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<b>let </b><font color="Maroon" title="c1">z</font>, <font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font>, <font color="Maroon" title="c5">D</font>, <font color="Maroon" title="c6">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>











<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E16">A1</font></i>: 
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_2.html#K2" title="MCART_2:func.2">[:</a><span class="default"><font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c6">E</font></span><a href="mcart_2.html#K2" title="MCART_2:func.2">:]</a></span>
 ;<br/>

<a NAME="E2:12"/><b>then </b>
( not <font color="Maroon" title="c2">A</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c3">B</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c4">C</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c5">D</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c6">E</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="ref" href="mcart_2.html#T13" title="MCART_2:th.13">MCART_2:13</a></i>;<br/>
<a NAME="E3:12"/><b>then </b>
 ex <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">A</font> ex <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">B</font> ex <font color="Olive" title="b3">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">C</font> ex <font color="Olive" title="b4">d</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">D</font> ex <font color="Olive" title="b5">e</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">E</font> st <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b5">e</font></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span>
 
<b>by </b><i><a class="txt" href="recdef_2.html#E1:12"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="mcart_2.html#T17" title="MCART_2:th.17">MCART_2:17</a></i>;<br/>
<b>hence </b><a NAME="E4:12"/>
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_2.html#K1" title="MCART_2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K8" title="RECDEF_2:func.8">`1_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K9" title="RECDEF_2:func.9">`2_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K10" title="RECDEF_2:func.10">`3_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K11" title="RECDEF_2:func.11">`4_5</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="recdef_2.html#K12" title="RECDEF_2:func.12">`5_5</a> </span>)</span></span><a href="mcart_2.html#K1" title="MCART_2:func.1">]</a></span>
 <b>by </b><i><a class="ref" href="recdef_2.html#T7" target="_self" title="RECDEF_2:th.7">Th7</a></i>;<br/>


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