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<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c3">X3</font>, <font color="Maroon" title="c4">X4</font>, <font color="Maroon" title="c5">X5</font>, <font color="Maroon" title="c6">X6</font>, <font color="Maroon" title="c7">X7</font>, <font color="Maroon" title="c8">X8</font>, <font color="Maroon" title="c9">X9</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

















<b>assume </b><a NAME="E1:128"/><i><font color="Green" title="E91">A1</font></i>: 
( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c9">X9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/>

<b>let </b><font color="Maroon" title="c10">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="mcart_3.html#K29" title="MCART_3:func.29">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font>,<font color="Maroon" title="c3">X3</font>,<font color="Maroon" title="c4">X4</font>,<font color="Maroon" title="c5">X5</font>,<font color="Maroon" title="c6">X6</font>,<font color="Maroon" title="c7">X7</font>,<font color="Maroon" title="c8">X8</font>,<font color="Maroon" title="c9">X9</font></span><a href="mcart_3.html#K29" title="MCART_3:func.29">:]</a></span>;<br/>

<b>consider </b><font color="Maroon" title="c11">xx1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c12">xx2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c13">xx3</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">X3</font>, <font color="Maroon" title="c14">xx4</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">X4</font>, <font color="Maroon" title="c15">xx5</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">X5</font>, <font color="Maroon" title="c16">xx6</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">X6</font>, <font color="Maroon" title="c17">xx7</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c7">X7</font>, <font color="Maroon" title="c18">xx8</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">X8</font>, <font color="Maroon" title="c19">xx9</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c9">X9</font><b> such that </b><br/><a NAME="E3:128"/><i><font color="Green" title="E92">A2</font></i>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><font color="Maroon" title="c11">xx1</font>,<font color="Maroon" title="c12">xx2</font>,<font color="Maroon" title="c13">xx3</font>,<font color="Maroon" title="c14">xx4</font>,<font color="Maroon" title="c15">xx5</font>,<font color="Maroon" title="c16">xx6</font>,<font color="Maroon" title="c17">xx7</font>,<font color="Maroon" title="c18">xx8</font>,<font color="Maroon" title="c19">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
 <b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="ref" href="mcart_3.html#T142" target="_self" title="MCART_3:th.142">Th65</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c10">x</font> = 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<font color="Maroon" title="c12">xx2</font>,<font color="Maroon" title="c13">xx3</font>,<font color="Maroon" title="c14">xx4</font>,<font color="Maroon" title="c15">xx5</font>,<font color="Maroon" title="c16">xx6</font>,<font color="Maroon" title="c17">xx7</font>,<font color="Maroon" title="c18">xx8</font>,<font color="Maroon" title="c19">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
<b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="mcart_3.html#E3:128"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="mcart_3.html#D30" target="_self" title="MCART_3:def.30">Def13</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K31" title="MCART_3:func.31">`2</a> </span>)</span>,<font color="Maroon" title="c13">xx3</font>,<font color="Maroon" title="c14">xx4</font>,<font color="Maroon" title="c15">xx5</font>,<font color="Maroon" title="c16">xx6</font>,<font color="Maroon" title="c17">xx7</font>,<font color="Maroon" title="c18">xx8</font>,<font color="Maroon" title="c19">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
<b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="mcart_3.html#E3:128"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="mcart_3.html#D31" target="_self" title="MCART_3:def.31">Def14</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K31" title="MCART_3:func.31">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K32" title="MCART_3:func.32">`3</a> </span>)</span>,<font color="Maroon" title="c14">xx4</font>,<font color="Maroon" title="c15">xx5</font>,<font color="Maroon" title="c16">xx6</font>,<font color="Maroon" title="c17">xx7</font>,<font color="Maroon" title="c18">xx8</font>,<font color="Maroon" title="c19">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
<b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="mcart_3.html#E3:128"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="mcart_3.html#D32" target="_self" title="MCART_3:def.32">Def15</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K31" title="MCART_3:func.31">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K32" title="MCART_3:func.32">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> </span>)</span>,<font color="Maroon" title="c15">xx5</font>,<font color="Maroon" title="c16">xx6</font>,<font color="Maroon" title="c17">xx7</font>,<font color="Maroon" title="c18">xx8</font>,<font color="Maroon" title="c19">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
<b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="mcart_3.html#E3:128"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="mcart_3.html#D33" target="_self" title="MCART_3:def.33">Def16</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K31" title="MCART_3:func.31">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K32" title="MCART_3:func.32">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K34" title="MCART_3:func.34">`5</a> </span>)</span>,<font color="Maroon" title="c16">xx6</font>,<font color="Maroon" title="c17">xx7</font>,<font color="Maroon" title="c18">xx8</font>,<font color="Maroon" title="c19">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
<b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="mcart_3.html#E3:128"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="mcart_3.html#D34" target="_self" title="MCART_3:def.34">Def17</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K31" title="MCART_3:func.31">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K32" title="MCART_3:func.32">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K34" title="MCART_3:func.34">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K35" title="MCART_3:func.35">`6</a> </span>)</span>,<font color="Maroon" title="c17">xx7</font>,<font color="Maroon" title="c18">xx8</font>,<font color="Maroon" title="c19">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
<b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="mcart_3.html#E3:128"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="mcart_3.html#D35" target="_self" title="MCART_3:def.35">Def18</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K31" title="MCART_3:func.31">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K32" title="MCART_3:func.32">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K34" title="MCART_3:func.34">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K35" title="MCART_3:func.35">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K36" title="MCART_3:func.36">`7</a> </span>)</span>,<font color="Maroon" title="c18">xx8</font>,<font color="Maroon" title="c19">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
<b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="mcart_3.html#E3:128"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="mcart_3.html#D36" target="_self" title="MCART_3:def.36">Def19</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K31" title="MCART_3:func.31">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K32" title="MCART_3:func.32">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K34" title="MCART_3:func.34">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K35" title="MCART_3:func.35">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K36" title="MCART_3:func.36">`7</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K37" title="MCART_3:func.37">`8</a> </span>)</span>,<font color="Maroon" title="c19">xx9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
<b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="mcart_3.html#E3:128"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="mcart_3.html#D37" target="_self" title="MCART_3:def.37">Def20</a></i>
<br/>.= 
<span class="p1"><a href="mcart_3.html#K28" title="MCART_3:func.28">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K30" title="MCART_3:func.30">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K31" title="MCART_3:func.31">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K32" title="MCART_3:func.32">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K33" title="MCART_3:func.33">`4</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K34" title="MCART_3:func.34">`5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K35" title="MCART_3:func.35">`6</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K36" title="MCART_3:func.36">`7</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K37" title="MCART_3:func.37">`8</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">x</font> <a href="mcart_3.html#K38" title="MCART_3:func.38">`9</a> </span>)</span></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span>
<b>by </b><i><a class="txt" href="mcart_3.html#E1:128"><i><font color="Green" title="E91">A1</font></i></a>, <a class="txt" href="mcart_3.html#E3:128"><i><font color="Green" title="E92">A2</font></i></a>, <a class="ref" href="mcart_3.html#D38" target="_self" title="MCART_3:def.38">Def21</a></i>
;<br/>


</div>
