<?xml version="1.0"?>
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<span class="kw">let </span><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">Y1</font>, <font color="Maroon" title="c10">Y2</font>, <font color="Maroon" title="c11">Y3</font>, <font color="Maroon" title="c12">Y4</font>, <font color="Maroon" title="c13">Y5</font>, <font color="Maroon" title="c14">Y6</font>, <font color="Maroon" title="c15">Y7</font>, <font color="Maroon" title="c16">Y8</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">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; <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</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></span><a href="mcart_2.html#K27" title="MCART_2:func.27">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</a><span class="default"><font color="Maroon" title="c9">Y1</font>,<font color="Maroon" title="c10">Y2</font>,<font color="Maroon" title="c11">Y3</font>,<font color="Maroon" title="c12">Y4</font>,<font color="Maroon" title="c13">Y5</font>,<font color="Maroon" title="c14">Y6</font>,<font color="Maroon" title="c15">Y7</font>,<font color="Maroon" title="c16">Y8</font></span><a href="mcart_2.html#K27" title="MCART_2:func.27">:]</a></span> implies ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">Y7</font> &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">Y8</font> ) )</span><br/>































<span class="kw">assume </span><a NAME="E1:117"/><span class="lab"><font color="Green" title="E79">A1</font></span>: 
( <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>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <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>  or  not <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</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></span><a href="mcart_2.html#K27" title="MCART_2:func.27">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</a><span class="default"><font color="Maroon" title="c9">Y1</font>,<font color="Maroon" title="c10">Y2</font>,<font color="Maroon" title="c11">Y3</font>,<font color="Maroon" title="c12">Y4</font>,<font color="Maroon" title="c13">Y5</font>,<font color="Maroon" title="c14">Y6</font>,<font color="Maroon" title="c15">Y7</font>,<font color="Maroon" title="c16">Y8</font></span><a href="mcart_2.html#K27" title="MCART_2:func.27">:]</a></span> or ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">Y7</font> &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">Y8</font> ) )</span><br/>

<a NAME="E2:117"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A2</font></span>: 
<span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</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></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_2.html#T88" target="_self" title="MCART_2:th.88">Th90</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:117"/><span class="lab"><font color="Green" title="E81">A3</font></span>: 
<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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</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></span><a href="mcart_2.html#K27" title="MCART_2:func.27">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</a><span class="default"><font color="Maroon" title="c9">Y1</font>,<font color="Maroon" title="c10">Y2</font>,<font color="Maroon" title="c11">Y3</font>,<font color="Maroon" title="c12">Y4</font>,<font color="Maroon" title="c13">Y5</font>,<font color="Maroon" title="c14">Y6</font>,<font color="Maroon" title="c15">Y7</font>,<font color="Maroon" title="c16">Y8</font></span><a href="mcart_2.html#K27" title="MCART_2:func.27">:]</a></span> or ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">Y7</font> &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">Y8</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E4:117"/><span class="lab"><font color="Green" title="E82">A4</font></span>: 
<span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</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></span><a href="mcart_2.html#K27" title="MCART_2:func.27">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K27" title="MCART_2:func.27">[:</a><span class="default"><font color="Maroon" title="c9">Y1</font>,<font color="Maroon" title="c10">Y2</font>,<font color="Maroon" title="c11">Y3</font>,<font color="Maroon" title="c12">Y4</font>,<font color="Maroon" title="c13">Y5</font>,<font color="Maroon" title="c14">Y6</font>,<font color="Maroon" title="c15">Y7</font>,<font color="Maroon" title="c16">Y8</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">Y7</font> &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">Y8</font> )</span><br/>

<a NAME="E5:117"/><span class="kw">then </span>
<span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</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></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K18" title="MCART_2:func.18">[:</a><span class="default"><font color="Maroon" title="c9">Y1</font>,<font color="Maroon" title="c10">Y2</font>,<font color="Maroon" title="c11">Y3</font>,<font color="Maroon" title="c12">Y4</font>,<font color="Maroon" title="c13">Y5</font>,<font color="Maroon" title="c14">Y6</font>,<font color="Maroon" title="c15">Y7</font></span><a href="mcart_2.html#K18" title="MCART_2:func.18">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:117"><span class="lab"><font color="Green" title="E80">A2</font></span></a>, <a class="txt" href="#E3:117"><span class="lab"><font color="Green" title="E81">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T110" title="ZFMISC_1:th.110">ZFMISC_1:110</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:117"/>
( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">Y7</font> &amp; <font color="Maroon" title="c8">X8</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">Y8</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:117"><span class="lab"><font color="Green" title="E79">A1</font></span></a>, <a class="txt" href="#E2:117"><span class="lab"><font color="Green" title="E80">A2</font></span></a>, <a class="txt" href="#E3:117"><span class="lab"><font color="Green" title="E81">A3</font></span></a>, <a class="txt" href="#E4:117"><span class="lab"><font color="Green" title="E82">A4</font></span></a>, <a class="ref" href="mcart_2.html#T89" target="_self" title="MCART_2:th.89">Th91</a>, <a class="ref" href="zfmisc_1.html#T110" title="ZFMISC_1:th.110">ZFMISC_1:110</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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