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<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">Y1</font>, <font color="Maroon" title="c3">X2</font>, <font color="Maroon" title="c4">Y2</font>, <font color="Maroon" title="c5">X3</font>, <font color="Maroon" title="c6">Y3</font>, <font color="Maroon" title="c7">X4</font>, <font color="Maroon" title="c8">Y4</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="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y1</font> &amp; <font color="Maroon" title="c3">X2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">Y2</font> &amp; <font color="Maroon" title="c5">X3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">Y3</font> &amp; <font color="Maroon" title="c7">X4</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">Y4</font> implies <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="c3">X2</font>,<font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c7">X4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font>,<font color="Maroon" title="c6">Y3</font>,<font color="Maroon" title="c8">Y4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> )</span><br/>















<b>assume </b><a NAME="E1:84"/>
( <font color="Maroon" title="c1">X1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y1</font> &amp; <font color="Maroon" title="c3">X2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">Y2</font> &amp; <font color="Maroon" title="c5">X3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">Y3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c7">X4</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">Y4</font> or <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="c3">X2</font>,<font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c7">X4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font>,<font color="Maroon" title="c6">Y3</font>,<font color="Maroon" title="c8">Y4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> )</span><br/>

<a NAME="E2:84"/><b>then </b><i><font color="Green" title="E48">A1</font></i>: 
<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="c3">X2</font>,<font color="Maroon" title="c5">X3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font>,<font color="Maroon" title="c6">Y3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T77" target="_self" title="MCART_1:th.77">Th77</a></i>;<br/>
<a NAME="E3:84"/><i><font color="Green" title="E49">A2</font></i>: 
( <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="c3">X2</font>,<font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c7">X4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><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="c3">X2</font>,<font color="Maroon" title="c5">X3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>,<font color="Maroon" title="c7">X4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font>,<font color="Maroon" title="c6">Y3</font>,<font color="Maroon" title="c8">Y4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font>,<font color="Maroon" title="c6">Y3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>,<font color="Maroon" title="c8">Y4</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D4" title="ZFMISC_1:def.4">ZFMISC_1:def 4</a></i>;<br/>
<b>assume </b><a NAME="E4:84"/>
<font color="Maroon" title="c7">X4</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">Y4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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="c3">X2</font>,<font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c7">X4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font>,<font color="Maroon" title="c6">Y3</font>,<font color="Maroon" title="c8">Y4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span></span><br/>

<b>hence </b><a NAME="E5:84"/>
<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="c3">X2</font>,<font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c7">X4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><font color="Maroon" title="c2">Y1</font>,<font color="Maroon" title="c4">Y2</font>,<font color="Maroon" title="c6">Y3</font>,<font color="Maroon" title="c8">Y4</font></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span>
 <b>by </b><i><a class="txt" href="mcart_1.html#E2:84"><i><font color="Green" title="E48">A1</font></i></a>, <a class="txt" href="mcart_1.html#E3:84"><i><font color="Green" title="E49">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</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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