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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  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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"> for <font color="Olive" title="b1">x</font>, <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#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>  st <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  &amp; <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font></span><br/><b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">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#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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  implies <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> )</span><br/>









<a NAME="E1:19"/>
( <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</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="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> &amp; <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">y</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="c6">y</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="c6">y</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="c6">y</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a> </span>)</span></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T60" title="MCART_1:th.60">MCART_1:60</a></i>;<br/>
<b>hence </b><a NAME="E2:19"/>
( <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  implies <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y</font> )
 ; <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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