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<b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>11</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>12</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>13</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>14</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>15</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>16</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>17</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>8</sub></font><b> such that </b><br/><a NAME="E2:24_3_2"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_5.html#K1" target="_self">[</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>17</sub></font></span><a href="mcart_5.html#K1" target="_self">]</a></span>
 <b>by </b><i><a class="txt" href="mcart_5.html#E1:24"><i><font color="Green">E11</font></i></a>, <a class="ref" href="mcart_5.html#T23" target="_self">Th23</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>19</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>assume </b><a NAME="E3:24_3_2"/>
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>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font>, <font color="Olive">b<sub>8</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_5.html#K1" target="_self">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<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>,<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font></span><a href="mcart_5.html#K1" target="_self">]</a></span> holds <br/><font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font>
 ;<br/>

<a NAME="E4:24_3_2"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="mcart_5.html#E2:24_3_2"><i><font color="Green">E12</font></i></a></i>;<br/>
<b>assume </b><a NAME="E5:24_3_2"/>
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>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font>, <font color="Olive">b<sub>8</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_5.html#K1" target="_self">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<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>,<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>8</sub></font></span><a href="mcart_5.html#K1" target="_self">]</a></span> holds <br/><font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font>
 ;<br/>

<b>hence </b><a NAME="E6:24_3_2"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="mcart_5.html#E2:24_3_2"><i><font color="Green">E12</font></i></a>, <a class="txt" href="mcart_5.html#E4:24_3_2"><i><font color="Green">E13</font></i></a></i>;<br/>


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