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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> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>







<b>assume </b><a NAME="E1:60"/><i><font color="Green" title="E42">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>  )
 ;<br/>

<b>let </b><font color="Maroon" title="c5">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#K4" title="ZFMISC_1:func.4">[:</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></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span>;<br/>

<b>thus </b><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#D1" target="_self" title="MCART_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> </span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <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="ref" href="mcart_1.html#D1" target="_self" title="MCART_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a> </span>)</span></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span> <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>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#D1" target="_self" title="MCART_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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>)</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#E1:60"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="mcart_1.html#T60" target="_self" title="MCART_1:th.60">Th60</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#D2" target="_self" title="MCART_1:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> </span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <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="ref" href="mcart_1.html#D1" target="_self" title="MCART_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a> </span>)</span></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span> <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>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#D1" target="_self" title="MCART_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">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>)</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#E1:60"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="mcart_1.html#T60" target="_self" title="MCART_1:th.60">Th60</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  = 
<span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> </span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#D2" target="_self" title="MCART_1:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a> </span>)</span></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span> <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="ref" href="mcart_1.html#D1" target="_self" title="MCART_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">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#E1:60"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="mcart_1.html#T60" target="_self" title="MCART_1:th.60">Th60</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  = 
<span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a> </span>)</span></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#D2" target="_self" title="MCART_1:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c5">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#E1:60"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="mcart_1.html#T60" target="_self" title="MCART_1:th.60">Th60</a></i>
;<br/>


</div>
