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<span class="kw">let </span><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> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</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> 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="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K26" title="MCART_2:func.26">[</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></span><a href="mcart_2.html#K26" title="MCART_2:func.26">]</a></span> ) )</span><br/>

















<span class="kw">assume </span><a NAME="E1:137"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</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_2.html#K27" title="MCART_2:func.27">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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> 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="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K26" title="MCART_2:func.26">[</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></span><a href="mcart_2.html#K26" title="MCART_2:func.26">]</a></span> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">x1234567</font>, <font color="Maroon" title="c11">x8</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:137"/><span class="lab"><font color="Green" title="E93">A1</font></span>: 
<font color="Maroon" title="c10">x1234567</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</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></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:137"/><span class="lab"><font color="Green" title="E94">A2</font></span>: 
<font color="Maroon" title="c11">x8</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X8</font>
 <span class="kw">and </span><br/><a NAME="E5:137"/><span class="lab"><font color="Green" title="E95">A3</font></span>: 
<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="c10">x1234567</font>,<font color="Maroon" title="c11">x8</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c12">x1</font>, <font color="Maroon" title="c13">x2</font>, <font color="Maroon" title="c14">x3</font>, <font color="Maroon" title="c15">x4</font>, <font color="Maroon" title="c16">x5</font>, <font color="Maroon" title="c17">x6</font>, <font color="Maroon" title="c18">x7</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E7:137"/><span class="lab"><font color="Green" title="E96">A4</font></span>: 
( <font color="Maroon" title="c12">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="c13">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="c14">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="c15">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="c16">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="c17">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="c18">x7</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">X7</font> )
 <span class="kw">and </span><br/><a NAME="E8:137"/><span class="lab"><font color="Green" title="E97">A5</font></span>: 
<font color="Maroon" title="c10">x1234567</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K17" title="MCART_2:func.17">[</a><span class="default"><font color="Maroon" title="c12">x1</font>,<font color="Maroon" title="c13">x2</font>,<font color="Maroon" title="c14">x3</font>,<font color="Maroon" title="c15">x4</font>,<font color="Maroon" title="c16">x5</font>,<font color="Maroon" title="c17">x6</font>,<font color="Maroon" title="c18">x7</font></span><a href="mcart_2.html#K17" title="MCART_2:func.17">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:137"><span class="lab"><font color="Green" title="E93">A1</font></span></a>, <a class="ref" href="mcart_2.html#T109" target="_self" title="MCART_2:th.109">Th109</a></span>;<br/>
<a NAME="E9:137"/>
<font color="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K26" title="MCART_2:func.26">[</a><span class="default"><font color="Maroon" title="c12">x1</font>,<font color="Maroon" title="c13">x2</font>,<font color="Maroon" title="c14">x3</font>,<font color="Maroon" title="c15">x4</font>,<font color="Maroon" title="c16">x5</font>,<font color="Maroon" title="c17">x6</font>,<font color="Maroon" title="c18">x7</font>,<font color="Maroon" title="c11">x8</font></span><a href="mcart_2.html#K26" title="MCART_2:func.26">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:137"><span class="lab"><font color="Green" title="E95">A3</font></span></a>, <a class="txt" href="#E8:137"><span class="lab"><font color="Green" title="E97">A5</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:137"/>
 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> 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="Maroon" title="c1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K26" title="MCART_2:func.26">[</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></span><a href="mcart_2.html#K26" title="MCART_2:func.26">]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:137"><span class="lab"><font color="Green" title="E94">A2</font></span></a>, <a class="txt" href="#E7:137"><span class="lab"><font color="Green" title="E96">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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