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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">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:()"><span class="comment"><font color="Red">::  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">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/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:76"/><span class="lab"><font color="Green" title="E45">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>  )
 <span class="kw">and </span><br/><a NAME="E2:76"/><span class="lab"><font color="Green" title="E46">A2</font></span>: 
( <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>



<span class="kw">assume </span><a NAME="E3:76"/><span class="lab"><font color="Green" title="E47">A3</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">thus </span><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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></span>
<br/>.= 
<font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="txt" href="#E3:76"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></span>
; <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="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/>

<span class="kw">thus </span><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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></span>
<br/>.= 
<font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="txt" href="#E3:76"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></span>
; <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="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/>

<span class="kw">thus </span><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> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></span>
<br/>.= 
<font color="Maroon" title="c8">y</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="txt" href="#E3:76"><span class="lab"><font color="Green" title="E47">A3</font></span></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</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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