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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    <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="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>  &amp; <font color="Maroon" title="c4">X4</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#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> 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#K8" title="MCART_1:func.8">`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#K9" title="MCART_1:func.9">`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#K10" title="MCART_1:func.10">`3</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#K11" title="MCART_1:func.11">`4</a>  ) )</span><br/>







<b>assume </b><a NAME="E1:61"/><i><font color="Green" title="E41">A1</font></i>: 
( <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>  &amp; <font color="Maroon" title="c4">X4</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:()"><i><font color="Red">::  thesis: </font></i></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#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> 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#K8" title="MCART_1:func.8">`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#K9" title="MCART_1:func.9">`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#K10" title="MCART_1:func.10">`3</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#K11" title="MCART_1:func.11">`4</a>  )</span><br/>

<a NAME="E2:61"/><b>then </b><i><font color="Green" title="E42">A2</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T113" title="ZFMISC_1:th.113">ZFMISC_1:113</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">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#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="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  )</span><br/>

<b>set </b><font color="Maroon" title="c6">Z'</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="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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c7">Z</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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p3">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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/>
<b>set </b><font color="Maroon" title="c8">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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p4">(<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="p4">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c9">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"><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p5">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p5">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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/>
<b>set </b><font color="Maroon" title="c10">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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0">(<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="p0">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p0">(<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><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="p4">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0">(<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="p0">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p0">(<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><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="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="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c11">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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p5">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p3">(<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="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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p5">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>;<br/>
<font color="Maroon" title="c5">x</font> = 
<span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</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="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
<b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="mcart_1.html#T60" target="_self" title="MCART_1:th.60">Th60</a></i>
<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"><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p5">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</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="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="tarski.html#D5" title="TARSKI:def.5">TARSKI:def 5</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0">(<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="p0">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p0">(<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><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="p4">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0">(<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="p0">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p0">(<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><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="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="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="tarski.html#D5" title="TARSKI:def.5">TARSKI:def 5</a></i>
<br/>.= 
<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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p5">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p3">(<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="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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p5">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<b>by </b><i><a class="ref" href="tarski.html#D5" title="TARSKI:def.5">TARSKI:def 5</a></i>
;<br/>
<a NAME="E4:61"/><b>then </b>
( ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p5">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p3">(<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="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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<span class="default"><font color="Maroon" 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title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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><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="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><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="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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p3">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p3">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p4">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p4">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p5">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p5">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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> &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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5">(<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="p5">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a> </span>)</span>,<span class="p5">(<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><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="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`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"><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0">(<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="p0">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p0">(<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><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="p4">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0">(<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="p0">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p0">(<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><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="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="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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0">(<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="p0">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p0">(<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><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="p4">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0">(<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="p0">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p0">(<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><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="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="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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p5">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p3">(<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="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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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="p5">(<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><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"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p0"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p1">(<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="p1">(<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><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p0"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p1">(<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><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> ) )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:61"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K8" title="MCART_1:func.8">`1</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K9" title="MCART_1:func.9">`2</a>  )
 <b>by </b><i><a class="ref" href="ordinal1.html#T6" title="ORDINAL1:th.6">ORDINAL1:6</a></i>; <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="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  )</span><br/>

<b>reconsider </b><font color="Maroon" title="c12">x'</font> = <font color="Maroon" title="c5">x</font> as    <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"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c3">X3</font>,<font color="Maroon" title="c4">X4</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#T54" target="_self" title="MCART_1:th.54">Th54</a></i>;<br/>
<i><font color="Green" title="E43">A3</font></i>: <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="mcart_1.html#T61" target="_self" title="MCART_1:th.61">Th61</a></i>
<br/>.= 
<font color="Maroon" title="c12">x'</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a> 
<b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="#E2:61"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></i>
;<br/>
<font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  = 
<font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="mcart_1.html#T61" target="_self" title="MCART_1:th.61">Th61</a></i>
<br/>.= 
<font color="Maroon" title="c12">x'</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a> 
<b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="#E2:61"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="mcart_1.html#T50" target="_self" title="MCART_1:th.50">Th50</a></i>
;<br/>
<b>hence </b><a NAME="E9:61"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K10" title="MCART_1:func.10">`3</a>  &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">x</font> <a href="mcart_1.html#K11" title="MCART_1:func.11">`4</a>  )
 <b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="#E2:61"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="#E7:61"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="mcart_1.html#T51" target="_self" title="MCART_1:th.51">Th51</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
