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<span class="kw">let </span><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font>, <font color="Maroon" title="c3">X3</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="Red">::  thesis: </font></span></a><span class="hide"> ( <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>  implies for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <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="c2">X2</font>,<font color="Maroon" title="c3">X3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:53"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
( <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>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <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="c2">X2</font>,<font color="Maroon" title="c3">X3</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">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#K3" title="ZFMISC_1:func.3">[:</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></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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">Y9</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">Y</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">X9</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">X</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<span class="lab"><font color="Green" title="E31">A2</font></span>: <font color="Maroon" title="c4">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="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`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="txt" href="#E1:53"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="mcart_1.html#T48" target="_self" title="MCART_1:th.48">Th48</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>

;<br/>
<a NAME="E3:53"/><span class="kw">then </span>
( ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  ) implies ( <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:53"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#T4" title="ORDINAL1:th.4">ORDINAL1:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> </span><br/>

<a NAME="E5:53"/>
<font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:53"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:53"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="mcart_1.html#T20" target="_self" title="MCART_1:th.20">Th20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
