_1:84</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>11</sub></font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="partfun1.html#K4">PFuncs</a> the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="zfmisc_1.html#K4">:]</a></span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = the <a href="graph_1.html#U1" target="_self">Vertices</a> of <font color="Maroon">c<sub>10</sub></font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="graph_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> = the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>10</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = the <a href="graph_1.html#U3" target="_self">Source</a> of <font color="Maroon">c<sub>10</sub></font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>13</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = the <a href="graph_1.html#U4" target="_self">Target</a> of <font color="Maroon">c<sub>10</sub></font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>13</sub></font> ;<br/>
<a NAME="E6:41_1_1_2"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="mcart_1.html#K8">`1</a>  &amp; the <a href="graph_1.html#U2" target="_self">Edges</a> of <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="mcart_1.html#K9">`2</a>  &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="mcart_1.html#K10">`3</a>  &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="mcart_1.html#K11">`4</a>  )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T59">MCART_1:59</a></i>;<br/>
<b>hence </b><a NAME="E7:41_1_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="graph_1.html#E3:41_1_1"><i><font color="Green">E23</font></i></a></i>;<br/>

<b>thus </b><a NAME="E8:41_1_1_2"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>9</sub></font>]
 <b>by </b><i><a class="txt" href="graph_1.html#E6:41_1_1_2"><i><font color="Green">E26</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E11:41_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="graph_1.html#E6:41_1_1"><i><font color="Green">E25</font></i></a></i>;<br/>


</div>
