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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> 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="firebrick">::  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#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> 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> 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="Maroon" title="c1">y</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="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></span><a href="mcart_2.html#K17" title="MCART_2:func.17">]</a></span> ) )</span><br/>















<span class="kw">assume </span><a NAME="E1:100"/>
<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#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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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> 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="Maroon" title="c1">y</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="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></span><a href="mcart_2.html#K17" title="MCART_2:func.17">]</a></span> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">x123456</font>, <font color="Maroon" title="c10">x7</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:100"/><span class="lab"><font color="Green" title="E70">A1</font></span>: 
<font color="Maroon" title="c9">x123456</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K10" title="MCART_2:func.10">[:</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></span><a href="mcart_2.html#K10" title="MCART_2:func.10">:]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:100"/><span class="lab"><font color="Green" title="E71">A2</font></span>: 
<font color="Maroon" title="c10">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="E5:100"/><span class="lab"><font color="Green" title="E72">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="c9">x123456</font>,<font color="Maroon" title="c10">x7</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="c11">x1</font>, <font color="Maroon" title="c12">x2</font>, <font color="Maroon" title="c13">x3</font>, <font color="Maroon" title="c14">x4</font>, <font color="Maroon" title="c15">x5</font>, <font color="Maroon" title="c16">x6</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E7:100"/><span class="lab"><font color="Green" title="E73">A4</font></span>: 
( <font color="Maroon" title="c11">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="c12">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="c13">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="c14">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="c15">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="c16">x6</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X6</font> )
 <span class="kw">and </span><br/><a NAME="E8:100"/><span class="lab"><font color="Green" title="E74">A5</font></span>: 
<font color="Maroon" title="c9">x123456</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K9" title="MCART_2:func.9">[</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Maroon" title="c12">x2</font>,<font color="Maroon" title="c13">x3</font>,<font color="Maroon" title="c14">x4</font>,<font color="Maroon" title="c15">x5</font>,<font color="Maroon" title="c16">x6</font></span><a href="mcart_2.html#K9" title="MCART_2:func.9">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:100"><span class="lab"><font color="Green" title="E70">A1</font></span></a>, <a class="ref" href="mcart_2.html#T67" target="_self" title="MCART_2:th.67">Th69</a></span>;<br/>
<a NAME="E9:100"/>
<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#K17" title="MCART_2:func.17">[</a><span class="default"><font color="Maroon" title="c11">x1</font>,<font color="Maroon" title="c12">x2</font>,<font color="Maroon" title="c13">x3</font>,<font color="Maroon" title="c14">x4</font>,<font color="Maroon" title="c15">x5</font>,<font color="Maroon" title="c16">x6</font>,<font color="Maroon" title="c10">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="#E5:100"><span class="lab"><font color="Green" title="E72">A3</font></span></a>, <a class="txt" href="#E8:100"><span class="lab"><font color="Green" title="E74">A5</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:100"/>
 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> 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="Maroon" title="c1">y</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="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></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="#E4:100"><span class="lab"><font color="Green" title="E71">A2</font></span></a>, <a class="txt" href="#E7:100"><span class="lab"><font color="Green" title="E73">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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