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<b>let </b><font color="Maroon" title="c1">y</font>, <font color="Maroon" title="c2">X1</font>, <font color="Maroon" title="c3">X2</font>, <font color="Maroon" title="c4">X3</font>, <font color="Maroon" title="c5">X4</font>, <font color="Maroon" title="c6">X5</font>, <font color="Maroon" title="c7">X6</font>, <font color="Maroon" title="c8">X7</font>, <font color="Maroon" title="c9">X8</font>, <font color="Maroon" title="c10">X9</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_3.html#K29" title="MCART_3:func.29">[:</a><span class="default"><font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font>,<font color="Maroon" title="c4">X3</font>,<font color="Maroon" title="c5">X4</font>,<font color="Maroon" title="c6">X5</font>,<font color="Maroon" title="c7">X6</font>,<font color="Maroon" title="c8">X7</font>,<font color="Maroon" title="c9">X8</font>,<font color="Maroon" title="c10">X9</font></span><a href="mcart_3.html#K29" title="MCART_3:func.29">:]</a></span> implies  ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">x5</font>, <font color="Olive" title="b6">x6</font>, <font color="Olive" title="b7">x7</font>, <font color="Olive" title="b8">x8</font>, <font color="Olive" title="b9">x9</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X1</font> &amp; <font color="Olive" title="b2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X2</font> &amp; <font color="Olive" title="b3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X3</font> &amp; <font color="Olive" title="b4">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X4</font> &amp; <font color="Olive" title="b5">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X5</font> &amp; <font color="Olive" title="b6">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X6</font> &amp; <font color="Olive" title="b7">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X7</font> &amp; <font color="Olive" title="b8">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X8</font> &amp; <font color="Olive" title="b9">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">X9</font> &amp; <font color="Maroon" title="c1">y</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="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font>,<font color="Olive" title="b5">x5</font>,<font color="Olive" title="b6">x6</font>,<font color="Olive" title="b7">x7</font>,<font color="Olive" title="b8">x8</font>,<font color="Olive" title="b9">x9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span> ) )</span><br/>



















<b>assume </b><a NAME="E1:141"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_3.html#K29" title="MCART_3:func.29">[:</a><span class="default"><font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font>,<font color="Maroon" title="c4">X3</font>,<font color="Maroon" title="c5">X4</font>,<font color="Maroon" title="c6">X5</font>,<font color="Maroon" title="c7">X6</font>,<font color="Maroon" title="c8">X7</font>,<font color="Maroon" title="c9">X8</font>,<font color="Maroon" title="c10">X9</font></span><a href="mcart_3.html#K29" title="MCART_3:func.29">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">x5</font>, <font color="Olive" title="b6">x6</font>, <font color="Olive" title="b7">x7</font>, <font color="Olive" title="b8">x8</font>, <font color="Olive" title="b9">x9</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X1</font> &amp; <font color="Olive" title="b2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X2</font> &amp; <font color="Olive" title="b3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X3</font> &amp; <font color="Olive" title="b4">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X4</font> &amp; <font color="Olive" title="b5">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X5</font> &amp; <font color="Olive" title="b6">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X6</font> &amp; <font color="Olive" title="b7">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X7</font> &amp; <font color="Olive" title="b8">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X8</font> &amp; <font color="Olive" title="b9">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">X9</font> &amp; <font color="Maroon" title="c1">y</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="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font>,<font color="Olive" title="b5">x5</font>,<font color="Olive" title="b6">x6</font>,<font color="Olive" title="b7">x7</font>,<font color="Olive" title="b8">x8</font>,<font color="Olive" title="b9">x9</font></span><a href="mcart_3.html#K28" title="MCART_3:func.28">]</a></span> )</span><br/>

<b>then consider </b><font color="Maroon" title="c11">x12345678</font>, <font color="Maroon" title="c12">x9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:141"/><i><font color="Green" title="E92">A1</font></i>: 
<font color="Maroon" title="c11">x12345678</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_3.html#K19" title="MCART_3:func.19">[:</a><span class="default"><font color="Maroon" title="c2">X1</font>,<font color="Maroon" title="c3">X2</font>,<font color="Maroon" title="c4">X3</font>,<font color="Maroon" title="c5">X4</font>,<font color="Maroon" title="c6">X5</font>,<font color="Maroon" title="c7">X6</font>,<font color="Maroon" title="c8">X7</font>,<font color="Maroon" title="c9">X8</font></span><a href="mcart_3.html#K19" title="MCART_3:func.19">:]</a></span>
 <b>and </b><br/><a NAME="E4:141"/><i><font color="Green" title="E93">A2</font></i>: 
<font color="Maroon" title="c12">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">X9</font>
 <b>and </b><br/><a NAME="E5:141"/><i><font color="Green" title="E94">A3</font></i>: 
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">x12345678</font>,<font color="Maroon" title="c12">x9</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c13">x1</font>, <font color="Maroon" title="c14">x2</font>, <font color="Maroon" title="c15">x3</font>, <font color="Maroon" title="c16">x4</font>, <font color="Maroon" title="c17">x5</font>, <font color="Maroon" title="c18">x6</font>, <font color="Maroon" title="c19">x7</font>, <font color="Maroon" title="c20">x8</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:141"/><i><font color="Green" title="E95">A4</font></i>: 
( <font color="Maroon" title="c13">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X1</font> &amp; <font color="Maroon" title="c14">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X2</font> &amp; <font color="Maroon" title="c15">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X3</font> &amp; <font color="Maroon" title="c16">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X4</font> &amp; <font color="Maroon" title="c17">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X5</font> &amp; <font color="Maroon" title="c18">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X6</font> &amp; <font color="Maroon" title="c19">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X7</font> &amp; <font color="Maroon" title="c20">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X8</font> &amp; <font color="Maroon" title="c11">x12345678</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K18" title="MCART_3:func.18">[</a><span class="default"><font color="Maroon" title="c13">x1</font>,<font color="Maroon" title="c14">x2</font>,<font color="Maroon" title="c15">x3</font>,<font color="Maroon" title="c16">x4</font>,<font color="Maroon" title="c17">x5</font>,<font color="Maroon" title="c18">x6</font>,<font color="Maroon" title="c19">x7</font>,<font color="Maroon" title="c20">x8</font></span><a href="mcart_3.html#K18" title="MCART_3:func.18">]</a></span> )
 <b>by </b><i><a class="txt" href="mcart_3.html#E3:141"><i><font color="Green" title="E92">A1</font></i></a>, <a class="ref" href="mcart_3.html#T114" target="_self" title="MCART_3:th.114">Th37</a></i>;<br/>
<a NAME="E8:141"/>
<font color="Maroon" title="c1">y</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="c13">x1</font>,<font color="Maroon" title="c14">x2</font>,<font color="Maroon" title="c15">x3</font>,<font color="Maroon" title="c16">x4</font>,<font color="Maroon" title="c17">x5</font>,<font color="Maroon" title="c18">x6</font>,<font color="Maroon" title="c19">x7</font>,<font color="Maroon" title="c20">x8</font>,<font color="Maroon" title="c12">x9</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#E5:141"><i><font color="Green" title="E94">A3</font></i></a>, <a class="txt" href="mcart_3.html#E7:141"><i><font color="Green" title="E95">A4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:141"/>
 ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">x5</font>, <font color="Olive" title="b6">x6</font>, <font color="Olive" title="b7">x7</font>, <font color="Olive" title="b8">x8</font>, <font color="Olive" title="b9">x9</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X1</font> &amp; <font color="Olive" title="b2">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X2</font> &amp; <font color="Olive" title="b3">x3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X3</font> &amp; <font color="Olive" title="b4">x4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X4</font> &amp; <font color="Olive" title="b5">x5</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">X5</font> &amp; <font color="Olive" title="b6">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X6</font> &amp; <font color="Olive" title="b7">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X7</font> &amp; <font color="Olive" title="b8">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X8</font> &amp; <font color="Olive" title="b9">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">X9</font> &amp; <font color="Maroon" title="c1">y</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="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font>,<font color="Olive" title="b5">x5</font>,<font color="Olive" title="b6">x6</font>,<font color="Olive" title="b7">x7</font>,<font color="Olive" title="b8">x8</font>,<font color="Olive" title="b9">x9</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#E4:141"><i><font color="Green" title="E93">A2</font></i></a>, <a class="txt" href="mcart_3.html#E7:141"><i><font color="Green" title="E95">A4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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