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<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:29"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7">DISJOINT_PAIRS</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:29"/><b>then </b>
( <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> is <a href="finset_1.html#V1">finite</a> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="normform.html#K7">DISJOINT_PAIRS</a> <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">B</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> as    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="normform.html#K7">DISJOINT_PAIRS</a> <font color="Maroon">A</font></span>)</span> <b>by </b><i><a class="ref" href="finsub_1.html#D5">FINSUB_1:def 5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7">DISJOINT_PAIRS</a> <font color="Maroon">A</font>, <font color="Maroon">b</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7">DISJOINT_PAIRS</a> <font color="Maroon">A</font>;<br/><b>assume </b><a NAME="E1:29_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">a</font> <a href="normform.html#R1">c=</a> <font color="Maroon">b</font> )
 ;<br/><a NAME="E2:29_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:29_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:29"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><a href="xboole_0.html#K1">{}</a> ,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> is    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8">Normal_forms_on</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="normform.html#T53">NORMFORM:53</a></i>;<br/>


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