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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">Y1</font>, <font color="Maroon" title="c5">Y2</font>, <font color="Maroon" title="c6">Y3</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">Y1</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">Y2</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">Y3</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>  implies for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</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></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span><br/> for <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c6">Y3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/>( <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  ) )</span><br/>











<b>assume </b><b>that </b><br/><a NAME="E1:72"/><i><font color="Green" title="E45">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>  )
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green" title="E46">A2</font></i>: 
( <font color="Maroon" title="c4">Y1</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">Y2</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">Y3</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"> for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</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></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span><br/> for <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c6">Y3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/>( <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  )</span><br/>

<b>let </b><font color="Maroon" title="c7">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</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></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c6">Y3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>  st <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> holds <br/>( <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  &amp; <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  &amp; <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  )</span><br/><b>let </b><font color="Maroon" title="c8">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c4">Y1</font>,<font color="Maroon" title="c5">Y2</font>,<font color="Maroon" title="c6">Y3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</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="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> implies ( <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  &amp; <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  &amp; <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  ) )</span><br/>



<b>assume </b><a NAME="E3:72"/><i><font color="Green" title="E47">A3</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  &amp; <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  &amp; <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  )</span><br/>

<b>thus </b><font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="txt" href="mcart_1.html#E1:72"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></i>
<br/>.= 
<font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> 
<b>by </b><i><a class="txt" href="mcart_1.html#E2:72"><i><font color="Green" title="E46">A2</font></i></a>, <a class="txt" href="mcart_1.html#E3:72"><i><font color="Green" title="E47">A3</font></i></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  &amp; <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  )</span><br/>

<b>thus </b><font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="mcart_1.html#E1:72"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></i>
<br/>.= 
<font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> 
<b>by </b><i><a class="txt" href="mcart_1.html#E2:72"><i><font color="Green" title="E46">A2</font></i></a>, <a class="txt" href="mcart_1.html#E3:72"><i><font color="Green" title="E47">A3</font></i></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span><br/>

<b>thus </b><font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  = 
<font color="Maroon" title="c7">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="mcart_1.html#E1:72"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></i>
<br/>.= 
<font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> 
<b>by </b><i><a class="txt" href="mcart_1.html#E2:72"><i><font color="Green" title="E46">A2</font></i></a>, <a class="txt" href="mcart_1.html#E3:72"><i><font color="Green" title="E47">A3</font></i></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</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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