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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">Y1</font>, <font color="Maroon" title="c9">Y2</font>, <font color="Maroon" title="c10">Y3</font>, <font color="Maroon" title="c11">Y4</font>, <font color="Maroon" title="c12">Y5</font>, <font color="Maroon" title="c13">Y6</font>, <font color="Maroon" title="c14">Y7</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">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; <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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_3.html#K10" title="MCART_3:func.10">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</a><span class="default"><font color="Maroon" title="c8">Y1</font>,<font color="Maroon" title="c9">Y2</font>,<font color="Maroon" title="c10">Y3</font>,<font color="Maroon" title="c11">Y4</font>,<font color="Maroon" title="c12">Y5</font>,<font color="Maroon" title="c13">Y6</font>,<font color="Maroon" title="c14">Y7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span> implies ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y7</font> ) )</span><br/>



























<b>assume </b><a NAME="E1:51"/><i><font color="Green" title="E34">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>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <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>  or  not <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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_3.html#K10" title="MCART_3:func.10">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</a><span class="default"><font color="Maroon" title="c8">Y1</font>,<font color="Maroon" title="c9">Y2</font>,<font color="Maroon" title="c10">Y3</font>,<font color="Maroon" title="c11">Y4</font>,<font color="Maroon" title="c12">Y5</font>,<font color="Maroon" title="c13">Y6</font>,<font color="Maroon" title="c14">Y7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span> or ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y7</font> ) )</span><br/>

<a NAME="E2:51"/><b>then </b><i><font color="Green" title="E35">A2</font></i>: 
<span class="p1"><a href="mcart_3.html#K2" title="MCART_3:func.2">[:</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></span><a href="mcart_3.html#K2" title="MCART_3:func.2">:]</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> 
 
<b>by </b><i><a class="ref" href="mcart_3.html#T13" target="_self" title="MCART_3:th.13">Th13</a></i>;<br/>
<b>assume </b><a NAME="E3:51"/><i><font color="Green" title="E36">A3</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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_3.html#K10" title="MCART_3:func.10">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</a><span class="default"><font color="Maroon" title="c8">Y1</font>,<font color="Maroon" title="c9">Y2</font>,<font color="Maroon" title="c10">Y3</font>,<font color="Maroon" title="c11">Y4</font>,<font color="Maroon" title="c12">Y5</font>,<font color="Maroon" title="c13">Y6</font>,<font color="Maroon" title="c14">Y7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span> or ( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y7</font> ) )</span><br/>

<b>assume </b><a NAME="E4:51"/>
<span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</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_3.html#K10" title="MCART_3:func.10">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K10" title="MCART_3:func.10">[:</a><span class="default"><font color="Maroon" title="c8">Y1</font>,<font color="Maroon" title="c9">Y2</font>,<font color="Maroon" title="c10">Y3</font>,<font color="Maroon" title="c11">Y4</font>,<font color="Maroon" title="c12">Y5</font>,<font color="Maroon" title="c13">Y6</font>,<font color="Maroon" title="c14">Y7</font></span><a href="mcart_3.html#K10" title="MCART_3:func.10">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="c8">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y7</font> )</span><br/>

<a NAME="E5:51"/><b>then </b>
( <span class="p1"><a href="mcart_3.html#K2" title="MCART_3:func.2">[:</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></span><a href="mcart_3.html#K2" title="MCART_3:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_3.html#K2" title="MCART_3:func.2">[:</a><span class="default"><font color="Maroon" title="c8">Y1</font>,<font color="Maroon" title="c9">Y2</font>,<font color="Maroon" title="c10">Y3</font>,<font color="Maroon" title="c11">Y4</font>,<font color="Maroon" title="c12">Y5</font>,<font color="Maroon" title="c13">Y6</font></span><a href="mcart_3.html#K2" title="MCART_3:func.2">:]</a></span> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y7</font> )
 
<b>by </b><i><a class="txt" href="mcart_3.html#E2:51"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="mcart_3.html#E3:51"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#T134" title="ZFMISC_1:th.134">ZFMISC_1:134</a></i>;<br/>
<b>hence </b><a NAME="E6:51"/>
( <font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">Y1</font> &amp; <font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">Y2</font> &amp; <font color="Maroon" title="c3">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Y3</font> &amp; <font color="Maroon" title="c4">X4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">Y4</font> &amp; <font color="Maroon" title="c5">X5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Y5</font> &amp; <font color="Maroon" title="c6">X6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y6</font> &amp; <font color="Maroon" title="c7">X7</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y7</font> )
 <b>by </b><i><a class="txt" href="mcart_3.html#E1:51"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="mcart_3.html#T14" target="_self" title="MCART_3:th.14">Th14</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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