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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>













<b>assume </b><a NAME="E1:23"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <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>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="mcart_4.html#K2" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="mcart_4.html#K2" target="_self">:]</a></span>;<br/>

<b>consider </b><font color="Maroon">c<sub>9</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>10</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>11</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>12</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>13</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>14</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>15</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>7</sub></font><b> such that </b><br/><a NAME="E3:23"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_4.html#K1" target="_self">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<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></span><a href="mcart_4.html#K1" target="_self">]</a></span>
 <b>by </b><i><a class="txt" href="mcart_4.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="ref" href="mcart_4.html#T21" target="_self">Th21</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>8</sub></font> = 
<span class="p1"><a href="mcart_4.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K3" target="_self">`1</a> </span>)</span>,<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></span><a href="mcart_4.html#K1" target="_self">]</a></span>
<b>by </b><i><a class="txt" href="mcart_4.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="mcart_4.html#E3:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mcart_4.html#D3" target="_self">Def3</a></i>
<br/>.= 
<span class="p1"><a href="mcart_4.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K3" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K4" target="_self">`2</a> </span>)</span>,<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></span><a href="mcart_4.html#K1" target="_self">]</a></span>
<b>by </b><i><a class="txt" href="mcart_4.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="mcart_4.html#E3:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mcart_4.html#D4" target="_self">Def4</a></i>
<br/>.= 
<span class="p1"><a href="mcart_4.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K3" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K4" target="_self">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K5" target="_self">`3</a> </span>)</span>,<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></span><a href="mcart_4.html#K1" target="_self">]</a></span>
<b>by </b><i><a class="txt" href="mcart_4.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="mcart_4.html#E3:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mcart_4.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1"><a href="mcart_4.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K3" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K4" target="_self">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K5" target="_self">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K6" target="_self">`4</a> </span>)</span>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="mcart_4.html#K1" target="_self">]</a></span>
<b>by </b><i><a class="txt" href="mcart_4.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="mcart_4.html#E3:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mcart_4.html#D6" target="_self">Def6</a></i>
<br/>.= 
<span class="p1"><a href="mcart_4.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K3" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K4" target="_self">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K5" target="_self">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K6" target="_self">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K7" target="_self">`5</a> </span>)</span>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="mcart_4.html#K1" target="_self">]</a></span>
<b>by </b><i><a class="txt" href="mcart_4.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="mcart_4.html#E3:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mcart_4.html#D7" target="_self">Def7</a></i>
<br/>.= 
<span class="p1"><a href="mcart_4.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K3" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K4" target="_self">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K5" target="_self">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K6" target="_self">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K7" target="_self">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K8" target="_self">`6</a> </span>)</span>,<font color="Maroon">c<sub>15</sub></font></span><a href="mcart_4.html#K1" target="_self">]</a></span>
<b>by </b><i><a class="txt" href="mcart_4.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="mcart_4.html#E3:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mcart_4.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1"><a href="mcart_4.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K3" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K4" target="_self">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K5" target="_self">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K6" target="_self">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K7" target="_self">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K8" target="_self">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="mcart_4.html#K9" target="_self">`7</a> </span>)</span></span><a href="mcart_4.html#K1" target="_self">]</a></span>
<b>by </b><i><a class="txt" href="mcart_4.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="mcart_4.html#E3:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mcart_4.html#D9" target="_self">Def9</a></i>
;<br/>


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