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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> be    <a href="hidden.html#M1">set</a> ;<br/>











<b>assume </b><a NAME="E1:11"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="mcart_2.html#K2">[:</a><span class="default"><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></span><a href="mcart_2.html#K2">:]</a></span>
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green">E17</font></i>: 
( not <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; not <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; not <font color="Maroon">c<sub>4</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; not <font color="Maroon">c<sub>5</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; not <font color="Maroon">c<sub>6</sub></font> is <a href="xboole_0.html#V1">empty</a> )
 
<b>by </b><i><a class="ref" href="mcart_2.html#T13">MCART_2:13</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>7</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>8</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>9</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>10</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>11</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>6</sub></font><b> such that </b><br/><a NAME="E4:11"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_2.html#K1">[</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="mcart_2.html#K1">]</a></span>
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:11"><i><font color="Green">E16</font></i></a>, <a class="ref" href="mcart_2.html#T17">MCART_2:17</a></i>;<br/>
<a NAME="E5:11"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K8" target="_self">`1_5</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K9" target="_self">`2_5</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K10" target="_self">`3_5</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K11" target="_self">`4_5</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K12" target="_self">`5_5</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="recdef_2.html#E4:11"><i><font color="Green">E18</font></i></a>, <a class="ref" href="recdef_2.html#D8" target="_self">Def8</a>, <a class="ref" href="recdef_2.html#D9" target="_self">Def9</a>, <a class="ref" href="recdef_2.html#D10" target="_self">Def10</a>, <a class="ref" href="recdef_2.html#D11" target="_self">Def11</a>, <a class="ref" href="recdef_2.html#D12" target="_self">Def12</a></i>;<br/>
<b>hence </b><a NAME="E6:11"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K8" target="_self">`1_5</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K9" target="_self">`2_5</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K10" target="_self">`3_5</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K11" target="_self">`4_5</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K12" target="_self">`5_5</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="recdef_2.html#E2:11"><i><font color="Green">E17</font></i></a></i>;<br/>


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