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









<b>assume </b><a NAME="E1:7"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K4">[:</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></span><a href="zfmisc_1.html#K4">:]</a></span>
 ;<br/>

<a NAME="E2:7"/><b>then </b><i><font color="Green">E11</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> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T55">MCART_1:55</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</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>7</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>8</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>9</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E4:7"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="mcart_1.html#K4">]</a></span>
 <b>by </b><i><a class="txt" href="recdef_2.html#E1:7"><i><font color="Green">E10</font></i></a>, <a class="ref" href="domain_1.html#T31">DOMAIN_1:31</a></i>;<br/>
<a NAME="E5:7"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K4" target="_self">`1_4</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K5" target="_self">`2_4</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#K6" target="_self">`3_4</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#K7" target="_self">`4_4</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="txt" href="recdef_2.html#E4:7"><i><font color="Green">E12</font></i></a>, <a class="ref" href="recdef_2.html#D4" target="_self">Def4</a>, <a class="ref" href="recdef_2.html#D5" target="_self">Def5</a>, <a class="ref" href="recdef_2.html#D6" target="_self">Def6</a>, <a class="ref" href="recdef_2.html#D7" target="_self">Def7</a></i>;<br/>
<b>hence </b><a NAME="E6:7"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="recdef_2.html#K4" target="_self">`1_4</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#K5" target="_self">`2_4</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#K6" target="_self">`3_4</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#K7" target="_self">`4_4</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="recdef_2.html#E2:7"><i><font color="Green">E11</font></i></a></i>;<br/>


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