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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">X</font>, <font color="Maroon" title="c4">Y</font>, <font color="Maroon" title="c5">Z</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="recdef_2.html#K1" title="RECDEF_2:func.1">`1_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> <a href="recdef_2.html#K1" title="RECDEF_2:func.1">`1_3</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="recdef_2.html#K3" title="RECDEF_2:func.3">`3_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> <a href="recdef_2.html#K3" title="RECDEF_2:func.3">`3_3</a>  &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font>,<font color="Maroon" title="c5">Z</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font>,<font color="Maroon" title="c5">Z</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> implies <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:28"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
( <font color="Maroon" title="c1">x</font> <a href="recdef_2.html#K1" title="RECDEF_2:func.1">`1_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> <a href="recdef_2.html#K1" title="RECDEF_2:func.1">`1_3</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="recdef_2.html#K3" title="RECDEF_2:func.3">`3_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> <a href="recdef_2.html#K3" title="RECDEF_2:func.3">`3_3</a>  &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font>,<font color="Maroon" title="c5">Z</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="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font>,<font color="Maroon" title="c5">Z</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> or <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:28"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font>,<font color="Maroon" title="c5">Z</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="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font></span><br/>

<span class="kw">hence </span><font color="Maroon" title="c1">x</font> = 
<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="c1">x</font> <a href="recdef_2.html#K1" title="RECDEF_2:func.1">`1_3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="recdef_2.html#K3" title="RECDEF_2:func.3">`3_3</a></span>)</span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#T3" target="_self" title="RECDEF_2:th.3">Th3</a></span>
<br/>.= 
<font color="Maroon" title="c2">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="recdef_2.html#T3" target="_self" title="RECDEF_2:th.3">Th3</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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